Coagulation equations with mass loss

Abstract

We derive and solve models for coagulation with mass loss arising, for example, from industrial processes in which growing inclusions are lost from the melt by colliding with the wall of the vessel. We consider a variety of loss laws and a variety of coagulation kernels, deriving exact results where possible, and more generally reducing the equations to similarity solutions valid in the large-time limit. One notable result is the effect that mass removal has on gelation: for small loss rates, gelation is delayed, whilst above a critical threshold, gelation is completely prevented. Finally, by forming an exact explicit solution for a more general initial cluster size distribution function, we illustrate how numerical results from earlier work can be interpreted in the light of the theory presented herein.

How initial condition impacts aggregation -- a systematic numerical study

“…Originally, it was studied by Smoluchowski [1]. Later, several authors investigated aggregation for formation of polymers [2], aerosols [3], or food and material processing [4,5]. In the last two decades, aggregation has * e-mail: lepek@if.pw.edu.pl been applied to a broad range of interdisciplinary topics, including percolation phenomena in random graphs and complex networks [7][8][9][10][11][12], pattern formation [14][15][16][17], and population genetics [13].…”

Combinatorial solutions to generalized electrorheological kernel aggregation

“…They govern many everyday-life phenomena (such as blood coagulation, milk curdling, and cloud formation) and are of great interest in physics [1][2][3], chemistry [4][5][6], biology [7], and mathematics [8][9][10]. Several technological applications are based on coagulation, including the formation of aerosols [11,12] and polymers [13] and material processing [14,15].…”

Coalescense with arbitrary-parameter kernels and monodisperse initial conditions: A study within combinatorial framework

“…A broad range of interdisciplinary applications can be found, including percolation phenomena in random graphs and complex networks [11][12][13][14][15][16], population genetics [17], pattern formation in social [18,19], biological [20], and man-made systems [21]. Several technological applications are based on coagulation, including formation of polymers [22], food processing [23], material processing [24,25], and water treatment [26,27]. The aggregation formalism has recently started to play a significant role in modeling physiological processes [28,29].…”