The Size-Based Population Balance interface (), found in the Precipitation and Crystallization group () of the Chemical Species Transport branch (), is used to model a size distribution of particles, droplets or bubbles.

The interface supports simulation of the space and time-dependent size distribution and mass transport by convection and diffusion. The interface can be used in 0D, 1D, 2D, and 3D as well as for axisymmetric components in 1D and 2D. The dependent variables are the population number density of each size interval, accounting for interval length, n (1/m4). The minimum number of dependent variables is five.

The Label is the default physics interface name.

The Name is used primarily as a scope prefix for variables defined by the physics interface. Refer to such physics interface variables in expressions using the pattern <name>.<variable_name>. In order to distinguish between variables belonging to different physics interfaces, the name string must be unique. Only letters, numbers and underscores (_) are permitted in the Name field. The first character must be a letter.

The default Name (for the first physics interface in the model) is pbsb.

For 1D components, the text field (default value: 1 m2) defines a parameter for the cross-sectional area perpendicular to the 1D component. Both constant and varying areas are supported.

To display this section, click the Show button () and select Stabilization.

Two consistent stabilization methods are available — Streamline Diffusion and Crosswind Diffusion. Both are active by default. When the Streamline Diffusion checkbox is selected a weak artificial diffusion in the streamline direction is added to the transport equation. When the Crosswind Diffusion checkbox is selected, a weak diffusive term orthogonal to the streamline direction that reduces spurious oscillations is added. The consistent stabilization methods do not perturb the original transport equation.

To display this section, click the Show button () and select Stabilization. One inconsistent stabilization method is available, isotropic diffusion. Isotropic diffusion can affect the accuracy of the original problem and the Isotropic Diffusion checkbox is not selected by default. For under resolved problems, this option can be used to get a good initial guess.

To display this section, click the Show button () and select Advanced Physics Options. Select Nonconservative or Conservative from the Material balance form list. Nonconservative is selected by default and does usually not need to be changed.

The Particle Properties section is used to specify properties of the particles in the population. Enter a value or expression for the density and molar mass in the Particle density and Particle molar mass fields.

Select the particle shape from the Particle shape list. Select Spherical for spherical particles or Cubic for cubic particles. For User defined, specify an Area shape factor and a Volume shape factor in the corresponding fields.

Select the size discretization approach from the Discretization list. Select Linear to use a linear discretization approach. For a non-linear discretization you can select Logarithmic or Geometric. For all options, enter the number of size intervals to model in the Number of intervals field and the smallest and largest size to model in the Minimum size and Maximum size fields. For the Geometric option, also enter a finite constant in the Geometric constant field that controls the size interval width.

Select an option from the Nucleation rate list to add a particle source to the smallest size interval. Three different options are available — User defined, Arrhenius expression, and Homogeneous nucleation.

Select an option from the list to apply a growth and dissolution rate to all intervals. The options that are available are — User defined and Transport controlled.

Select User defined to enter a value or expression. When this option is selected, the text field also accepts an expression written as a function of the particle size, pop.L. When solving, pop.L will be replaced by the discretized particle sizes. Separate text fields are available for growth and dissolution. A positive growth rate results in particles becoming larger while a positive dissolution rate results in particles becoming smaller.

Select Transport controlled to define a growth and dissolution rate that is limited by the transport of a dissolved species.

Select the Include checkbox to include aggregation. When selected, enter an aggregation kernel in the Aggregation kernel field. The field supports expressions that are functions of the two colliding particle sizes, pop.Lj and pop.Lk.

Select the Include checkbox to include breakage. When selected, enter a breakage rate constant and an average number of particles resulting from breakage in the Breakage rate constant and Average number of resulting particles fields, respectively.

This section is only visible when additional information is requested by the Growth or Nucleation section. This is when Homogeneous nucleation is selected in the Nucleation section or Transport controlled is selected in the Growth section. Enter a value or expression in the Concentration, Equilibrium concentration, and Diffusion coefficient fields.

To display all settings available in this section, click the Show button () and select Advanced Physics Options.

The Compute boundary fluxes checkbox is activated by default so that COMSOL Multiphysics computes the predefined accurate boundary flux variables storing accurate boundary fluxes from each boundary into the adjacent domain.

The Apply smoothing to boundary fluxes checkbox is available if the previous checkbox is selected. The smoothing can provide a more well-behaved flux value close to singularities.

For details about the boundary fluxes settings, see Computing Accurate Fluxes in the COMSOL Multiphysics Reference Manual.

The Value type when using splitting of complex variables setting should in most pure mass transfer problems be set to Real, which is the default. It makes sure that the dependent variable does not get affected by small imaginary contributions, which can occur, for example when combining a Time Dependent or Stationary study with a frequency-domain study. For more information, see Splitting Complex-Valued Variables in the COMSOL Multiphysics Reference Manual.