Analysis of Smoluchowski’s Coagulation Equation with Injection

The stationary solution of Smoluchowski’s coagulation equation with injection is found analytically with different exponentially decaying source terms. The latter involve a factor in the form of a power law function that plays a decisive role in forming the steady-state particle distribution shape....

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Bibliographic Details
Published inCrystals (Basel) Vol. 12; no. 8; p. 1159
Main Authors Makoveeva, Eugenya V., Alexandrov, Dmitri V., Fedotov, Sergei P.
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.08.2022
Subjects
analytical solutions
Coagulation
Crystals
Exact solutions
Laplace transforms
Lipoproteins
Nanoparticles
particle coagulation
Smoluchowski’s equation with injection
Steady state
Stitching
United Kingdom
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Summary:The stationary solution of Smoluchowski’s coagulation equation with injection is found analytically with different exponentially decaying source terms. The latter involve a factor in the form of a power law function that plays a decisive role in forming the steady-state particle distribution shape. An unsteady analytical solution to the coagulation equation is obtained for the exponentially decaying initial distribution without injection. An approximate unsteady solution is constructed by stitching the initial and final (steady-state) distributions. The obtained solutions are in good agreement with experimental data for the distributions of endocytosed low-density lipoproteins.
ISSN:2073-4352
2073-4352
DOI:10.3390/cryst12081159