Interfaces and Free Boundaries

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Volume 14, Issue 2, 2012, pp. 185–203
DOI: 10.4171/IFB/279

Published online: 2012-07-25

Two-phase flow problem coupled with mean curvature flow

Chun Liu[1], Norifumi Sato[2] and Yoshihiro Tonegawa[3]

(1) The Pennsylvania State University, University Park, USA
(2) Furano H.S., Furano (Hokkaido), Japan
(3) Hokkaido University, Sapporo, Japan

We prove the existence of generalized solution for incompressible and viscous non-Newtonian two-phase fluid flow for spatial dimension $d =2$ and 3. Separating two shear thickening fluids with power law viscosity strictly above critical growth $p = (d + 2)/2$, the phase boundary moves along with the fluid flow plus its mean curvature while exerting surface tension force to the fluid. An approximation scheme combining the Galerkin method and the phase field method is adopted.

Keywords: Two-phase fluid, surface energy, varifold, phase field method

Liu Chun, Sato Norifumi, Tonegawa Yoshihiro: Two-phase flow problem coupled with mean curvature flow. Interfaces Free Bound. 14 (2012), 185-203. doi: 10.4171/IFB/279