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diff --git a/master/_sources/interface/flux_reconstruction.rst.txt b/master/_sources/interface/flux_reconstruction.rst.txt
index dd864a528..d9dddd68d 100644
--- a/master/_sources/interface/flux_reconstruction.rst.txt
+++ b/master/_sources/interface/flux_reconstruction.rst.txt
@@ -3,7 +3,7 @@
 Flux reconstruction methods
 ===========================
 
-Group /input/model/unit_XXX/discretization/weno - WENO Parameters
+Group /input/model/unit_XXX/discretization/reconstruction = WENO
 -----------------------------------------------------------------
 
 ``BOUNDARY_MODEL``
@@ -37,3 +37,17 @@ Group /input/model/unit_XXX/discretization/weno - WENO Parameters
    **Type:** int  **Range:** :math:`\{1, 2, 3\}`  **Length:** 1
    =============  ==============================  =============
 
+
+Group /input/model/unit_XXX/discretization/reconstruction = KOREN
+-----------------------------------------------------------------
+
+The Koren scheme implemented in CADET intrinsically uses a van Leer flux limiter. It can reach a maximum order of 2 depending on the smoothness of the solution. The
+BOUNDARY_MODEL is intrinsically set to 0 (stable).
+
+``KOREN_EPS``
+
+   Set :math:`\varepsilon` in the van Leer flux limiter
+
+   ================  =========================  =============
+   **Type:** double  **Range:** :math:`\qe 0\`  **Length:** 1
+   ================  =========================  =============
\ No newline at end of file
diff --git a/master/_sources/interface/input_group.rst.txt b/master/_sources/interface/input_group.rst.txt
index 9859c0a0d..e23e52457 100644
--- a/master/_sources/interface/input_group.rst.txt
+++ b/master/_sources/interface/input_group.rst.txt
@@ -9,13 +9,13 @@ Input Group
     system
     unit_operations/index
     binding/index
+    population_balance_model
     reaction/index
-    spatial_discretization_methods
     flux_reconstruction
     consistent_initialization
     return_data
     sensitivities
     solver
     parameter_dependencies
-
+    spatial_discretization_methods
 
diff --git a/master/_sources/interface/population_balance_model.rst.txt b/master/_sources/interface/population_balance_model.rst.txt
new file mode 100644
index 000000000..b0c5a31e5
--- /dev/null
+++ b/master/_sources/interface/population_balance_model.rst.txt
@@ -0,0 +1,157 @@
+.. _pbm_config:
+
+Population balance model
+========================
+
+The PBM in CADET is implemented as part of the reaction module and can thus be used in any unit operation that includes reactions.
+Typical applications consider crystallization in a :ref:`cstr_config` or, to model continuous processes, in a Dispersive Plug-Flow Reactor (DPFR), which is modelled by a :ref:`lumped_rate_model_without_pores_config`.
+
+The particle size domain (internal coordinate) is discretized by the FV method, giving us a finite set of particle sizes under consideration :math:`\{x_1, \dots, x_{N_x}\}`.
+Every particle size considered is treated as an individual component of the unit operation and the field ``NCOMP`` of that unit operation in which the crystallization happens, must be specified accordingly as :math:`N_x + 2`.
+The two additional components account for the solute :math:`c` and solubility :math:`c_\text{eq}`.
+*That is, by setting the ``NCOMP`` field, you specify the number of FV cells for the internal coordinate.*
+
+Group /input/model/unit_XXX
+---------------------------
+
+``NCOMP``
+
+   Number of components, which is given by two plus the number discrete particle sizes, which is given by the number of FV cells discretizing the internal coordinate
+   
+   =============  =========================  =============
+   **Type:** int  **Range:** :math:`\geq 3`  **Length:** 1
+   =============  =========================  =============
+   
+``REACTION_MODEL``
+
+   The crystallization code is implemented as a reaction module, which is why crystallization needs to be specified here
+   
+   ================  ========================================  =============
+   **Type:** String  **Range:** :math:`\{ CRYSTALLIZATION \}`  **Length:** 1
+   ================  ========================================  =============
+
+Group /input/model/unit_XXX/reaction_bulk - REACTION_MODEL = CRYSTALLIZATION - UNIT_TYPE = CSTR
+-----------------------------------------------------------------------------------------------
+
+*The following parameters need to be specified under Group /input/model/unit_XXX/reaction/reaction_bulk/ for CSTR units, and Group /input/model/unit_XXX/reaction/reaction/ for transport units like the LRM.*
+
+``CRY_BINS``
+
+   Coordinates of the cell faces, e.g. equidistant or logarithmic discretization of the internal coordinate :math:`x \in [x_c, x_\text{end}]`, including the end points.
+   
+   ================  =========================  =====================================
+   **Type:** double  **Range:** :math:`\geq 1`   **Length:** :math:`\mathrm{N_x} + 1`
+   ================  =========================  =====================================
+   
+``CRY_NUCLEI_MASS_DENSITY``
+
+   Nulcei mass density
+   
+   ================  =========================  =============
+   **Type:** double  **Range:** :math:`\geq 0`  **Length:** 1
+   ================  =========================  =============
+   
+``CRY_VOL_SHAPE_FACTOR``
+
+   Volumetric shape factor of the particles
+   
+   ================  =========================  =============
+   **Type:** double  **Range:** :math:`\geq 0`  **Length:** 1
+   ================  =========================  =============
+   
+``CRY_PRIMARY_NUCLEATION_RATE``
+
+   Primary nucleation rate constant :math:`k_p`
+   
+   ================  =========================  =============
+   **Type:** double  **Range:** :math:`\geq 0`  **Length:** 1
+   ================  =========================  =============
+   
+``CRY_SECONDARY_NUCLEATION_RATE``
+
+   Secondary nucleation rate :math:`k_b`
+   
+   ================  =========================  =============
+   **Type:** double  **Range:** :math:`\geq 0`  **Length:** 1
+   ================  =========================  =============
+   
+``CRY_GROWTH_RATE_CONSTANT``
+
+   Growth rate constant :math:`k_g`
+   
+   ================  =========================  =============
+   **Type:** double  **Range:** :math:`\geq 0`  **Length:** 1
+   ================  =========================  =============
+   
+``CRY_GROWTH_CONSTANT``
+
+   Growth constant :math:`\gamma`
+   
+   ================  =========================  =============
+   **Type:** double  **Range:** :math:`\geq 0`  **Length:** 1
+   ================  =========================  =============
+   
+``CRY_A``
+
+   Defines constant :math:`a` used to determine the growth rate
+   
+   ================  =========================  =============
+   **Type:** double  **Range:** :math:`\geq 0`  **Length:** 1
+   ================  =========================  =============
+   
+``CRY_G``
+
+   Defines constant :math:`g` used to determine the growth rate
+   
+   ================  =========================  =============
+   **Type:** double  **Range:** :math:`\geq 0`  **Length:** 1
+   ================  =========================  =============
+   
+``CRY_P``
+
+   Defines constant :math:`p`  used to determine the growth rate
+   
+   ================  =========================  =============
+   **Type:** double  **Range:** :math:`\geq 0`  **Length:** 1
+   ================  =========================  =============
+   
+``CRY_GROWTH_DISPERSION_RATE``
+
+   Growth dispersion rate :math:`D_g`
+   
+   ================  =========================  =============
+   **Type:** double  **Range:** :math:`\geq 0`  **Length:** 1
+   ================  =========================  =============
+   
+``CRY_U``
+
+   Defines constant :math:`u` used to determine the primary nucleation
+   
+   ================  =========================  =============
+   **Type:** double  **Range:** :math:`\geq 0`  **Length:** 1
+   ================  =========================  =============
+   
+``CRY_B``
+
+   Defines constant :math:`b` used to determine the secondary nucleation
+   
+   ================  =========================  =============
+   **Type:** double  **Range:** :math:`\geq 0`  **Length:** 1
+   ================  =========================  =============
+   
+``CRY_K``
+
+   Defines constant :math:`k` used to determine the secondary nucleation
+   
+   ================  =========================  =============
+   **Type:** double  **Range:** :math:`\geq 0`  **Length:** 1
+   ================  =========================  =============
+   
+``CRY_GROWTH_SCHEME_ORDER``
+
+   Defines the growth flux FV reconstruction scheme. It can only be :math:`1`: upwind scheme; :math:`2`: HR Koren scheme; :math:`3`: WENO23 scheme; :math:`4`: WENO35 scheme.
+   We recommend using the HR Koren scheme, which showed to be the most performant in our benchmarks.
+   
+   =============  ================================  =============
+   **Type:** int  **Range:** :math:`[1, \dots, 4]`  **Length:** 1
+   =============  ================================  =============
diff --git a/master/_sources/interface/unit_operations/index.rst.txt b/master/_sources/interface/unit_operations/index.rst.txt
index 1d80a6b36..078802e29 100644
--- a/master/_sources/interface/unit_operations/index.rst.txt
+++ b/master/_sources/interface/unit_operations/index.rst.txt
@@ -15,4 +15,5 @@ Unit Operations
     cstr
     radial_flow_models
     multi_channel_transport_model
+    population_balance_model
 
