A diffuse domain method for two-phase flows with large density ratio in complex geometries

Zhenlin Guo (Lead / Corresponding author), Fei Yu, Ping Lin, Steven Wise, John Lowengrub

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Abstract

We present a quasi-incompressible Navier-Stokes-Cahn-Hilliard (q-NSCH) diffuse interface model for two-phase fluid flows with variable physical properties that maintains thermodynamic consistency. Then, we couple the diffuse domain method with this two-phase fluid model-yielding a new q-NSCH-DD model-to simulate the two-phase flows with moving contact lines in complex geometries. The original complex domain is extended to a larger regular domain, usually a cuboid, and the complex domain boundary is replaced by an interfacial region with finite thickness. A phase-field function is introduced to approximate the characteristic function of the original domain of interest. The original fluid model, q-NSCH, is reformulated on the larger domain with additional source terms that approximate the boundary conditions on the solid surface. We show that the q-NSCH-DD system converges to the q-NSCH system asymptotically as the thickness of the diffuse domain interface introduced by the phase-field function shrinks to zero with. Our analytic results are confirmed numerically by measuring the errors in both and norms. In addition, we show that the q-NSCH-DD system not only allows the contact line to move on curved boundaries, but also makes the fluid-fluid interface intersect the solid object at an angle that is consistent with the prescribed contact angle.

Original languageEnglish
Article numberA38
Number of pages28
JournalJournal of Fluid Mechanics
Volume907
Early online date26 Nov 2020
DOIs
Publication statusPublished - 25 Jan 2021

Keywords

  • computational methods
  • contact lines
  • multiphase flow

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