# Verification and Validation of FCMOM

To numerically validate the proposed implementation procedure, three cases have been studied. The first case is a linear growth problem when the growth rate of the particle size is proportional to the size itself. This kind of behavior is typical in particle growth processes due to volumetric chemical reactions as studied by McMurry and Wilson (1983) and Strumendo and Arastoopour (2008). The second case is a homogeneous aggregation problem when the aggregation kernel is proportional to the summation of the sizes of the two aggregating particles.

For the first two cases, there are analytical solutions provided by McGraw (1997) and Scott (1968), respectively. Therefore, comparison of the numerical results with the analytical solutions is possible, which ensures appropriate implementation of the source terms and correct numerical integration of the differential equations.

The third case is the application of FCMOM in CFD simulations of an oil-water emulsion flow in a backward-facing step geometry including the aggregation/ coalescence process as proposed by Silva et al. (2008). In this case, treatment of the convective term was studied and results were verified against the solution obtained by the QMOM method for the same case.