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

Published online by Cambridge University Press:  26 November 2020

Zhenlin Guo Open the ORCID record for Zhenlin Guo [Opens in a new window] ,
Fei Yu ,
Ping Lin ,
Steven Wise  and
John Lowengrub
Zhenlin Guo*
Affiliation:
Mechanics Division, Beijing Computational Science Research Center, Building 9, East Zone, ZPark II, No. 10 East Xibeiwang Road, Haidian District, Beijing100193, PR China Department of Mathematics, University of California, Irvine, CA92697, USA
Fei Yu
Affiliation:
Department of Mathematics, University of California, Irvine, CA92697, USA
Ping Lin
Affiliation:
Department of Mathematics, University of Dundee, DundeeDD1 4HN, UK
Steven Wise
Affiliation:
Department of Mathematics, University of Tennessee, Knoxville, TN37996, USA
John Lowengrub
Affiliation:
Department of Mathematics, University of California, Irvine, CA92697, USA
*
†Email address for correspondence: [email protected]
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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 ($\epsilon \rightarrow 0$) with $\mathcal {O}(\epsilon )$. Our analytic results are confirmed numerically by measuring the errors in both $L^{2}$ and $L^{\infty }$ 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.

JFM classification

Multiphase and Particle-laden Flows: Multiphase flow Interfacial Flows (free surface): Contact lines Mathematical Foundations: Computational methods
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 907 , 25 January 2021 , A38
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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