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ARTICLE

# Surface Phase Separation and Flow in a Simple Model of Multicomponent Drops and Vesicles

J.S. Lowengrub1, J-J. Xu2, A. Voigt3

Department of Mathematics, University of California, Irvine. lowengrb@math.uci.edu. Corresponding author.
Department of Mathematics, University of California, Irvine. jxu@math.uci.edu
Institut fur Wissenschaftliches rechnen, Technische Universität Dresden, Zellescher Weg 12-14, 01062 Dresden,Germany. voigt@caesar.de.

Fluid Dynamics & Materials Processing 2007, 3(1), 1-20. https://doi.org/10.3970/fdmp.2007.003.001

## Abstract

We introduce and investigate numerically a thermodynamically consistent simple model of a drop or vesicle in which the interfacial surface contains multiple constitutive components (e.g. amphiphilic molecules). The model describes the nonlinear coupling among the flow, drop/vesicle morphology and the evolution of the surface phases. We consider a highly simplified version of the Helfrich model for fluid-like vesicle membranes in which we neglect the effects of bending forces and spontaneous curvature but keep the effects of inhomogeneous surface tension forces. Thus, this model may also describe liquid drops. To solve the highly nonlinear, coupled system a new numerical method is developed. This method combines the immersed interface method to solve the flow equations, and the Laplace-Young jump conditions, with the level-set method to represent and evolve the interface and a non-stiff Eulerian algorithm to update the mass concentration on the drop interface. Results are presented for drops/vesicles in an applied shear flow where an initially unstable mixture of the surface mass separates into distinct phases.

Lowengrub, J., Xu, J., Voigt, A. (2007). Surface Phase Separation and Flow in a Simple Model of Multicomponent Drops and Vesicles. FDMP-Fluid Dynamics & Materials Processing, 3(1), 1–20.