diff --git a/master/_sources/modelling/crystallization.rst.txt b/master/_sources/modelling/crystallization.rst.txt
new file mode 100644
index 000000000..5d8c858b2
--- /dev/null
+++ b/master/_sources/modelling/crystallization.rst.txt
@@ -0,0 +1,170 @@
+.. _pbm_model:
+
+Population Balance Models
+~~~~~~~~~~~~~~~~~~~~~~~~~
+
+The population balance model (PBM) is given by a particle-number continuity equation which describes the evolution of the number density :math:`n` of the particles over time :math:`t` and with respect to a so-called internal coordinate :math:`x` and external coordinate :math:`z`. 
+The internal coordinate can be chosen as any characteristic property of the particles such as the particle size or volume.
+The external coordinate can be a characteristic dimension of the reactor itself, including its axial length. 
+
+In CADET, we chose particle size and axial coordinate as the internal and external coodinate respectively.
+The PBM in CADET is implemented so that it can be used in any unit operation that supports reactions.
+Typical applications consider crystallization in a CSTR or, to model continuous processes, in a Dispersive Plug-Flow Reactor (DPFR), which is described by the LRM without solid phase.
+
+In the following, we give a brief overview on the modelling equations, for more information on the PBM as implemented in CADET, please refer to :cite:`zhang2024solving`.
+
+Population Balance Model in a CSTR
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+We assume a well-mixed tank and choose the particle size :math:`x\in (x_c, \infty)` as the internal coodinate, with :math:`x_c>0` being the minimal particle size considered.
+The corresponding PBM is given as
+
+.. math::
+
+    \begin{aligned}
+        \frac{\partial (n V)}{\partial t} = F_{in}n_{in} - F_{out}n - V \left( \frac{\partial (v_{G}n)}{\partial x} - D_g \frac{\partial^2 n}{\partial x^2} - B_0 \delta (x-x_c) \right),
+    \end{aligned}
+
+where :math:`F_{in}, F_{out}\in \mathbb{R}^+` are the volumetric inflow and outflow rates, :math:`V\in\mathbb{R}^+` is the reactor volume,
+:math:`n(t, x)\colon [0, T_\text{end}] \times (x_c, \infty) \mapsto \mathbb{R}^+` is the number density distribution,
+:math:`n_{in}\in\mathbb{R}^+` is the number density distribution of the inlet feed, :math:`v_{G}\in\mathbb{R}^+` is the particle growth rate,
+:math:`D_g\in\mathbb{R}^+` is the growth dispersion rate. 
+
+The boundary conditions are given by the regularity boundary condition
+
+.. math::
+    :label: RegularityBC
+
+    \begin{aligned}
+        \left. \left( nv_{G} - D_g \frac{\partial n}{\partial x} \right) \right|_{x \to \infty}=0,
+    \end{aligned}
+
+and the nucleation kinetics boundary condition
+
+.. math::
+    :label: NucleationBC
+
+    \begin{aligned}
+        \left. \left( nv_{G}-D_g \frac{\partial n}{\partial x} \right)\right|_{x=x_c} = B_0,
+    \end{aligned}
+
+where :math:`B_0\in\mathbb{R}^+` is the nucleation kinetics factor representing particle nucleations of size :math:`x_c\in\mathbb{R}^+`.
+
+The model is complemented by the following mass balance equation which accounts for the mass transfer between the particle phase and the solute phase
+
+.. math::
+
+    \begin{aligned}
+        \frac{\partial (cV)}{\partial t} = F_{in}c_{in} - F_{out}c -\rho k_v  V \left( B_0x^3_c + 3\int_{x_c}^{\infty} v_{G}n\ x^2 \;\mathrm{d}x \right),
+    \end{aligned}
+
+where :math:`c(t)\colon [0, T_\text{end}] \mapsto \mathbb{R}^+` is the solute concentration in the bulk phase, :math:`c_{in}\in\mathbb{R}^+` is the inlet solute mass concentration, :math:`\rho > 0` is the nuclei mass density and :math:`k_v > 0` is the volumetric shape factor of the particles.
+
+Evolution of the reactor's volume is governed by
+
+.. math::
+
+    \begin{aligned}
+        \frac{\mathrm{d}V}{\mathrm{d}t} &= F_{\text{in}} - F_{\text{out}}.
+    \end{aligned}
+
+
+Population Balance Model in a DPFR
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+The PBM can also be formulated for a DPFR to model continuous processes.
+That is, we choose the axial position within a DPFR as the external coordinate :math:`z\in[0, L]` and formulate the :math:`2D` PBM
+
+.. math::
+
+    \begin{aligned}
+        \frac{\partial n}{\partial t} = -v_\text{ax} \frac{\partial n}{\partial z} +D_{ax} \frac{\partial^2 n}{\partial z^2}  - \frac{\partial (v_{G}n)}{\partial x} + D_g \frac{\partial^2 n}{\partial x^2},
+    \end{aligned}
+
+where :math:`n(t, x, z)\colon [0, T_\text{end}] \times (x_c, \infty) \times [0, L] \mapsto \mathbb{R}^+` is the number density distribution,
+:math:`v_\text{ax}\in\mathbb{R}^+` is the axial velocity and :math:`D_{ax}\in\mathbb{R}^+` is the axial dispersion coefficient.
+
+Boundary conditions for the internal coordinate are again given by Eq. :eq:`RegularityBC` and Eq. :eq:`NucleationBC`.
+
+For the external coordinate :math:`z`, Danckwerts boundary conditions are applied:
+
+.. math::
+
+    \begin{aligned}
+        \left. \left( n v_\text{ax}-D_{ax}\frac{\partial n}{\partial z} \right) \right|_{z=0} = v_\text{ax} n_{in,x}, \qquad \left.\frac{\partial n}{\partial z}\right|_{z=L}=0.
+    \end{aligned}
+
+The mass balance equation for the solute :math:`c(t, z)\colon [0,T-\text{end}] \times [0,L] \mapsto \mathbb{R}^+` is given by
+
+.. math::
+
+    \begin{aligned}
+        \frac{\partial c}{\partial t} = -v_\text{ax} \frac{\partial c}{\partial z} +D_{ax} \frac{\partial^2 c}{\partial z^2} -\rho k_v \left( B_0x^3_c + 3\int_{x_c}^{\infty} v_{G}n x^2 \;\mathrm{d}x \right).
+    \end{aligned}
+
+As for the particle phase, the solute mass concentration subjects to the Danckwerts boundary conditions
+
+.. math::
+
+    \begin{aligned}
+        \left.\left( c v_\text{ax}-D_{ax}\frac{\partial c}{\partial z} \right) \right|_{z=0} = v_\text{ax} c_{in}, \qquad \left.\frac{\partial c}{\partial z}\right|_{z=L}=0.
+    \end{aligned}
+
+
+Constitutive equations
+^^^^^^^^^^^^^^^^^^^^^^
+
+Constitutive equations describe the kinetic processes in the governing equations. The relative supersaturation :math:`s>0` is:
+
+.. math::
+
+    \begin{aligned}
+        s=\frac{c-c_{eq}}{c_{eq}},
+    \end{aligned}
+
+where :math:`c_{eq}>0` is the solute solubility in the solvent.
+The nucleation kinetics can be split into primary and secondary nucleation:
+
+.. math::
+
+    \begin{aligned}
+        B_0 = B_p + B_s,
+    \end{aligned}
+
+Which are in turn defined by the following constitutive equations.
+An empirical equation for primary nucleation is given by:
+
+.. math::
+
+    \begin{aligned}
+        B_p=k_ps^u,
+    \end{aligned}
+
+where :math:`k_p\in\mathbb{R}^+` is the primary nucleation rate constant and :math:`u\in\mathbb{R}^+` is a constant.
+An empirical power-law expression is used for the secondary nucleation:
+
+.. math::
+
+    \begin{aligned}
+        B_s=k_bs^bM^k,
+    \end{aligned}
+
+where :math:`k_b\in\mathbb{R}^+` is the secondary nucleation rate constant, :math:`b\in\mathbb{R}^+` and :math:`k\in\mathbb{R}^+` are system-related parameters and :math:`M\in\mathbb{R}^+` is the suspension density defined as
+
+.. math::
+
+    \begin{aligned}
+        M=k_v\rho\int_{0}^{\infty}n\ x^3\;\mathrm{d}x.
+    \end{aligned}
+
+The following expression for the growth rate is implemented:
+
+.. math::
+
+    \begin{aligned}
+        v_{G}=k_gs^g(a+\gamma x^p),
+    \end{aligned}
+
+where :math:`k_g\in\mathbb{R}^+` is the growth rate constant, :math:`\gamma\in\mathbb{R}^+` quantifies the size dependence, and :math:`g, a, p\in\mathbb{R}^+` are system-related constants.
+
+For information on model parameters and how to specify the model interface, see :ref:`pbm_config`.
diff --git a/master/_sources/modelling/index.rst.txt b/master/_sources/modelling/index.rst.txt
index 283c9f3a9..8f0beb9b0 100644
--- a/master/_sources/modelling/index.rst.txt
+++ b/master/_sources/modelling/index.rst.txt
@@ -10,3 +10,4 @@ This section gives complete information about the supported unit operations, bin
     binding/index
     reaction/index
     networks
+    crystallization
diff --git a/master/_sources/modelling/unit_operations/index.rst.txt b/master/_sources/modelling/unit_operations/index.rst.txt
index d712f21a3..12cc6fae8 100644
--- a/master/_sources/modelling/unit_operations/index.rst.txt
+++ b/master/_sources/modelling/unit_operations/index.rst.txt
@@ -53,6 +53,12 @@ is given in :numref:`table_features_unit_operations`.
      - ×
      - ×
      - ×
+   * - :ref:`pbm_model`
+     - ×
+     - ×
+     - ×
+     - ×
+     - ×
 
 
 Moreover, the pseudo unit operations :ref:`inlet_model`, and :ref:`outlet_model` act as sources and sinks for the system. 
diff --git a/master/interface/binding/bi_steric_mass_action.html b/master/interface/binding/bi_steric_mass_action.html
index aab45894a..f9ff49b7d 100644
--- a/master/interface/binding/bi_steric_mass_action.html
+++ b/master/interface/binding/bi_steric_mass_action.html
@@ -52,14 +52,15 @@ <h3>Navigation</h3>
 <li class="toctree-l3"><a class="reference internal" href="../system.html">System of unit operations</a></li>
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 <li class="toctree-l3 current"><a class="reference internal" href="index.html">Binding models</a></li>
+<li class="toctree-l3"><a class="reference internal" href="../population_balance_model.html">Population balance model</a></li>
 <li class="toctree-l3"><a class="reference internal" href="../reaction/index.html">Reaction models</a></li>
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+<li class="toctree-l3"><a class="reference internal" href="../spatial_discretization_methods.html">Spatial discretization methods</a></li>
 </ul>
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diff --git a/master/interface/binding/extended_mobile_phase_modulator_langmuir.html b/master/interface/binding/extended_mobile_phase_modulator_langmuir.html
index a4deea5a3..ec9338be7 100644
--- a/master/interface/binding/extended_mobile_phase_modulator_langmuir.html
+++ b/master/interface/binding/extended_mobile_phase_modulator_langmuir.html
@@ -52,14 +52,15 @@ <h3>Navigation</h3>
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+<li class="toctree-l3"><a class="reference internal" href="../population_balance_model.html">Population balance model</a></li>
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+<li class="toctree-l3"><a class="reference internal" href="../spatial_discretization_methods.html">Spatial discretization methods</a></li>
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diff --git a/master/interface/binding/freundlich_ldf.html b/master/interface/binding/freundlich_ldf.html
index c8d9ee89b..b468e5e9f 100644
--- a/master/interface/binding/freundlich_ldf.html
+++ b/master/interface/binding/freundlich_ldf.html
@@ -52,14 +52,15 @@ <h3>Navigation</h3>
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+<li class="toctree-l3"><a class="reference internal" href="../population_balance_model.html">Population balance model</a></li>
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+<li class="toctree-l3"><a class="reference internal" href="../spatial_discretization_methods.html">Spatial discretization methods</a></li>
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diff --git a/master/interface/binding/generalized_ion_exchange.html b/master/interface/binding/generalized_ion_exchange.html
index 517ca4e08..bb3743e92 100644
--- a/master/interface/binding/generalized_ion_exchange.html
+++ b/master/interface/binding/generalized_ion_exchange.html
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+<li class="toctree-l3"><a class="reference internal" href="../population_balance_model.html">Population balance model</a></li>
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+<li class="toctree-l3"><a class="reference internal" href="../spatial_discretization_methods.html">Spatial discretization methods</a></li>
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diff --git a/master/interface/binding/hic_constant_water_activity.html b/master/interface/binding/hic_constant_water_activity.html
index d42731631..938cec290 100644
--- a/master/interface/binding/hic_constant_water_activity.html
+++ b/master/interface/binding/hic_constant_water_activity.html
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+<li class="toctree-l3"><a class="reference internal" href="../population_balance_model.html">Population balance model</a></li>
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index 56f2953f7..f3e556da3 100644
--- a/master/interface/binding/hic_water_on_hydrophobic_surfaces.html
+++ b/master/interface/binding/hic_water_on_hydrophobic_surfaces.html
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diff --git a/master/interface/binding/index.html b/master/interface/binding/index.html
index c947905bc..6c779870e 100644
--- a/master/interface/binding/index.html
+++ b/master/interface/binding/index.html
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diff --git a/master/interface/binding/linear.html b/master/interface/binding/linear.html
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diff --git a/master/interface/binding/mobile_phase_modulator_langmuir.html b/master/interface/binding/mobile_phase_modulator_langmuir.html
index 6962ee8d0..d1c272c2d 100644
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+++ b/master/interface/binding/mobile_phase_modulator_langmuir.html
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 <li class="toctree-l3 current"><a class="reference internal" href="index.html">Binding models</a></li>
+<li class="toctree-l3"><a class="reference internal" href="../population_balance_model.html">Population balance model</a></li>
 <li class="toctree-l3"><a class="reference internal" href="../reaction/index.html">Reaction models</a></li>
-<li class="toctree-l3"><a class="reference internal" href="../spatial_discretization_methods.html">Spatial discretization methods</a></li>
 <li class="toctree-l3"><a class="reference internal" href="../flux_reconstruction.html">Flux reconstruction methods</a></li>
 <li class="toctree-l3"><a class="reference internal" href="../consistent_initialization.html">Nonlinear solver for consistent initialization</a></li>
 <li class="toctree-l3"><a class="reference internal" href="../return_data.html">Return data</a></li>
 <li class="toctree-l3"><a class="reference internal" href="../sensitivities.html">Parameter Sensitivities</a></li>
 <li class="toctree-l3"><a class="reference internal" href="../solver.html">Solver Configuration</a></li>
 <li class="toctree-l3"><a class="reference internal" href="../parameter_dependencies.html">Parameter Dependencies</a></li>
+<li class="toctree-l3"><a class="reference internal" href="../spatial_discretization_methods.html">Spatial discretization methods</a></li>
 </ul>
 </li>
 <li class="toctree-l2"><a class="reference internal" href="../output_group.html">Output Group</a></li>
diff --git a/master/interface/consistent_initialization.html b/master/interface/consistent_initialization.html
index 5a3fcf37f..69de829d1 100644
--- a/master/interface/consistent_initialization.html
+++ b/master/interface/consistent_initialization.html
@@ -52,14 +52,15 @@ <h3>Navigation</h3>
 <li class="toctree-l3"><a class="reference internal" href="system.html">System of unit operations</a></li>
 <li class="toctree-l3"><a class="reference internal" href="unit_operations/index.html">Unit Operations</a></li>
 <li class="toctree-l3"><a class="reference internal" href="binding/index.html">Binding models</a></li>
+<li class="toctree-l3"><a class="reference internal" href="population_balance_model.html">Population balance model</a></li>
 <li class="toctree-l3"><a class="reference internal" href="reaction/index.html">Reaction models</a></li>
-<li class="toctree-l3"><a class="reference internal" href="spatial_discretization_methods.html">Spatial discretization methods</a></li>
 <li class="toctree-l3"><a class="reference internal" href="flux_reconstruction.html">Flux reconstruction methods</a></li>
 <li class="toctree-l3 current"><a class="current reference internal" href="#">Nonlinear solver for consistent initialization</a></li>
 <li class="toctree-l3"><a class="reference internal" href="return_data.html">Return data</a></li>
 <li class="toctree-l3"><a class="reference internal" href="sensitivities.html">Parameter Sensitivities</a></li>
 <li class="toctree-l3"><a class="reference internal" href="solver.html">Solver Configuration</a></li>
 <li class="toctree-l3"><a class="reference internal" href="parameter_dependencies.html">Parameter Dependencies</a></li>
+<li class="toctree-l3"><a class="reference internal" href="spatial_discretization_methods.html">Spatial discretization methods</a></li>
 </ul>
 </li>
 <li class="toctree-l2"><a class="reference internal" href="output_group.html">Output Group</a></li>
diff --git a/master/interface/flux_reconstruction.html b/master/interface/flux_reconstruction.html
index 611d7f129..5521f9720 100644
--- a/master/interface/flux_reconstruction.html
+++ b/master/interface/flux_reconstruction.html
@@ -17,7 +17,7 @@
     <link rel="index" title="Index" href="../genindex.html" />
     <link rel="search" title="Search" href="../search.html" />
     <link rel="next" title="Nonlinear solver for consistent initialization" href="consistent_initialization.html" />
-    <link rel="prev" title="Spatial discretization methods" href="spatial_discretization_methods.html" />
+    <link rel="prev" title="Michaelis Menten kinetics" href="reaction/michaelis_menten_kinetics.html" />
    
