Monte Carlo simulation of coagulation in discrete particle-size distributions. Part 2. Interparticle forces and the quasi-stationary equilibrium hypothesis

Abstract

Hunt (1982) and Friedlander (1960a, b) used dimensional analysis to derive expressions for the steady-state particle-size distribution in aerosols and hydrosols. Their results were supported by the Monte Carlo simulation of a non -interacting coagulating population of suspended spherical particles developed by Pearson, V alioulis & List (1984). Here the realism of the Monte Carlo simulation is improved by accounting for the modification to the coagulation rate caused by van der Waals', electrostatic and hydrodynamic forces acting between particles. The results indicate that the major hypothesis underlying the dimensional reasoning, that is, collisions between particles of similar size are most important in determining the shape of the particle size distribution, is valid only for shear-induced coagulation. It is shown that dimensional analysis cannot, in general, be used to predict equilibrium particle-size distributions, mainly because of the strong dependence of the interparticle force on the absolute and relative size of the interacting particles.

Sediment transport: Physical modelling of flocculation

“…Pearson et al (1984) simulated the evolution of a population using Monte Carlo methods and found good agreement with the quasi-stationary approximation using the simple forms for / 3 given above. When Valioulis, List and Pearson (1984) used more elaborate forms taken from Adler (1981), shear induced aggregation still obeyed the assumptions, although the other sub-ranges, such as Brownian motion, did not. Fortunately, shear induced aggregation is the principal mechanism in estuaries.…”

Coalescence of particles by differential sedimentation

“…A B where q > 1 is the number representing the maximal volume ratio for the particle merging. Compared to a more involved form of collision efficiency used by Valioulis et al [14], the simplified kernel we use mimics the behavior for particles with r = 0.01cm which is similar to the regime we study numerically. We will refer to the model with finite q as "forced locality".…”

“…This is relevant if it is Figure 3: Distribution of particle volumes averaged over several times after 140,000 time steps for the forced locality situation with q = 2. The dashed slope represents the −13/6 KZ spectrum (compare with [14]).…”

Floc Breakage Analysis— A Simulation Approach

“…Monte Carlo simulation has also been adopted to model both aggregation and deaggregation phenomena. Various simulation algorithms have been proposed (see, e.g., Collins and Knudsen, 1970;Shah et al, 1977;Hsia and Tavlarides, 1980;Hsia and Tavlarides, 1983;Valioulis et al, 1984). Often, the functional form of the breakage frequency and daughter particle size distribution are predetermined in both population balance and simulation approaches and the resulting model is fitted to experimental data.…”