(358f) Fcmom: Moments and Moving Boundaries for an Accurate and Convergent Psd Reconstruction

A new approach, FCMOM (Finite size domain Complete set of trial functions Method Of Moments), is used to solve population balance equations (PBE) and to reconstruct the particle size distribution (PSD). The solution of the PBE is sought in the finite domain of the internal variable, between the minimum and the maximum size values, while the particle size distribution function is represented by a series expansion over a complete system of orthonormal functions. The moments evolution equations are developed integrating the PBE over the finite size domain. Some properties of the approach followed are: an explicit expression for the PSD is available; no problem specific assumption is made regarding the shape of the PSD; the completeness of the set of trial functions in the size distribution function expansion provides properties of convergence and the convergence to the solution is reasonably fast for computational purposes. The rapidity of convergence is verified by specific applications to: 1) particle growth (constant, linear, diffusion-controlled); 2) particle growth and nucleation (primary and secondary); 3) coagulation (Brownian, gravitational). The knowledge of the moments coupled with the moving boundaries positions allow for an accurate reconstruction of the PSD. The number of moments necessary to obtain accurate solutions for the PSD depends generally on the case considered and on the initial shape of the PSD, however in our computations it has been usually equal or lower than 10 moments. When the solution for the PSD was not available analytically (particle growth and nucleation coupled with the solute mass balance), the numerical solution was compared with experimental data [A.F. Blandin, D. Mangin, V. Nallet, J.P. Klein, J.M. Bossoutrot, ?Kinetics identification of salicylic acid precipitation through experiments in a batch stirred vessel and a T-mixer?, Chemical Engineering Journal 81 (2001) 91-100] and a very nice agreement was obtained between the experimental and the numerical PSD. If the target of the simulations are just the first moments of the PSD (not the PSD itself), the number of moments necessary for a precise representation of the moments decreases remarkably with respect to the value necessary for the convergence to the PSD, for example from 10 to 6 in the case of diffusion-controlled growth.