   <link rel="stylesheet" href="../_static/custom.css" type="text/css" />
   
@@ -52,14 +52,15 @@ <h3>Navigation</h3>
 <li class="toctree-l3"><a class="reference internal" href="system.html">System of unit operations</a></li>
 <li class="toctree-l3"><a class="reference internal" href="unit_operations/index.html">Unit Operations</a></li>
 <li class="toctree-l3"><a class="reference internal" href="binding/index.html">Binding models</a></li>
+<li class="toctree-l3"><a class="reference internal" href="population_balance_model.html">Population balance model</a></li>
 <li class="toctree-l3"><a class="reference internal" href="reaction/index.html">Reaction models</a></li>
-<li class="toctree-l3"><a class="reference internal" href="spatial_discretization_methods.html">Spatial discretization methods</a></li>
 <li class="toctree-l3 current"><a class="current reference internal" href="#">Flux reconstruction methods</a></li>
 <li class="toctree-l3"><a class="reference internal" href="consistent_initialization.html">Nonlinear solver for consistent initialization</a></li>
 <li class="toctree-l3"><a class="reference internal" href="return_data.html">Return data</a></li>
 <li class="toctree-l3"><a class="reference internal" href="sensitivities.html">Parameter Sensitivities</a></li>
 <li class="toctree-l3"><a class="reference internal" href="solver.html">Solver Configuration</a></li>
 <li class="toctree-l3"><a class="reference internal" href="parameter_dependencies.html">Parameter Dependencies</a></li>
+<li class="toctree-l3"><a class="reference internal" href="spatial_discretization_methods.html">Spatial discretization methods</a></li>
 </ul>
 </li>
 <li class="toctree-l2"><a class="reference internal" href="output_group.html">Output Group</a></li>
@@ -116,8 +117,8 @@ <h3>Branches</h3>
 
   <section id="flux-reconstruction-methods">
 <span id="id1"></span><h1>Flux reconstruction methods<a class="headerlink" href="#flux-reconstruction-methods" title="Link to this heading">¶</a></h1>
-<section id="group-input-model-unit-xxx-discretization-weno-weno-parameters">
-<h2>Group /input/model/unit_XXX/discretization/weno - WENO Parameters<a class="headerlink" href="#group-input-model-unit-xxx-discretization-weno-weno-parameters" title="Link to this heading">¶</a></h2>
+<section id="group-input-model-unit-xxx-discretization-reconstruction-weno">
+<h2>Group /input/model/unit_XXX/discretization/reconstruction = WENO<a class="headerlink" href="#group-input-model-unit-xxx-discretization-reconstruction-weno" title="Link to this heading">¶</a></h2>
 <p><code class="docutils literal notranslate"><span class="pre">BOUNDARY_MODEL</span></code></p>
 <blockquote>
 <div><p>Boundary model type:
@@ -163,6 +164,23 @@ <h2>Group /input/model/unit_XXX/discretization/weno - WENO Parameters<a class="h
 </table>
 </div></blockquote>
 </section>
+<section id="group-input-model-unit-xxx-discretization-reconstruction-koren">
+<h2>Group /input/model/unit_XXX/discretization/reconstruction = KOREN<a class="headerlink" href="#group-input-model-unit-xxx-discretization-reconstruction-koren" title="Link to this heading">¶</a></h2>
+<p>The Koren scheme implemented in CADET intrinsically uses a van Leer flux limiter. It can reach a maximum order of 2 depending on the smoothness of the solution. The
+BOUNDARY_MODEL is intrinsically set to 0 (stable).</p>
+<p><code class="docutils literal notranslate"><span class="pre">KOREN_EPS</span></code></p>
+<blockquote>
+<div><p>Set <span class="math notranslate nohighlight">\(\varepsilon\)</span> in the van Leer flux limiter</p>
+<table class="docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><strong>Type:</strong> double</p></td>
+<td><p><strong>Range:</strong> :math:<a href="#id2"><span class="problematic" id="id3">`</span></a>qe 0`</p></td>
+<td><p><strong>Length:</strong> 1</p></td>
+</tr>
+</tbody>
+</table>
+</div></blockquote>
+</section>
 </section>
 
