Add aggregation and breakage to crystallization module

CITATION.bib

@@ -44,6 +44,17 @@ @article{Breuer2023
 
 % Crystallization:
 
+@article{Zhang2025,
+title = {Solving crystallization/precipitation population balance models in CADET, Part II: Size-based Smoluchowski coagulation and fragmentation equations in batch and continuous modes},
+year = {2025},
+author = {Wendi Zhang and Todd Przybycien and Jan Michael Breuer and Eric {von Lieres}},
+doi = {https://doi.org/10.1016/j.compchemeng.2024.108860},
+journal = {Computers & Chemical Engineering},
+volume = {192},
+pages = {108860},
+issn = {0098-1354}
+}
+
 @article{Zhang2024,
 title = {Solving crystallization/precipitation population balance models in CADET, part I: Nucleation growth and growth rate dispersion in batch and continuous modes on nonuniform grids},
 year = {2024},

README.rst

@@ -50,6 +50,8 @@ Therefore, we kindly ask that any publications or projects leveraging the capabi
 
 - Breuer, J. M.; Leweke, S.; Schmölder, J.; Gassner, G.; von Lieres, E.: `Spatial discontinuous Galerkin spectral element method for a family of chromatography models in CADET <https://doi.org/10.1016/j.compchemeng.2023.108340>`_, Computers and Chemical Engineering **177** (2023), 108340.
 
+- Zhang, W.; Przybycien T., Breuer J. M. , Leweke S. , von Lieres E.: `Solving crystallization/precipitation population balance models in CADET, part II: Size-based Smoluchowski coagulation and fragmentation equations in batch and continuous modes <https://doi.org/10.1016/j.compchemeng.2024.108860>`_, Computers and Chemical Engineering **192** (2025), 108860.
+
 - Zhang, W.; Przybycien T., Schmölder J. , Leweke S. , von Lieres E.: `Solving crystallization/precipitation population balance models in CADET, part I: Nucleation growth and growth rate dispersion in batch and continuous modes on nonuniform grids <https://doi.org/10.1016/j.compchemeng.2024.108612>`_, Computers and Chemical Engineering **183** (2024), 108612.
 
 - Püttmann, A.; Schnittert, S.; Naumann, U.; von Lieres, E.: `Fast and accurate parameter sensitivities for the general rate model of column liquid chromatography <http://dx.doi.org/10.1016/j.compchemeng.2013.04.021>`_, Computers and Chemical Engineering **56** (2013), 46–57.

doc/index.rst

@@ -98,6 +98,8 @@ Therefore, we kindly ask that any publications or projects leveraging the capabi
 
 - Breuer, J. M.; Leweke, S.; Schmölder, J.; Gassner, G.; von Lieres, E.: `Spatial discontinuous Galerkin spectral element method for a family of chromatography models in CADET <https://doi.org/10.1016/j.compchemeng.2023.108340>`_, Computers and Chemical Engineering **177** (2023), 108340.
 
+- Zhang, W.; Przybycien T., Breuer J. M. , Leweke S. , von Lieres E.: `Solving crystallization/precipitation population balance models in CADET, part II: Size-based Smoluchowski coagulation and fragmentation equations in batch and continuous modes <https://doi.org/10.1016/j.compchemeng.2024.108860>`_, Computers and Chemical Engineering **192** (2025), 108860.
+
 - Zhang, W.; Przybycien T., Schmölder J. , Leweke S. , von Lieres E.: `Solving crystallization/precipitation population balance models in CADET, part I: Nucleation growth and growth rate dispersion in batch and continuous modes on nonuniform grids <https://doi.org/10.1016/j.compchemeng.2024.108612>`_, Computers and Chemical Engineering 183 (2024), 108612.
 
 - Püttmann, A.; Schnittert, S.; Naumann, U.; von Lieres, E.: `Fast and accurate parameter sensitivities for the general rate model of column liquid chromatography <http://dx.doi.org/10.1016/j.compchemeng.2013.04.021>`_, Computers and Chemical Engineering **56** (2013), 46–57.

doc/interface/population_balance_model.rst

@@ -1,26 +1,29 @@
 .. _pbm_config:
 
-Population balance model
-========================
+Crystallization / Precipitation models
+======================================
 
-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`.
+Crystallization / Precipitation in CADET is modeled by :ref:`pbm_model`, :ref:`aggregation_model`, :ref:`fragmentation_model`, as well as their combinations.
+The configurations of these models have many overlaps, which is why the interface is described here in a unified manner.
+For more information on the model equations, please refer to :ref:`FFCrystallization`.
 
-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.*
+Note that any of these models can be used in any unit operation that supports reactions.
 
+*Note that, by setting the ``NCOMP`` field, you specify the number of FV cells for the internal coordinate:*
+If the PBM is considered, we have two components that account for the solute :math:`c` and solubility :math:`c_\text{eq}`. 
 Note that the first component must be solute :math:`c` and the last component must be the solubility :math:`c_\text{eq}`.
+Additionally, we discretize the particle size domain (internal coordinate) by some customary FV methods, 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` or :math:`N_x + 2` if the model includes the PBM.
 
