Finite domain Complete Trial Functions Method of Moments (FCMOM) for Particulate Flow

To account for continuous variations of the particle size and density distributions due to phenomena such as reaction, agglomeration, nucleation and growth using a low computational time, a new approach to solve PBE (Population Balance Equations), the FCMOM (Finite size domain Complete set of trial functions Method of Moments), was developed. The solution of the PBE is sought, instead of the [0,��] range, in the finite interval between the minimum and maximum particle size; their evolution is tracked imposing moving boundaries conditions. After reformulating the PBE in the standard interval [-1,1], the size distribution function is presented as a series expansion by a complete system of orthonormal functions. Moments evolution equations are developed from the PBE in the interval [-1,1]. The FCMOM is implemented through an efficient algorithm and provides the solution of the PBE both in terms of the moments and in terms of the particle size distribution function. The FCMOM was validated with applications to particle growth, dissolution, nucleation, particle aggregation, and linked to the fluid phase governing equations (CFD) to solve problems in gas/particle systems.