 
diff --git a/master/interface/index.html b/master/interface/index.html
index c49fe0acc..3e1444df5 100644
--- a/master/interface/index.html
+++ b/master/interface/index.html
@@ -151,6 +151,11 @@ <h3>Branches</h3>
 <li class="toctree-l3"><a class="reference internal" href="binding/index.html#multiple-particle-types">Multiple particle types</a></li>
 </ul>
 </li>
+<li class="toctree-l2"><a class="reference internal" href="population_balance_model.html">Population balance model</a><ul>
+<li class="toctree-l3"><a class="reference internal" href="population_balance_model.html#group-input-model-unit-xxx">Group /input/model/unit_XXX</a></li>
+<li class="toctree-l3"><a class="reference internal" href="population_balance_model.html#group-input-model-unit-xxx-reaction-bulk-reaction-model-crystallization-unit-type-cstr">Group /input/model/unit_XXX/reaction_bulk - REACTION_MODEL = CRYSTALLIZATION - UNIT_TYPE = CSTR</a></li>
+</ul>
+</li>
 <li class="toctree-l2"><a class="reference internal" href="reaction/index.html">Reaction models</a><ul>
 <li class="toctree-l3"><a class="reference internal" href="reaction/mass_action_law.html">Mass Action Law</a></li>
 <li class="toctree-l3"><a class="reference internal" href="reaction/michaelis_menten_kinetics.html">Michaelis Menten kinetics</a></li>
@@ -158,19 +163,9 @@ <h3>Branches</h3>
 <li class="toctree-l3"><a class="reference internal" href="reaction/index.html#multiple-particle-types">Multiple particle types</a></li>
 </ul>
 </li>
-<li class="toctree-l2"><a class="reference internal" href="spatial_discretization_methods.html">Spatial discretization methods</a><ul>
-<li class="toctree-l3"><a class="reference internal" href="spatial_discretization_methods.html#group-input-model-unit-xxx-discretization-spatial-method-details-on-the-methods">Group /input/model/unit_XXX/discretization/SPATIAL_METHOD - Details on the methods</a></li>
-<li class="toctree-l3"><a class="reference internal" href="spatial_discretization_methods.html#discrete-system-size">Discrete system size</a></li>
-<li class="toctree-l3"><a class="reference internal" href="spatial_discretization_methods.html#order-of-convergence">Order of convergence</a></li>
-<li class="toctree-l3"><a class="reference internal" href="spatial_discretization_methods.html#smooth-solutions">Smooth solutions</a></li>
-<li class="toctree-l3"><a class="reference internal" href="spatial_discretization_methods.html#recommendations-on-the-choice-of-spatial-discretization-methods">Recommendations on the choice of spatial discretization methods</a></li>
-<li class="toctree-l3"><a class="reference internal" href="spatial_discretization_methods.html#recommendations-on-dg-discretization-parameters">Recommendations on DG discretization parameters</a></li>
-<li class="toctree-l3"><a class="reference internal" href="spatial_discretization_methods.html#refinement-strategy">Refinement strategy</a></li>
-<li class="toctree-l3"><a class="reference internal" href="spatial_discretization_methods.html#note-on-dg-solution-vector">Note on DG solution vector</a></li>
-</ul>
-</li>
 <li class="toctree-l2"><a class="reference internal" href="flux_reconstruction.html">Flux reconstruction methods</a><ul>
-<li class="toctree-l3"><a class="reference internal" href="flux_reconstruction.html#group-input-model-unit-xxx-discretization-weno-weno-parameters">Group /input/model/unit_XXX/discretization/weno - WENO Parameters</a></li>
+<li class="toctree-l3"><a class="reference internal" href="flux_reconstruction.html#group-input-model-unit-xxx-discretization-reconstruction-weno">Group /input/model/unit_XXX/discretization/reconstruction = WENO</a></li>
+<li class="toctree-l3"><a class="reference internal" href="flux_reconstruction.html#group-input-model-unit-xxx-discretization-reconstruction-koren">Group /input/model/unit_XXX/discretization/reconstruction = KOREN</a></li>
 </ul>
 </li>
 <li class="toctree-l2"><a class="reference internal" href="consistent_initialization.html">Nonlinear solver for consistent initialization</a><ul>
@@ -198,6 +193,17 @@ <h3>Branches</h3>
 <li class="toctree-l3"><a class="reference internal" href="parameter_dependencies.html#parameter-state-dependencies">Parameter-State Dependencies</a></li>
 </ul>
 </li>
+<li class="toctree-l2"><a class="reference internal" href="spatial_discretization_methods.html">Spatial discretization methods</a><ul>
+<li class="toctree-l3"><a class="reference internal" href="spatial_discretization_methods.html#group-input-model-unit-xxx-discretization-spatial-method-details-on-the-methods">Group /input/model/unit_XXX/discretization/SPATIAL_METHOD - Details on the methods</a></li>
+<li class="toctree-l3"><a class="reference internal" href="spatial_discretization_methods.html#discrete-system-size">Discrete system size</a></li>
+<li class="toctree-l3"><a class="reference internal" href="spatial_discretization_methods.html#order-of-convergence">Order of convergence</a></li>
+<li class="toctree-l3"><a class="reference internal" href="spatial_discretization_methods.html#smooth-solutions">Smooth solutions</a></li>
+<li class="toctree-l3"><a class="reference internal" href="spatial_discretization_methods.html#recommendations-on-the-choice-of-spatial-discretization-methods">Recommendations on the choice of spatial discretization methods</a></li>
+<li class="toctree-l3"><a class="reference internal" href="spatial_discretization_methods.html#recommendations-on-dg-discretization-parameters">Recommendations on DG discretization parameters</a></li>
+<li class="toctree-l3"><a class="reference internal" href="spatial_discretization_methods.html#refinement-strategy">Refinement strategy</a></li>
+<li class="toctree-l3"><a class="reference internal" href="spatial_discretization_methods.html#note-on-dg-solution-vector">Note on DG solution vector</a></li>
+</ul>
+</li>
 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="output_group.html">Output Group</a><ul>
diff --git a/master/interface/input_group.html b/master/interface/input_group.html
index 322bb9aa8..70bc5cff2 100644
--- a/master/interface/input_group.html
+++ b/master/interface/input_group.html
@@ -52,14 +52,15 @@ <h3>Navigation</h3>
 <li class="toctree-l3"><a class="reference internal" href="system.html">System of unit operations</a></li>
 <li class="toctree-l3"><a class="reference internal" href="unit_operations/index.html">Unit Operations</a></li>
 <li class="toctree-l3"><a class="reference internal" href="binding/index.html">Binding models</a></li>
+<li class="toctree-l3"><a class="reference internal" href="population_balance_model.html">Population balance model</a></li>
 <li class="toctree-l3"><a class="reference internal" href="reaction/index.html">Reaction models</a></li>
-<li class="toctree-l3"><a class="reference internal" href="spatial_discretization_methods.html">Spatial discretization methods</a></li>
 <li class="toctree-l3"><a class="reference internal" href="flux_reconstruction.html">Flux reconstruction methods</a></li>
 <li class="toctree-l3"><a class="reference internal" href="consistent_initialization.html">Nonlinear solver for consistent initialization</a></li>
 <li class="toctree-l3"><a class="reference internal" href="return_data.html">Return data</a></li>
 <li class="toctree-l3"><a class="reference internal" href="sensitivities.html">Parameter Sensitivities</a></li>
 <li class="toctree-l3"><a class="reference internal" href="solver.html">Solver Configuration</a></li>
 <li class="toctree-l3"><a class="reference internal" href="parameter_dependencies.html">Parameter Dependencies</a></li>
+<li class="toctree-l3"><a class="reference internal" href="spatial_discretization_methods.html">Spatial discretization methods</a></li>
 </ul>
 </li>
 <li class="toctree-l2"><a class="reference internal" href="output_group.html">Output Group</a></li>
@@ -210,6 +211,11 @@ <h3>Branches</h3>
 </li>
 </ul>
 </li>
+<li class="toctree-l1"><a class="reference internal" href="population_balance_model.html">Population balance model</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="population_balance_model.html#group-input-model-unit-xxx">Group /input/model/unit_XXX</a></li>
+<li class="toctree-l2"><a class="reference internal" href="population_balance_model.html#group-input-model-unit-xxx-reaction-bulk-reaction-model-crystallization-unit-type-cstr">Group /input/model/unit_XXX/reaction_bulk - REACTION_MODEL = CRYSTALLIZATION - UNIT_TYPE = CSTR</a></li>
+</ul>
+</li>
 <li class="toctree-l1"><a class="reference internal" href="reaction/index.html">Reaction models</a><ul>
 <li class="toctree-l2"><a class="reference internal" href="reaction/mass_action_law.html">Mass Action Law</a></li>
 <li class="toctree-l2"><a class="reference internal" href="reaction/michaelis_menten_kinetics.html">Michaelis Menten kinetics</a></li>
@@ -217,19 +223,9 @@ <h3>Branches</h3>
 <li class="toctree-l2"><a class="reference internal" href="reaction/index.html#multiple-particle-types">Multiple particle types</a></li>
 </ul>
 </li>
-<li class="toctree-l1"><a class="reference internal" href="spatial_discretization_methods.html">Spatial discretization methods</a><ul>
-<li class="toctree-l2"><a class="reference internal" href="spatial_discretization_methods.html#group-input-model-unit-xxx-discretization-spatial-method-details-on-the-methods">Group /input/model/unit_XXX/discretization/SPATIAL_METHOD - Details on the methods</a></li>
-<li class="toctree-l2"><a class="reference internal" href="spatial_discretization_methods.html#discrete-system-size">Discrete system size</a></li>
-<li class="toctree-l2"><a class="reference internal" href="spatial_discretization_methods.html#order-of-convergence">Order of convergence</a></li>
-<li class="toctree-l2"><a class="reference internal" href="spatial_discretization_methods.html#smooth-solutions">Smooth solutions</a></li>
-<li class="toctree-l2"><a class="reference internal" href="spatial_discretization_methods.html#recommendations-on-the-choice-of-spatial-discretization-methods">Recommendations on the choice of spatial discretization methods</a></li>
-<li class="toctree-l2"><a class="reference internal" href="spatial_discretization_methods.html#recommendations-on-dg-discretization-parameters">Recommendations on DG discretization parameters</a></li>
-<li class="toctree-l2"><a class="reference internal" href="spatial_discretization_methods.html#refinement-strategy">Refinement strategy</a></li>
-<li class="toctree-l2"><a class="reference internal" href="spatial_discretization_methods.html#note-on-dg-solution-vector">Note on DG solution vector</a></li>
-</ul>
-</li>
 <li class="toctree-l1"><a class="reference internal" href="flux_reconstruction.html">Flux reconstruction methods</a><ul>
-<li class="toctree-l2"><a class="reference internal" href="flux_reconstruction.html#group-input-model-unit-xxx-discretization-weno-weno-parameters">Group /input/model/unit_XXX/discretization/weno - WENO Parameters</a></li>
+<li class="toctree-l2"><a class="reference internal" href="flux_reconstruction.html#group-input-model-unit-xxx-discretization-reconstruction-weno">Group /input/model/unit_XXX/discretization/reconstruction = WENO</a></li>
+<li class="toctree-l2"><a class="reference internal" href="flux_reconstruction.html#group-input-model-unit-xxx-discretization-reconstruction-koren">Group /input/model/unit_XXX/discretization/reconstruction = KOREN</a></li>
 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="consistent_initialization.html">Nonlinear solver for consistent initialization</a><ul>
@@ -263,6 +259,17 @@ <h3>Branches</h3>
 </li>
 </ul>
 </li>
+<li class="toctree-l1"><a class="reference internal" href="spatial_discretization_methods.html">Spatial discretization methods</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="spatial_discretization_methods.html#group-input-model-unit-xxx-discretization-spatial-method-details-on-the-methods">Group /input/model/unit_XXX/discretization/SPATIAL_METHOD - Details on the methods</a></li>
+<li class="toctree-l2"><a class="reference internal" href="spatial_discretization_methods.html#discrete-system-size">Discrete system size</a></li>
+<li class="toctree-l2"><a class="reference internal" href="spatial_discretization_methods.html#order-of-convergence">Order of convergence</a></li>
+<li class="toctree-l2"><a class="reference internal" href="spatial_discretization_methods.html#smooth-solutions">Smooth solutions</a></li>
+<li class="toctree-l2"><a class="reference internal" href="spatial_discretization_methods.html#recommendations-on-the-choice-of-spatial-discretization-methods">Recommendations on the choice of spatial discretization methods</a></li>
+<li class="toctree-l2"><a class="reference internal" href="spatial_discretization_methods.html#recommendations-on-dg-discretization-parameters">Recommendations on DG discretization parameters</a></li>
+<li class="toctree-l2"><a class="reference internal" href="spatial_discretization_methods.html#refinement-strategy">Refinement strategy</a></li>
+<li class="toctree-l2"><a class="reference internal" href="spatial_discretization_methods.html#note-on-dg-solution-vector">Note on DG solution vector</a></li>
+</ul>
+</li>
 </ul>
 </div>
 </section>
diff --git a/master/interface/output_group.html b/master/interface/output_group.html
index 2544c3589..4d5035066 100644
--- a/master/interface/output_group.html
+++ b/master/interface/output_group.html
@@ -17,7 +17,7 @@
     <link rel="index" title="Index" href="../genindex.html" />
     <link rel="search" title="Search" href="../search.html" />
     <link rel="next" title="Meta Group" href="meta_group.html" />
-    <link rel="prev" title="Parameter Dependencies" href="parameter_dependencies.html" />
+    <link rel="prev" title="Spatial discretization methods" href="spatial_discretization_methods.html" />
    
   <link rel="stylesheet" href="../_static/custom.css" type="text/css" />
   
diff --git a/master/interface/parameter_dependencies.html b/master/interface/parameter_dependencies.html
index 79fdfd691..5892bfea6 100644
--- a/master/interface/parameter_dependencies.html
+++ b/master/interface/parameter_dependencies.html
@@ -16,7 +16,7 @@
     <link rel="icon" href="../_static/cadet_icon.png"/>
     <link rel="index" title="Index" href="../genindex.html" />
     <link rel="search" title="Search" href="../search.html" />
-    <link rel="next" title="Output Group" href="output_group.html" />
+    <link rel="next" title="Spatial discretization methods" href="spatial_discretization_methods.html" />
     <link rel="prev" title="Solver Configuration" href="solver.html" />
    
