Asymptotic analysis of thin viscous plate model
https://doi.org/10.17586/2220-8054-2018-9-4-447-456
Abstract
A cell membrane is a very complex medium, which is difficult to study. One of the simplest approaches is to assume it purely elastic or purely viscous. In this paper, we follow the second assumption and derive mathematical model of nearly-planar viscous plate evolving under action of applied forces. The obtained model is non-linear and covers both stretching and bending of the membrane. In contrast to analogous works on viscous sheets, we use a unique scale for velocity components and take a few first terms in asymptotic expansion. The developed approach can be used for description of the cell membrane with nanoparticles inserted.
Supporting agencies: This work was partially financially supported by the Government of the Russian Federation (grant 08-08), by grant 16-11-10330 of Russian Science Foundation.
About the Authors
I. F. Melikhov
ITMO University
Russian Federation
Russian Federation
Kronverkskiy, 49, St. Petersburg, 197101
I. Y. Popov
ITMO University
Russian Federation
Russian Federation
Kronverkskiy, 49, St. Petersburg, 197101
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Review
For citations:
Melikhov I.F., Popov I.Y. Asymptotic analysis of thin viscous plate model. Nanosystems: Physics, Chemistry, Mathematics. 2018;9(4):447-456. https://doi.org/10.17586/2220-8054-2018-9-4-447-456
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