Analytical Solutions for Composition-Dependent Coagulation

Analytical Solutions for Composition-Dependent Coagulation

Exact solutions of the bicomponent Smoluchowski’s equation with a composition-dependent additive kernel K(va,vb;va′,vb′)=α(va+va′)+(vb+vb′) are derived by using the Laplace transform for any initial particle size distribution. The exact solution for an exponential initial distribution is then used t...

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Main Authors: Manli Yang, Zhiming Lu, Jie Shen
Format: Article
Language:English
Published: Hindawi Limited 2016-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2016/1735897
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spelling doaj-a6ffb4ced1974b339c6e1e0fd28b4f642020-11-24T21:01:27ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472016-01-01201610.1155/2016/17358971735897Analytical Solutions for Composition-Dependent CoagulationManli Yang0Zhiming Lu1Jie Shen2Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, ChinaShanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, ChinaShanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, ChinaExact solutions of the bicomponent Smoluchowski’s equation with a composition-dependent additive kernel K(va,vb;va′,vb′)=α(va+va′)+(vb+vb′) are derived by using the Laplace transform for any initial particle size distribution. The exact solution for an exponential initial distribution is then used to analyse the effects of parameter α on mixing degree of such bicomponent mixtures and the conditional distribution of the first component for particles with given mass. The main finding is that the conditional distribution of large particles at larger time is a Gaussian function which is independent of the parameter α.http://dx.doi.org/10.1155/2016/1735897
collection DOAJ
language English
format Article
sources DOAJ
author Manli Yang
Zhiming Lu
Jie Shen
spellingShingle Manli Yang
Zhiming Lu
Jie Shen
Analytical Solutions for Composition-Dependent Coagulation
Mathematical Problems in Engineering
author_facet Manli Yang
Zhiming Lu
Jie Shen
author_sort Manli Yang
title Analytical Solutions for Composition-Dependent Coagulation
title_short Analytical Solutions for Composition-Dependent Coagulation
title_full Analytical Solutions for Composition-Dependent Coagulation
title_fullStr Analytical Solutions for Composition-Dependent Coagulation
title_full_unstemmed Analytical Solutions for Composition-Dependent Coagulation
title_sort analytical solutions for composition-dependent coagulation
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2016-01-01
description Exact solutions of the bicomponent Smoluchowski’s equation with a composition-dependent additive kernel K(va,vb;va′,vb′)=α(va+va′)+(vb+vb′) are derived by using the Laplace transform for any initial particle size distribution. The exact solution for an exponential initial distribution is then used to analyse the effects of parameter α on mixing degree of such bicomponent mixtures and the conditional distribution of the first component for particles with given mass. The main finding is that the conditional distribution of large particles at larger time is a Gaussian function which is independent of the parameter α.
url http://dx.doi.org/10.1155/2016/1735897
work_keys_str_mv AT manliyang analyticalsolutionsforcompositiondependentcoagulation
AT zhiminglu analyticalsolutionsforcompositiondependentcoagulation
AT jieshen analyticalsolutionsforcompositiondependentcoagulation
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