   <link rel="stylesheet" href="../_static/custom.css" type="text/css" />
@@ -52,14 +52,15 @@ <h3>Navigation</h3>
 <li class="toctree-l3"><a class="reference internal" href="system.html">System of unit operations</a></li>
 <li class="toctree-l3"><a class="reference internal" href="unit_operations/index.html">Unit Operations</a></li>
 <li class="toctree-l3"><a class="reference internal" href="binding/index.html">Binding models</a></li>
+<li class="toctree-l3"><a class="reference internal" href="population_balance_model.html">Population balance model</a></li>
 <li class="toctree-l3"><a class="reference internal" href="reaction/index.html">Reaction models</a></li>
-<li class="toctree-l3"><a class="reference internal" href="spatial_discretization_methods.html">Spatial discretization methods</a></li>
 <li class="toctree-l3"><a class="reference internal" href="flux_reconstruction.html">Flux reconstruction methods</a></li>
 <li class="toctree-l3"><a class="reference internal" href="consistent_initialization.html">Nonlinear solver for consistent initialization</a></li>
 <li class="toctree-l3"><a class="reference internal" href="return_data.html">Return data</a></li>
 <li class="toctree-l3"><a class="reference internal" href="sensitivities.html">Parameter Sensitivities</a></li>
 <li class="toctree-l3"><a class="reference internal" href="solver.html">Solver Configuration</a></li>
 <li class="toctree-l3 current"><a class="current reference internal" href="#">Parameter Dependencies</a></li>
+<li class="toctree-l3"><a class="reference internal" href="spatial_discretization_methods.html">Spatial discretization methods</a></li>
 </ul>
 </li>
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+
+  <section id="population-balance-model">
+<span id="pbm-config"></span><h1>Population balance model<a class="headerlink" href="#population-balance-model" title="Link to this heading">¶</a></h1>
+<p>The PBM in CADET is implemented as part of the reaction module and can thus be used in any unit operation that includes reactions.
+Typical applications consider crystallization in a <a class="reference internal" href="unit_operations/cstr.html#cstr-config"><span class="std std-ref">Continuous stirred tank reactor model</span></a> or, to model continuous processes, in a Dispersive Plug-Flow Reactor (DPFR), which is modelled by a <a class="reference internal" href="unit_operations/lumped_rate_model_without_pores.html#lumped-rate-model-without-pores-config"><span class="std std-ref">Lumped Rate Model Without Pores</span></a>.</p>
+<p>The particle size domain (internal coordinate) is discretized by the FV method, giving us a finite set of particle sizes under consideration <span class="math notranslate nohighlight">\(\{x_1, \dots, x_{N_x}\}\)</span>.
+Every particle size considered is treated as an individual component of the unit operation and the field <code class="docutils literal notranslate"><span class="pre">NCOMP</span></code> of that unit operation in which the crystallization happens, must be specified accordingly as <span class="math notranslate nohighlight">\(N_x + 2\)</span>.
+The two additional components account for the solute <span class="math notranslate nohighlight">\(c\)</span> and solubility <span class="math notranslate nohighlight">\(c_\text{eq}\)</span>.
+<em>That is, by setting the ``NCOMP`` field, you specify the number of FV cells for the internal coordinate.</em></p>
+<section id="group-input-model-unit-xxx">
+<h2>Group /input/model/unit_XXX<a class="headerlink" href="#group-input-model-unit-xxx" title="Link to this heading">¶</a></h2>
+<p><code class="docutils literal notranslate"><span class="pre">NCOMP</span></code></p>
+<blockquote>
+<div><p>Number of components, which is given by two plus the number discrete particle sizes, which is given by the number of FV cells discretizing the internal coordinate</p>
+<table class="docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><strong>Type:</strong> int</p></td>
+<td><p><strong>Range:</strong> <span class="math notranslate nohighlight">\(\geq 3\)</span></p></td>
+<td><p><strong>Length:</strong> 1</p></td>
+</tr>
+</tbody>
+</table>
+</div></blockquote>
+<p><code class="docutils literal notranslate"><span class="pre">REACTION_MODEL</span></code></p>
+<blockquote>
+<div><p>The crystallization code is implemented as a reaction module, which is why crystallization needs to be specified here</p>
+<table class="docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><strong>Type:</strong> String</p></td>
+<td><p><strong>Range:</strong> <span class="math notranslate nohighlight">\(\{ CRYSTALLIZATION \}\)</span></p></td>
+<td><p><strong>Length:</strong> 1</p></td>
+</tr>
+</tbody>
+</table>
+</div></blockquote>
+</section>
+<section id="group-input-model-unit-xxx-reaction-bulk-reaction-model-crystallization-unit-type-cstr">
+<h2>Group /input/model/unit_XXX/reaction_bulk - REACTION_MODEL = CRYSTALLIZATION - UNIT_TYPE = CSTR<a class="headerlink" href="#group-input-model-unit-xxx-reaction-bulk-reaction-model-crystallization-unit-type-cstr" title="Link to this heading">¶</a></h2>
+<p><em>The following parameters need to be specified under Group /input/model/unit_XXX/reaction/reaction_bulk/ for CSTR units, and Group /input/model/unit_XXX/reaction/reaction/ for transport units like the LRM.</em></p>
+<p><code class="docutils literal notranslate"><span class="pre">CRY_BINS</span></code></p>
+<blockquote>
+<div><p>Coordinates of the cell faces, e.g. equidistant or logarithmic discretization of the internal coordinate <span class="math notranslate nohighlight">\(x \in [x_c, x_\text{end}]\)</span>, including the end points.</p>
+<table class="docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><strong>Type:</strong> double</p></td>
+<td><p><strong>Range:</strong> <span class="math notranslate nohighlight">\(\geq 1\)</span></p></td>
+<td><p><strong>Length:</strong> <span class="math notranslate nohighlight">\(\mathrm{N_x} + 1\)</span></p></td>
+</tr>
+</tbody>
+</table>
+</div></blockquote>
+<p><code class="docutils literal notranslate"><span class="pre">CRY_NUCLEI_MASS_DENSITY</span></code></p>
+<blockquote>
+<div><p>Nulcei mass density</p>
+<table class="docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><strong>Type:</strong> double</p></td>
+<td><p><strong>Range:</strong> <span class="math notranslate nohighlight">\(\geq 0\)</span></p></td>
+<td><p><strong>Length:</strong> 1</p></td>
+</tr>
+</tbody>
+</table>
+</div></blockquote>
+<p><code class="docutils literal notranslate"><span class="pre">CRY_VOL_SHAPE_FACTOR</span></code></p>
+<blockquote>
+<div><p>Volumetric shape factor of the particles</p>
+<table class="docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><strong>Type:</strong> double</p></td>
+<td><p><strong>Range:</strong> <span class="math notranslate nohighlight">\(\geq 0\)</span></p></td>
+<td><p><strong>Length:</strong> 1</p></td>
+</tr>
+</tbody>
+</table>
+</div></blockquote>
+<p><code class="docutils literal notranslate"><span class="pre">CRY_PRIMARY_NUCLEATION_RATE</span></code></p>
+<blockquote>
+<div><p>Primary nucleation rate constant <span class="math notranslate nohighlight">\(k_p\)</span></p>
+<table class="docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><strong>Type:</strong> double</p></td>
+<td><p><strong>Range:</strong> <span class="math notranslate nohighlight">\(\geq 0\)</span></p></td>
+<td><p><strong>Length:</strong> 1</p></td>
+</tr>
+</tbody>
+</table>
+</div></blockquote>
+<p><code class="docutils literal notranslate"><span class="pre">CRY_SECONDARY_NUCLEATION_RATE</span></code></p>
+<blockquote>
+<div><p>Secondary nucleation rate <span class="math notranslate nohighlight">\(k_b\)</span></p>
+<table class="docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><strong>Type:</strong> double</p></td>
+<td><p><strong>Range:</strong> <span class="math notranslate nohighlight">\(\geq 0\)</span></p></td>
+<td><p><strong>Length:</strong> 1</p></td>
+</tr>
+</tbody>
+</table>
+</div></blockquote>
+<p><code class="docutils literal notranslate"><span class="pre">CRY_GROWTH_RATE_CONSTANT</span></code></p>
+<blockquote>
+<div><p>Growth rate constant <span class="math notranslate nohighlight">\(k_g\)</span></p>
+<table class="docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><strong>Type:</strong> double</p></td>
+<td><p><strong>Range:</strong> <span class="math notranslate nohighlight">\(\geq 0\)</span></p></td>
+<td><p><strong>Length:</strong> 1</p></td>
+</tr>
+</tbody>
+</table>
+</div></blockquote>
+<p><code class="docutils literal notranslate"><span class="pre">CRY_GROWTH_CONSTANT</span></code></p>
+<blockquote>
+<div><p>Growth constant <span class="math notranslate nohighlight">\(\gamma\)</span></p>
+<table class="docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><strong>Type:</strong> double</p></td>
+<td><p><strong>Range:</strong> <span class="math notranslate nohighlight">\(\geq 0\)</span></p></td>
+<td><p><strong>Length:</strong> 1</p></td>
+</tr>
+</tbody>
+</table>
+</div></blockquote>
+<p><code class="docutils literal notranslate"><span class="pre">CRY_A</span></code></p>
+<blockquote>
+<div><p>Defines constant <span class="math notranslate nohighlight">\(a\)</span> used to determine the growth rate</p>
+<table class="docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><strong>Type:</strong> double</p></td>
+<td><p><strong>Range:</strong> <span class="math notranslate nohighlight">\(\geq 0\)</span></p></td>
+<td><p><strong>Length:</strong> 1</p></td>
+</tr>
+</tbody>
+</table>
+</div></blockquote>
+<p><code class="docutils literal notranslate"><span class="pre">CRY_G</span></code></p>
+<blockquote>
+<div><p>Defines constant <span class="math notranslate nohighlight">\(g\)</span> used to determine the growth rate</p>
+<table class="docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><strong>Type:</strong> double</p></td>
+<td><p><strong>Range:</strong> <span class="math notranslate nohighlight">\(\geq 0\)</span></p></td>
+<td><p><strong>Length:</strong> 1</p></td>
+</tr>
+</tbody>
+</table>
+</div></blockquote>
+<p><code class="docutils literal notranslate"><span class="pre">CRY_P</span></code></p>
+<blockquote>
+<div><p>Defines constant <span class="math notranslate nohighlight">\(p\)</span>  used to determine the growth rate</p>
+<table class="docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><strong>Type:</strong> double</p></td>
+<td><p><strong>Range:</strong> <span class="math notranslate nohighlight">\(\geq 0\)</span></p></td>
+<td><p><strong>Length:</strong> 1</p></td>
+</tr>
+</tbody>
+</table>
+</div></blockquote>
+<p><code class="docutils literal notranslate"><span class="pre">CRY_GROWTH_DISPERSION_RATE</span></code></p>
+<blockquote>
+<div><p>Growth dispersion rate <span class="math notranslate nohighlight">\(D_g\)</span></p>
+<table class="docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><strong>Type:</strong> double</p></td>
+<td><p><strong>Range:</strong> <span class="math notranslate nohighlight">\(\geq 0\)</span></p></td>
+<td><p><strong>Length:</strong> 1</p></td>
+</tr>
+</tbody>
+</table>
+</div></blockquote>
+<p><code class="docutils literal notranslate"><span class="pre">CRY_U</span></code></p>
+<blockquote>
+<div><p>Defines constant <span class="math notranslate nohighlight">\(u\)</span> used to determine the primary nucleation</p>
+<table class="docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><strong>Type:</strong> double</p></td>
+<td><p><strong>Range:</strong> <span class="math notranslate nohighlight">\(\geq 0\)</span></p></td>
+<td><p><strong>Length:</strong> 1</p></td>
+</tr>
+</tbody>
+</table>
+</div></blockquote>
+<p><code class="docutils literal notranslate"><span class="pre">CRY_B</span></code></p>
+<blockquote>
+<div><p>Defines constant <span class="math notranslate nohighlight">\(b\)</span> used to determine the secondary nucleation</p>
+<table class="docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><strong>Type:</strong> double</p></td>
+<td><p><strong>Range:</strong> <span class="math notranslate nohighlight">\(\geq 0\)</span></p></td>
+<td><p><strong>Length:</strong> 1</p></td>
+</tr>
+</tbody>
+</table>
+</div></blockquote>
+<p><code class="docutils literal notranslate"><span class="pre">CRY_K</span></code></p>
+<blockquote>
+<div><p>Defines constant <span class="math notranslate nohighlight">\(k\)</span> used to determine the secondary nucleation</p>
+<table class="docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><strong>Type:</strong> double</p></td>
+<td><p><strong>Range:</strong> <span class="math notranslate nohighlight">\(\geq 0\)</span></p></td>
+<td><p><strong>Length:</strong> 1</p></td>
+</tr>
+</tbody>
+</table>
+</div></blockquote>
+<p><code class="docutils literal notranslate"><span class="pre">CRY_GROWTH_SCHEME_ORDER</span></code></p>
+<blockquote>
+<div><p>Defines the growth flux FV reconstruction scheme. It can only be <span class="math notranslate nohighlight">\(1\)</span>: upwind scheme; <span class="math notranslate nohighlight">\(2\)</span>: HR Koren scheme; <span class="math notranslate nohighlight">\(3\)</span>: WENO23 scheme; <span class="math notranslate nohighlight">\(4\)</span>: WENO35 scheme.
+We recommend using the HR Koren scheme, which showed to be the most performant in our benchmarks.</p>
+<table class="docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><strong>Type:</strong> int</p></td>
+<td><p><strong>Range:</strong> <span class="math notranslate nohighlight">\([1, \dots, 4]\)</span></p></td>
+<td><p><strong>Length:</strong> 1</p></td>
+</tr>
+</tbody>
+</table>
+</div></blockquote>
+</section>
+</section>
+
+
+
+          </div>
+          
+        </div>
+      </div>
+    <div class="clearer"></div>
+  </div>
+    <div class="footer">
+      &#169;2008-2024.
+      
+      |
+      <a href="../_sources/interface/population_balance_model.rst.txt"
+          rel="nofollow">Page source</a>
+    </div>
+
+    
+
+    
+  </body>
+</html>
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diff --git a/master/interface/reaction/index.html b/master/interface/reaction/index.html
index 7675d7f80..ecc8ce53c 100644
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+++ b/master/interface/reaction/index.html
@@ -17,7 +17,7 @@
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-    <link rel="prev" title="Multi Component Colloidal" href="../binding/multi_component_colloidal.html" />
+    <link rel="prev" title="Population balance model" href="../population_balance_model.html" />
    
