GEOMETRIC EVOLUTION OF BILAYERS UNDER THE DEGENERATE FUNCTIONALIZED CAHN-HILLIARD EQUATION

被引：0

作者：

Dai, Shibin ^{[1
]}

Luong, Toai ^{[1
]}

Ma, X., I ^{[1
,2
]}

机构：

[1] Univ Alabama, Dept Math, Tuscaloosa, AL 35487 USA

[2] Grand View Univ, Dept Chem, Des Moines, IA 50316 USA

来源：

MULTISCALE MODELING & SIMULATION | 2022年 / 20卷 / 03期

基金：

美国国家科学基金会;

关键词：

bilayers; functionalized Cahn-Hilliard energy; degenerate mobility; asymptotic analysis; geometric evolution; INTERFACES; CHEMISTRY; SYSTEMS;

D O I：

10.1137/21M1467791

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Using a multiscale analysis, we derive a sharp interface limit for the dynamics of bilayer structures of the functionalized Cahn-Hilliard equation with a cutoff diffusion mobility M(u) that is degenerate for u <= 0 and a continuously differentiable double-well potential W(u). We show that the bilayer interface does not move in the t = O(1) time scale. The interface motion occurs in the t = O(epsilon-1) time scale and is determined by porous medium diffusion processes in both phases with no jumps on the interface. In the longer O(epsilon-2) time scale, the interface motion is a complex combination of porous medium diffusion processes in both phases and the property of mass conservation.

引用

页码：1127 / 1146

页数：20

共 30 条

[1] Liposomal drug delivery systems: From concept to clinical applications [J].