-Example code to configure the PBM can be found in `CADET-Verification <https://github.com/cadet/CADET-Verification/blob/main/src/test_cadet_core/crystallization.py>`_ .
+
+Example code to configure the PBM can be found in `CADET-Verification <https://github.com/cadet/CADET-Verification/>`_ .
 
 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
+   Number of components, which is defined by the number of considered particle sizes (i.e. discretization with FV cells) plus, in the case that the PBM is employed, 2 (for solute and solubility).
 
    =============  =========================  =============
    **Type:** int  **Range:** :math:`\geq 3`  **Length:** 1
@@ -38,6 +41,22 @@ Group /input/model/unit_XXX/reaction_bulk - REACTION_MODEL = CRYSTALLIZATION - U
 -----------------------------------------------------------------------------------------------
 
 *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_MODE``
+
+   Crystallization mode, which determines the exact model equation to be employed.
+
+  1. Pure PBM, as described in :ref:`pbm_model`.
+  2. Pure aggregation, as described in
+  3. Combined PBM and aggregation.
+  4. Pure fragmentation, as described in
+  5. Combined PBM and fragmentation.
+  6. Combined aggregation and fragmentation.
+  7. Combined PBM, aggregation, and fragmentation.
+
+   ================  =========================  =====================================
+   **Type:** double  **Range:** :math:`\geq 1`   **Length:** :math:`\mathrm{N_x} + 1`
+   ================  =========================  =====================================
 
 ``CRY_BINS``
 
@@ -47,6 +66,9 @@ Group /input/model/unit_XXX/reaction_bulk - REACTION_MODEL = CRYSTALLIZATION - U
    **Type:** double  **Range:** :math:`\geq 1`   **Length:** :math:`\mathrm{N_x} + 1`
    ================  =========================  =====================================
 
+Population Mass Balance input parameters
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
 ``CRY_NUCLEI_MASS_DENSITY``
 
    Nulcei mass density
@@ -159,3 +181,31 @@ Group /input/model/unit_XXX/reaction_bulk - REACTION_MODEL = CRYSTALLIZATION - U
    =============  ================================  =============
    **Type:** int  **Range:** :math:`[1, \dots, 4]`  **Length:** 1
    =============  ================================  =============
+
+   Aggregation input parameters
+   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+``CRY_AGGREGATION_RATE_CONSTANT``
+
+   Aggregation rate constant :math:`todo`
+
+   ================  =========================  =============
+   **Type:** double  **Range:** :math:`\geq 0`  **Length:** 1
+   ================  =========================  =============
+
+   todo: cry_aggregation_index
+
+   Fragmentation input parameters
+   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+``CRY_FRAGMENTATION_RATE_CONSTANT``
+
+   Fragmentation rate constant :math:`todo`
+
+   ================  =========================  =============
+   **Type:** double  **Range:** :math:`\geq 0`  **Length:** 1
+   ================  =========================  =============
+
+   todo: cry_fragmentation_kernel_gamma
+
+   todo: cry_fragmentation_selection_function_alpha

doc/modelling/crystallization/aggregation.rst

@@ -0,0 +1,10 @@
+.. _aggregation_model:
+
+Aggregation Models
+~~~~~~~~~~~~~~~~~~
+
+TODO:
+^^^^^
+- [ ] add equations
+- [ ] combination with the PBM and fragmentation modules
+- [ ] incorporation into CSTR, DPFR and, theoretically, any transport model

doc/modelling/crystallization/fragmentation.rst

@@ -0,0 +1,10 @@
+.. _fragmentation_model:
+
+Fragmentation Models
+~~~~~~~~~~~~~~~~~~~~
+
+TODO:
+^^^^^
+- [ ] add equations
+- [ ] combination with the PBM and aggregation modules
+- [ ] incorporation into CSTR, DPFR and, theoretically, any transport model

doc/modelling/crystallization/index.rst

@@ -0,0 +1,14 @@
+.. _FFCrystallization:
+
+Crystallization / Precipitation Models
+======================================
+
+CADET features various crystallization / precipitation mechanisms:
+
+ - :ref:`pbm_model`
+ - :ref:`aggregation_model`
+ - :ref:`fragmentation_model`
+
+ Additionally, any combination of these models is featured.
+ Any of these crystallization \ precipitation models can be combined with any of the transport models listed among the :ref:`unit_operation_models`.
+ To this end, most common use-cases consider a :ref:`cstr_model` or a dispersive plug-flow reactor (which can be modeled with the :ref:`lumped_rate_model_without_pores_model`).

doc/modelling/index.rst

@@ -10,4 +10,4 @@ This section gives complete information about the supported unit operations, bin
     binding/index
     reaction/index
     networks
-    crystallization
+    crystallization/index