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+<li class="toctree-l3"><a class="reference internal" href="../population_balance_model.html">Population balance model</a></li>
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+<li class="toctree-l3"><a class="reference internal" href="../spatial_discretization_methods.html">Spatial discretization methods</a></li>
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index 339dbf7a7..19484f860 100644
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+<li class="toctree-l3"><a class="reference internal" href="../population_balance_model.html">Population balance model</a></li>
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diff --git a/master/interface/reaction/michaelis_menten_kinetics.html b/master/interface/reaction/michaelis_menten_kinetics.html
index b10842fc9..ca6b39f14 100644
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+++ b/master/interface/reaction/michaelis_menten_kinetics.html
@@ -16,7 +16,7 @@
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index 2129455bb..bd88eead1 100644
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@@ -16,8 +16,8 @@
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@@ -147,7 +148,7 @@ <h2>Order of convergence<a class="headerlink" href="#order-of-convergence" title
 <p>The theoretical order of convergence is an asymptotic property, i.e. holds for infinite refinements, but can be numerivcally observed for finite refinements as well.
 Having the exact solution, we can compute an experimental order of convergence (EOC) via the formula</p>
 <div class="math notranslate nohighlight" id="equation-modelcolumn">
-<span class="eqno">(28)<a class="headerlink" href="#equation-modelcolumn" title="Link to this equation">¶</a></span>\[\begin{aligned}
+<span class="eqno">(30)<a class="headerlink" href="#equation-modelcolumn" title="Link to this equation">¶</a></span>\[\begin{aligned}
     EOC_k = \frac{log(\varepsilon_{k+1} / \varepsilon_{k}) }{log(n_{k} / n_{k+1})},
 \end{aligned}\]</div>
 <p>with <span class="math notranslate nohighlight">\(\varepsilon_{k}\)</span> and <span class="math notranslate nohighlight">\(n_{k}\)</span> denoting some error norm and the degrees of freedom of the $k$th approximation.
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+  <section id="population-balance-models">
+<span id="pbm-model"></span><h1>Population Balance Models<a class="headerlink" href="#population-balance-models" title="Link to this heading">¶</a></h1>
+<p>The population balance model (PBM) is given by a particle-number continuity equation which describes the evolution of the number density <span class="math notranslate nohighlight">\(n\)</span> of the particles over time <span class="math notranslate nohighlight">\(t\)</span> and with respect to a so-called internal coordinate <span class="math notranslate nohighlight">\(x\)</span> and external coordinate <span class="math notranslate nohighlight">\(z\)</span>.
+The internal coordinate can be chosen as any characteristic property of the particles such as the particle size or volume.
+The external coordinate can be a characteristic dimension of the reactor itself, including its axial length.</p>
+<p>In CADET, we chose particle size and axial coordinate as the internal and external coodinate respectively.
+The PBM in CADET is implemented so that it can be used in any unit operation that supports reactions.
+Typical applications consider crystallization in a CSTR or, to model continuous processes, in a Dispersive Plug-Flow Reactor (DPFR), which is described by the LRM without solid phase.</p>
+<p>In the following, we give a brief overview on the modelling equations, for more information on the PBM as implemented in CADET, please refer to <span id="id1">[<a class="reference internal" href="../zbibliography.html#id42" title="Wendi Zhang, Todd Przybycien, Johannes Schmölder, Samuel Leweke, and Eric von Lieres. Solving crystallization/precipitation population balance models in cadet, part i: nucleation growth and growth rate dispersion in batch and continuous modes on nonuniform grids. Computers &amp; Chemical Engineering, pages 108612, 2024. doi:https://doi.org/10.1016/j.compchemeng.2024.108612.">24</a>]</span>.</p>
+<section id="population-balance-model-in-a-cstr">
+<h2>Population Balance Model in a CSTR<a class="headerlink" href="#population-balance-model-in-a-cstr" title="Link to this heading">¶</a></h2>
+<p>We assume a well-mixed tank and choose the particle size <span class="math notranslate nohighlight">\(x\in (x_c, \infty)\)</span> as the internal coodinate, with <span class="math notranslate nohighlight">\(x_c&gt;0\)</span> being the minimal particle size considered.
+The corresponding PBM is given as</p>
+<div class="math notranslate nohighlight">
+\[\begin{aligned}
+    \frac{\partial (n V)}{\partial t} = F_{in}n_{in} - F_{out}n - V \left( \frac{\partial (v_{G}n)}{\partial x} - D_g \frac{\partial^2 n}{\partial x^2} - B_0 \delta (x-x_c) \right),
+\end{aligned}\]</div>
+<p>where <span class="math notranslate nohighlight">\(F_{in}, F_{out}\in \mathbb{R}^+\)</span> are the volumetric inflow and outflow rates, <span class="math notranslate nohighlight">\(V\in\mathbb{R}^+\)</span> is the reactor volume,
+<span class="math notranslate nohighlight">\(n(t, x)\colon [0, T_\text{end}] \times (x_c, \infty) \mapsto \mathbb{R}^+\)</span> is the number density distribution,
+<span class="math notranslate nohighlight">\(n_{in}\in\mathbb{R}^+\)</span> is the number density distribution of the inlet feed, <span class="math notranslate nohighlight">\(v_{G}\in\mathbb{R}^+\)</span> is the particle growth rate,
+<span class="math notranslate nohighlight">\(D_g\in\mathbb{R}^+\)</span> is the growth dispersion rate.</p>
+<p>The boundary conditions are given by the regularity boundary condition</p>
+<div class="math notranslate nohighlight" id="equation-regularitybc">
+<span class="eqno">(27)<a class="headerlink" href="#equation-regularitybc" title="Link to this equation">¶</a></span>\[\begin{aligned}
+    \left. \left( nv_{G} - D_g \frac{\partial n}{\partial x} \right) \right|_{x \to \infty}=0,
+\end{aligned}\]</div>
+<p>and the nucleation kinetics boundary condition</p>
+<div class="math notranslate nohighlight" id="equation-nucleationbc">
+<span class="eqno">(28)<a class="headerlink" href="#equation-nucleationbc" title="Link to this equation">¶</a></span>\[\begin{aligned}
+    \left. \left( nv_{G}-D_g \frac{\partial n}{\partial x} \right)\right|_{x=x_c} = B_0,
+\end{aligned}\]</div>
+<p>where <span class="math notranslate nohighlight">\(B_0\in\mathbb{R}^+\)</span> is the nucleation kinetics factor representing particle nucleations of size <span class="math notranslate nohighlight">\(x_c\in\mathbb{R}^+\)</span>.</p>
+<p>The model is complemented by the following mass balance equation which accounts for the mass transfer between the particle phase and the solute phase</p>
+<div class="math notranslate nohighlight">
+\[\begin{aligned}
+    \frac{\partial (cV)}{\partial t} = F_{in}c_{in} - F_{out}c -\rho k_v  V \left( B_0x^3_c + 3\int_{x_c}^{\infty} v_{G}n\ x^2 \;\mathrm{d}x \right),
+\end{aligned}\]</div>
+<p>where <span class="math notranslate nohighlight">\(c(t)\colon [0, T_\text{end}] \mapsto \mathbb{R}^+\)</span> is the solute concentration in the bulk phase, <span class="math notranslate nohighlight">\(c_{in}\in\mathbb{R}^+\)</span> is the inlet solute mass concentration, <span class="math notranslate nohighlight">\(\rho &gt; 0\)</span> is the nuclei mass density and <span class="math notranslate nohighlight">\(k_v &gt; 0\)</span> is the volumetric shape factor of the particles.</p>
+<p>Evolution of the reactor’s volume is governed by</p>
+<div class="math notranslate nohighlight">
+\[\begin{aligned}
+    \frac{\mathrm{d}V}{\mathrm{d}t} &amp;= F_{\text{in}} - F_{\text{out}}.
+\end{aligned}\]</div>
+</section>
+<section id="population-balance-model-in-a-dpfr">
+<h2>Population Balance Model in a DPFR<a class="headerlink" href="#population-balance-model-in-a-dpfr" title="Link to this heading">¶</a></h2>
+<p>The PBM can also be formulated for a DPFR to model continuous processes.
+That is, we choose the axial position within a DPFR as the external coordinate <span class="math notranslate nohighlight">\(z\in[0, L]\)</span> and formulate the <span class="math notranslate nohighlight">\(2D\)</span> PBM</p>
+<div class="math notranslate nohighlight">
+\[\begin{aligned}
+    \frac{\partial n}{\partial t} = -v_\text{ax} \frac{\partial n}{\partial z} +D_{ax} \frac{\partial^2 n}{\partial z^2}  - \frac{\partial (v_{G}n)}{\partial x} + D_g \frac{\partial^2 n}{\partial x^2},
+\end{aligned}\]</div>
+<p>where <span class="math notranslate nohighlight">\(n(t, x, z)\colon [0, T_\text{end}] \times (x_c, \infty) \times [0, L] \mapsto \mathbb{R}^+\)</span> is the number density distribution,
+<span class="math notranslate nohighlight">\(v_\text{ax}\in\mathbb{R}^+\)</span> is the axial velocity and <span class="math notranslate nohighlight">\(D_{ax}\in\mathbb{R}^+\)</span> is the axial dispersion coefficient.</p>
+<p>Boundary conditions for the internal coordinate are again given by Eq. <a class="reference internal" href="#equation-regularitybc">27</a> and Eq. <a class="reference internal" href="#equation-nucleationbc">28</a>.</p>
+<p>For the external coordinate <span class="math notranslate nohighlight">\(z\)</span>, Danckwerts boundary conditions are applied:</p>
+<div class="math notranslate nohighlight">
+\[\begin{aligned}
+    \left. \left( n v_\text{ax}-D_{ax}\frac{\partial n}{\partial z} \right) \right|_{z=0} = v_\text{ax} n_{in,x}, \qquad \left.\frac{\partial n}{\partial z}\right|_{z=L}=0.
+\end{aligned}\]</div>
+<p>The mass balance equation for the solute <span class="math notranslate nohighlight">\(c(t, z)\colon [0,T-\text{end}] \times [0,L] \mapsto \mathbb{R}^+\)</span> is given by</p>
+<div class="math notranslate nohighlight">
+\[\begin{aligned}
+    \frac{\partial c}{\partial t} = -v_\text{ax} \frac{\partial c}{\partial z} +D_{ax} \frac{\partial^2 c}{\partial z^2} -\rho k_v \left( B_0x^3_c + 3\int_{x_c}^{\infty} v_{G}n x^2 \;\mathrm{d}x \right).
+\end{aligned}\]</div>
+<p>As for the particle phase, the solute mass concentration subjects to the Danckwerts boundary conditions</p>
+<div class="math notranslate nohighlight">
+\[\begin{aligned}
+    \left.\left( c v_\text{ax}-D_{ax}\frac{\partial c}{\partial z} \right) \right|_{z=0} = v_\text{ax} c_{in}, \qquad \left.\frac{\partial c}{\partial z}\right|_{z=L}=0.
+\end{aligned}\]</div>
+</section>
+<section id="constitutive-equations">
+<h2>Constitutive equations<a class="headerlink" href="#constitutive-equations" title="Link to this heading">¶</a></h2>
+<p>Constitutive equations describe the kinetic processes in the governing equations. The relative supersaturation <span class="math notranslate nohighlight">\(s&gt;0\)</span> is:</p>
+<div class="math notranslate nohighlight">
+\[\begin{aligned}
+    s=\frac{c-c_{eq}}{c_{eq}},
+\end{aligned}\]</div>
+<p>where <span class="math notranslate nohighlight">\(c_{eq}&gt;0\)</span> is the solute solubility in the solvent.
+The nucleation kinetics can be split into primary and secondary nucleation:</p>
+<div class="math notranslate nohighlight">
+\[\begin{aligned}
+    B_0 = B_p + B_s,
+\end{aligned}\]</div>
+<p>Which are in turn defined by the following constitutive equations.
+An empirical equation for primary nucleation is given by:</p>
+<div class="math notranslate nohighlight">
+\[\begin{aligned}
+    B_p=k_ps^u,
+\end{aligned}\]</div>
