Year: 2009
Author: Ming-Chih Lai, Che-Wei Hsu, Huaxiong Huang
Advances in Applied Mathematics and Mechanics, Vol. 1 (2009), Iss. 2 : pp. 288–300
Abstract
In this paper, we present a finite difference method to track a network of curves whose motion is determined by mean curvature. To study the effect of inhomogeneous surface tension on the evolution of the network of curves, we include surfactant which can diffuse along the curves. The governing equations consist of one parabolic equation for the curve motion coupled with a convection-diffusion equation for the surfactant concentration along each curve. Our numerical method is based on a direct discretization of the governing equations which conserves the total surfactant mass in the curve network. Numerical experiments are carried out to examine the effects of inhomogeneous surface tension on the motion of the network, including the von Neumann law for cell growth in two space dimensions.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2009-AAMM-8370
Advances in Applied Mathematics and Mechanics, Vol. 1 (2009), Iss. 2 : pp. 288–300
Published online: 2009-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Front-tracking method motion by mean curvature triple-junction surface tension surfactant.