TY - JOUR
T1 - A Front-Tracking Method for Motion by Mean Curvature with Surfactant
AU - Lai , Ming-Chih
AU - Hsu , Che-Wei
AU - Huang , Huaxiong
JO - Advances in Applied Mathematics and Mechanics
VL - 2
SP - 288
EP - 300
PY - 2009
DA - 2009/01
SN - 1
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/aamm/8370.html
KW - Front-tracking method, motion by mean curvature, triple-junction, surface tension, surfactant.
AB - <p style="text-align: justify;">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.</p>