+<p>where <span class="math notranslate nohighlight">\(k_p\in\mathbb{R}^+\)</span> is the primary nucleation rate constant and <span class="math notranslate nohighlight">\(u\in\mathbb{R}^+\)</span> is a constant.
+An empirical power-law expression is used for the secondary nucleation:</p>
+<div class="math notranslate nohighlight">
+\[\begin{aligned}
+    B_s=k_bs^bM^k,
+\end{aligned}\]</div>
+<p>where <span class="math notranslate nohighlight">\(k_b\in\mathbb{R}^+\)</span> is the secondary nucleation rate constant, <span class="math notranslate nohighlight">\(b\in\mathbb{R}^+\)</span> and <span class="math notranslate nohighlight">\(k\in\mathbb{R}^+\)</span> are system-related parameters and <span class="math notranslate nohighlight">\(M\in\mathbb{R}^+\)</span> is the suspension density defined as</p>
+<div class="math notranslate nohighlight">
+\[\begin{aligned}
+    M=k_v\rho\int_{0}^{\infty}n\ x^3\;\mathrm{d}x.
+\end{aligned}\]</div>
+<p>The following expression for the growth rate is implemented:</p>
+<div class="math notranslate nohighlight">
+\[\begin{aligned}
+    v_{G}=k_gs^g(a+\gamma x^p),
+\end{aligned}\]</div>
+<p>where <span class="math notranslate nohighlight">\(k_g\in\mathbb{R}^+\)</span> is the growth rate constant, <span class="math notranslate nohighlight">\(\gamma\in\mathbb{R}^+\)</span> quantifies the size dependence, and <span class="math notranslate nohighlight">\(g, a, p\in\mathbb{R}^+\)</span> are system-related constants.</p>
+<p>For information on model parameters and how to specify the model interface, see <a class="reference internal" href="../interface/population_balance_model.html#pbm-config"><span class="std std-ref">Population balance model</span></a>.</p>
+</section>
+</section>
+
+
+
+          </div>
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+      </div>
+    <div class="clearer"></div>
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+      &#169;2008-2024.
+      
+      |
+      <a href="../_sources/modelling/crystallization.rst.txt"
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diff --git a/master/modelling/index.html b/master/modelling/index.html
index de959dc78..ec1c90f13 100644
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+++ b/master/modelling/index.html
@@ -49,6 +49,7 @@ <h3>Navigation</h3>
 <li class="toctree-l2"><a class="reference internal" href="binding/index.html">Binding models</a></li>
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 <li class="toctree-l2"><a class="reference internal" href="networks.html">Networks of unit operations</a></li>
+<li class="toctree-l2"><a class="reference internal" href="crystallization.html">Population Balance Models</a></li>
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@@ -126,6 +127,12 @@ <h3>Branches</h3>
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+<li class="toctree-l1"><a class="reference internal" href="crystallization.html">Population Balance Models</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="crystallization.html#population-balance-model-in-a-cstr">Population Balance Model in a CSTR</a></li>
+<li class="toctree-l2"><a class="reference internal" href="crystallization.html#population-balance-model-in-a-dpfr">Population Balance Model in a DPFR</a></li>
+<li class="toctree-l2"><a class="reference internal" href="crystallization.html#constitutive-equations">Constitutive equations</a></li>
+</ul>
+</li>
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diff --git a/master/modelling/networks.html b/master/modelling/networks.html
index fce1ef608..e89bfb52c 100644
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 </section>
 <section id="solution-of-the-linear-systems">
 <span id="muopnetworklinearsolver"></span><h2>Solution of the linear systems<a class="headerlink" href="#solution-of-the-linear-systems" title="Link to this heading">¶</a></h2>
-<p>Each time step in the simulation requires the solution of a nonlinear system Eq. <a class="reference internal" href="../simulation/index.html#equation-bdfnonlinsystem">27</a> (see Sec. <a class="reference internal" href="../simulation/index.html#simtimeintegration"><span class="std std-ref">Time stepping</span></a>).
+<p>Each time step in the simulation requires the solution of a nonlinear system Eq. <a class="reference internal" href="../simulation/index.html#equation-bdfnonlinsystem">29</a> (see Sec. <a class="reference internal" href="../simulation/index.html#simtimeintegration"><span class="std std-ref">Time stepping</span></a>).
 The nonlinear problem is solved by a Newton iteration, which, in turn, requires the solution of a linear system that essentially consists of the Jacobians of the unit operations and some coupling matrices from Eqs. <a class="reference internal" href="#equation-networkinletconnection">25</a> and <a class="reference internal" href="#equation-networkconnection">26</a>.</p>
 <p>These linear systems are either solved in parallel or sequentially. The parallel method first solves each unit operation (in parallel) to compute the solution at its outlet.
 Using these values, the inlets are adjusted and the unit operations are solved again.
diff --git a/master/modelling/reaction/index.html b/master/modelling/reaction/index.html
index e72cac733..b0118c8d7 100644
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 </ul>
 </li>
 <li class="toctree-l2"><a class="reference internal" href="../networks.html">Networks of unit operations</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../crystallization.html">Population Balance Models</a></li>
 </ul>
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 <li class="toctree-l1"><a class="reference internal" href="../../simulation/index.html">Simulation</a></li>
diff --git a/master/modelling/unit_operations/2d_general_rate_model.html b/master/modelling/unit_operations/2d_general_rate_model.html
index 694e36755..c740cbc79 100644
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@@ -59,6 +59,7 @@ <h3>Navigation</h3>
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 <li class="toctree-l2"><a class="reference internal" href="../networks.html">Networks of unit operations</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../crystallization.html">Population Balance Models</a></li>
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 <li class="toctree-l1"><a class="reference internal" href="../../simulation/index.html">Simulation</a></li>
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 <li class="toctree-l2"><a class="reference internal" href="../binding/index.html">Binding models</a></li>
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 <li class="toctree-l2"><a class="reference internal" href="../networks.html">Networks of unit operations</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../crystallization.html">Population Balance Models</a></li>
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 <li class="toctree-l1"><a class="reference internal" href="../../simulation/index.html">Simulation</a></li>
diff --git a/master/modelling/unit_operations/general_rate_model.html b/master/modelling/unit_operations/general_rate_model.html
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@@ -59,6 +59,7 @@ <h3>Navigation</h3>
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 <li class="toctree-l2"><a class="reference internal" href="../networks.html">Networks of unit operations</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../crystallization.html">Population Balance Models</a></li>
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 <li class="toctree-l1"><a class="reference internal" href="../../simulation/index.html">Simulation</a></li>
diff --git a/master/modelling/unit_operations/index.html b/master/modelling/unit_operations/index.html
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 <li class="toctree-l2"><a class="reference internal" href="../networks.html">Networks of unit operations</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../crystallization.html">Population Balance Models</a></li>
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+<tr class="row-even"><td><p><a class="reference internal" href="../crystallization.html#pbm-model"><span class="std std-ref">Population Balance Models</span></a></p></td>
+<td><p>×</p></td>
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+<td><p>×</p></td>
+<td><p>×</p></td>
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+</tr>
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 <p>Moreover, the pseudo unit operations <a class="reference internal" href="inlet.html#inlet-model"><span class="std std-ref">Inlet</span></a>, and <a class="reference internal" href="outlet.html#outlet-model"><span class="std std-ref">Outlet</span></a> act as sources and sinks for the system.
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 <li class="toctree-l2"><a class="reference internal" href="../networks.html">Networks of unit operations</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../crystallization.html">Population Balance Models</a></li>
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 <li class="toctree-l1"><a class="reference internal" href="../../simulation/index.html">Simulation</a></li>
diff --git a/master/modelling/unit_operations/lumped_rate_model_with_pores.html b/master/modelling/unit_operations/lumped_rate_model_with_pores.html
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@@ -59,6 +59,7 @@ <h3>Navigation</h3>
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 <li class="toctree-l2"><a class="reference internal" href="../networks.html">Networks of unit operations</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../crystallization.html">Population Balance Models</a></li>
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diff --git a/master/modelling/unit_operations/lumped_rate_model_without_pores.html b/master/modelling/unit_operations/lumped_rate_model_without_pores.html
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 <li class="toctree-l2"><a class="reference internal" href="../networks.html">Networks of unit operations</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../crystallization.html">Population Balance Models</a></li>
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 <li class="toctree-l1"><a class="reference internal" href="../../simulation/index.html">Simulation</a></li>
diff --git a/master/modelling/unit_operations/multi_channel_transport_model.html b/master/modelling/unit_operations/multi_channel_transport_model.html
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 <li class="toctree-l2"><a class="reference internal" href="../networks.html">Networks of unit operations</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../crystallization.html">Population Balance Models</a></li>
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diff --git a/master/modelling/unit_operations/outlet.html b/master/modelling/unit_operations/outlet.html
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\ No newline at end of file
diff --git a/master/simulation/index.html b/master/simulation/index.html
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@@ -17,7 +17,7 @@
     <link rel="index" title="Index" href="../genindex.html" />
     <link rel="search" title="Search" href="../search.html" />
     <link rel="next" title="Interface specifications" href="../interface/index.html" />
-    <link rel="prev" title="Networks of unit operations" href="../modelling/networks.html" />
+    <link rel="prev" title="Population Balance Models" href="../modelling/crystallization.html" />
    
