(498e) Effects of More Realistic Single-Particle Rate Laws in the Eulerian Population-Balance Equation;Two Further Examples ('Growth' and Sintering)

Considerable insight has been obtained by introducing deliberately (over-) simplified rate laws (for suspended particle nucleation, coagulation, growth/dissolution, sintering, breakage,?) into the generally nonlinear integro-partial differential equation called the ?population balance' equation (PBE). This approach has been justified by the complexity of this equation, and the need to satisfy it along with many other local PDE-balance principles in multi-dimensional transient flow environments[1]. However, current requirements for process design, and the practical need to infer meaningful physico-chemical parameters based on accessible measurements on large continuous populations rather than individual ?particles', make the introduction of more accurate rate laws an essential ingredient for the next generation of such process models[2]. Following up on our earlier analyses of the effects of more accurate collision frequency rate laws for fractal-like aggregates [3], we further demonstrate this claim here by examining two further instructive linear, univariate examples, both in the context of a well-mixed steady-flow vessel: E1 Non quasi-steady diffusion-controlled particle dissolution E2 Non-relaxation type sintering (area-reduction) by surface-diffusion In both cases our focus is on the systematic effects of introducing more realistic single-particle rate laws on the exiting particle population distribution functions---with respect to particle volume (Case E1) or particle surface area (Case E2). This is revealed by systematic shifts in the relevant moments of these distribution functions, displayed here for some cases of physical interest over a range of appropriate Damkohler numbers based on mean residence time. The present results provide further support for our contention that the systematic introduction of more accurate rate laws (including nucleation, sintering, growth, ?.) will be essential to meet the quantitative demands of the next-generation of simulation models for particulate processing/synthesis equipment, and QMOM-methods are capable of incorporating these more realistic rate laws into a PBE/CFD approach to particulate process simulation. ______________________________________________________

[1] Rosner, D.E., McGraw, R. and Tandon, P., Ind.& Eng. Chem Res.(ACS) 42 2699-2711(2003); see, also ibid. 44 ; to appear: August 2005)

[2] Rosner, D.E., to appear in IJCRE: Proc. Tenth Intl. Conference on Chemical Reaction Engineering (CRE-X);Fall 2005.

[3] Zurita-Gotor, M. and Rosner, D.E., J. Colloid Int. Sci. 274, 502-514( 2004), see, also: ibid. 255, 10-26 (2002)

Prepared 5/25/05 for presentation at AIChE '05, Cincinnati OH, November 2005