Beyond Log-Normal Distributions: Hermite Spectra for Solving Population Balances

The oft-used log-normal distribution for sol®ing many population-balance problems is in fact a degenerate case of a Hermite function expansion of the solution in log particle-size coordinate. Correcti®e capabilities of such an expansion constitute ®ast impro®ements not only o®er those using the log-normal distribution, but also o®er discretization methods in that moments other than those designed for in the latter are predicted with much higher accuracy, although at greater computational cost. The Hermite spectral method is compared with known analytical results and other computational techniques for particle dynamic processes in®ol®ing agglomeration, breakage, and growth. This method is extremely accurate and flexible, as e®idenced by the wide range of problems it can sol®e, both transient and steady state, along with perfectly mixed or con®ection dominant problems. Particle distributions are allowed to e®ol®e according to the physics of the process, not constrained by restricti®e assumptions inherent in the prespecified form of the distribution.