   <link rel="stylesheet" href="../_static/custom.css" type="text/css" />
   
@@ -114,7 +114,7 @@ <h3>Branches</h3>
   <section id="simulation">
 <span id="id1"></span><h1>Simulation<a class="headerlink" href="#simulation" title="Link to this heading">¶</a></h1>
 <p>This chapter gives an overview of the simulation process and the different steps involved.</p>
-<p>CADET uses a backward-differentiation-formula (BDF) time discretization as implemented by the IDAS solver from SUNDIALS <span id="id2">[<a class="reference internal" href="../zbibliography.html#id21" title="Alan C. Hindmarsh, Peter N. Brown, Keith E. Grant, Steven L. Lee, Radu Serban, Dan E. Shumaker, and Carol S. Woodward. SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers. ACM Transactions on Mathematical Software, 31(3):363–396, September 2005. URL: http://portal.acm.org/citation.cfm?doid=1089014.1089020, doi:10.1145/1089014.1089020.">24</a>]</span>.
+<p>CADET uses a backward-differentiation-formula (BDF) time discretization as implemented by the IDAS solver from SUNDIALS <span id="id2">[<a class="reference internal" href="../zbibliography.html#id21" title="Alan C. Hindmarsh, Peter N. Brown, Keith E. Grant, Steven L. Lee, Radu Serban, Dan E. Shumaker, and Carol S. Woodward. SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers. ACM Transactions on Mathematical Software, 31(3):363–396, September 2005. URL: http://portal.acm.org/citation.cfm?doid=1089014.1089020, doi:10.1145/1089014.1089020.">25</a>]</span>.
 Each time step requires the solution of a nonlinear algebraic system of equations is performed by a Newton method.
 Since chromatographic systems can exhibit strong nonlinearity and stiff systems, the Jacobian of the equation system is always updated (i.e., an “exact” Newton method is used).</p>
 <figure class="align-default" id="id5">
@@ -205,7 +205,7 @@ <h3>Branches</h3>
 The IDAS time integrator adaptively changes the step size <span class="math notranslate nohighlight">\({\Delta t_\tau = t_\tau-t_{\tau-1}}\)</span> and order <span class="math notranslate nohighlight">\(1 \le q_{\tau} \le 5\)</span> in each time step and automatically determines the corresponding coefficients <span class="math notranslate nohighlight">\(\alpha_{\tau,i}\)</span>.
 This <em>ansatz</em> is inserted into the DAE and the resulting nonlinear algebraic equation system is solved for <span class="math notranslate nohighlight">\(y_{\tau} = y\left( t_\tau \right)\)</span> using a Newton method.</p>
 <div class="math notranslate nohighlight" id="equation-bdfnonlinsystem">
-<span class="eqno">(27)<a class="headerlink" href="#equation-bdfnonlinsystem" title="Link to this equation">¶</a></span>\[\begin{aligned}
+<span class="eqno">(29)<a class="headerlink" href="#equation-bdfnonlinsystem" title="Link to this equation">¶</a></span>\[\begin{aligned}
     H(y_\tau) = F\left(t_\tau,y_\tau,\frac{1}{\Delta t_\tau} \,\sum_{i=0}^{q_\tau}{\alpha_{\tau,i} \, y_{\tau-i}}, p\right) = 0
 \end{aligned}\]</div>
 <p>This requires (possibly many) solutions of linear equation systems involving the Jacobian of <span class="math notranslate nohighlight">\(H\)</span> given by</p>
@@ -221,11 +221,11 @@ <h3>Branches</h3>
 <section id="adaptivity">
 <span id="simtimeintegrationadaptivity"></span><h3>Adaptivity<a class="headerlink" href="#adaptivity" title="Link to this heading">¶</a></h3>
 <p>The BDF order <span class="math notranslate nohighlight">\(q_{\tau}\)</span> and size of the time step <span class="math notranslate nohighlight">\(t_\tau\)</span> are chosen such that the error bounds are satisfied with minimal work.
-Equation <a class="reference internal" href="#equation-bdfnonlinsystem">27</a> is solved with a Newton iteration using very few iterations (<code class="docutils literal notranslate"><span class="pre">MAX_NEWTON_ITER</span></code> from Table <a class="reference internal" href="../interface/solver.html#ffsolvertime"><span class="std std-ref">Group /solver/time_integrator</span></a>) since the starting point is assumed to be close to the solution as the time steps are small.
+Equation <a class="reference internal" href="#equation-bdfnonlinsystem">29</a> is solved with a Newton iteration using very few iterations (<code class="docutils literal notranslate"><span class="pre">MAX_NEWTON_ITER</span></code> from Table <a class="reference internal" href="../interface/solver.html#ffsolvertime"><span class="std std-ref">Group /solver/time_integrator</span></a>) since the starting point is assumed to be close to the solution as the time steps are small.
 If the solution of the Newton iteration does not pass the <em>convergence test</em>, the step size <span class="math notranslate nohighlight">\(t_\tau\)</span> is reduced and the Newton iteration is tried again.
 This may happen at most <code class="docutils literal notranslate"><span class="pre">MAX_CONVTEST_FAIL</span></code> times, otherwise time integration is aborted with failure.
 Having a solution of the Newton iteration at hand, a <em>local truncation error test</em> is performed which controls the error of the BDF method.
-If this test fails, step size <span class="math notranslate nohighlight">\(t_\tau\)</span> and order <span class="math notranslate nohighlight">\(q_{\tau}\)</span> are adapted and the process restarts with solving the nonlinear system Eq. <a class="reference internal" href="#equation-bdfnonlinsystem">27</a>.
+If this test fails, step size <span class="math notranslate nohighlight">\(t_\tau\)</span> and order <span class="math notranslate nohighlight">\(q_{\tau}\)</span> are adapted and the process restarts with solving the nonlinear system Eq. <a class="reference internal" href="#equation-bdfnonlinsystem">29</a>.
 The error test may be failed at most <code class="docutils literal notranslate"><span class="pre">MAX_ERRTEST_FAIL</span></code> times before time integration is aborted with failure.</p>
 <p>Error bounds for the local truncation error test are specified by an absolute tolerance (<code class="docutils literal notranslate"><span class="pre">ABSTOL</span></code>) and a relative tolerance (<code class="docutils literal notranslate"><span class="pre">RELTOL</span></code>).
 Note that the relative tolerance only works for non-zero values, whereas zero values are accounted for by the absolute tolerance.
@@ -254,15 +254,15 @@ <h3>Branches</h3>
     &amp;= \frac{\partial F}{\partial y}(t, y, \dot{y}, p) s + \frac{\partial F}{\partial \dot{y}}(t, y, \dot{y}, p) \dot{s} + \frac{\partial F}{\partial p}(t, y, \dot{y}, p).
 \end{aligned}\end{split}\]</div>
 <p>These linear DAEs depend on the solution <span class="math notranslate nohighlight">\(y\)</span>, <span class="math notranslate nohighlight">\(\dot{y}\)</span> of the original DAE system.
-Consequently, the sensitivity systems are solved together with the original DAE system in a staggered approach <span id="id3">[<a class="reference internal" href="../zbibliography.html#id30" title="William F. Feehery, John E. Tolsma, and Paul I. Barton. Efficient sensitivity analysis of large-scale differential-algebraic systems. Applied Numerical Mathematics, 25(1):41–54, October 1997. URL: http://dl.acm.org/citation.cfm?id=264193.264573, doi:10.1016/S0168-9274(97)00050-0.">25</a>]</span>.</p>
-<p>After the nonlinear Eq. <a class="reference internal" href="#equation-bdfnonlinsystem">27</a> has been successfully solved using Newton iteration (i.e., it has passed the convergence test), each sensitivity is solved using the same Newton iteration.
+Consequently, the sensitivity systems are solved together with the original DAE system in a staggered approach <span id="id3">[<a class="reference internal" href="../zbibliography.html#id30" title="William F. Feehery, John E. Tolsma, and Paul I. Barton. Efficient sensitivity analysis of large-scale differential-algebraic systems. Applied Numerical Mathematics, 25(1):41–54, October 1997. URL: http://dl.acm.org/citation.cfm?id=264193.264573, doi:10.1016/S0168-9274(97)00050-0.">26</a>]</span>.</p>
+<p>After the nonlinear Eq. <a class="reference internal" href="#equation-bdfnonlinsystem">29</a> has been successfully solved using Newton iteration (i.e., it has passed the convergence test), each sensitivity is solved using the same Newton iteration.
 If direct linear solvers were used, this iteration would convergence with a single iteration as there is no nonlinearity.
 The Newton method for the sensitivities performs at most <code class="docutils literal notranslate"><span class="pre">MAX_NEWTON_ITER_SENS</span></code> (see Table <a class="reference internal" href="../interface/solver.html#ffsolvertime"><span class="std std-ref">Group /solver/time_integrator</span></a>) iterations.
 Assuming the convergence test has passed for each sensitivity, the local truncation error test is performed for the full set of variables (i.e., original system and sensitivities).
 The sensitivities can be excluded from the local truncation error test by setting <code class="docutils literal notranslate"><span class="pre">ERRORTEST_SENS</span></code> appropriately.
 Note that time integration step size is always affected by sensitivities due to possible convergence test failures.</p>
 <p>While the Jacobians <span class="math notranslate nohighlight">\(\partial F / \partial y\)</span> and <span class="math notranslate nohighlight">\(\partial F / \partial \dot{y}\)</span> can be computed either analytically or via AD, the last term <span class="math notranslate nohighlight">\(\partial F / \partial p\)</span> is always computed by AD.
-In fact, the terms <span class="math notranslate nohighlight">\(\partial F / \partial y\)</span> and <span class="math notranslate nohighlight">\(\partial F / \partial p\)</span> can be computed by one AD-enabled evaluation of <span class="math notranslate nohighlight">\(F\)</span> using the vector mode with appropriate seed vectors <span id="id4">[<a class="reference internal" href="../zbibliography.html#id10" title="Andreas Püttmann, Sebastian Schnittert, Samuel Leweke, and Eric von Lieres. Utilizing algorithmic differentiation to efficiently compute chromatograms and parameter sensitivities. Chemical Engineering Science, 139:152–162, January 2016. URL: http://linkinghub.elsevier.com/retrieve/pii/S0009250915006168, doi:10.1016/j.ces.2015.08.050.">26</a>]</span>.</p>
+In fact, the terms <span class="math notranslate nohighlight">\(\partial F / \partial y\)</span> and <span class="math notranslate nohighlight">\(\partial F / \partial p\)</span> can be computed by one AD-enabled evaluation of <span class="math notranslate nohighlight">\(F\)</span> using the vector mode with appropriate seed vectors <span id="id4">[<a class="reference internal" href="../zbibliography.html#id10" title="Andreas Püttmann, Sebastian Schnittert, Samuel Leweke, and Eric von Lieres. Utilizing algorithmic differentiation to efficiently compute chromatograms and parameter sensitivities. Chemical Engineering Science, 139:152–162, January 2016. URL: http://linkinghub.elsevier.com/retrieve/pii/S0009250915006168, doi:10.1016/j.ces.2015.08.050.">27</a>]</span>.</p>
 <p>A parameter sensitivity is specified by identifying the involved parameters, which can be more than one (see below).
 Parameters are identified by name and multiple indices, which may not all be used (see Tab. <a class="reference internal" href="../interface/sensitivities.html#ffsensitivityparam"><span class="std std-ref">Group /input/sensitivity/param_XXX</span></a>). Indices that are not used for identification (e.g., flow rate is independent of bound phase or component) are set to <span class="math notranslate nohighlight">\(-1\)</span>. All other indices are zero-based.</p>
 <p>Note that the sensitivity systems need to be consistently initialized, too.
diff --git a/master/sitemap.xml b/master/sitemap.xml
index 631edb5a6..350e81d6c 100644
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