A diffuse domain method for two-phase flows with large density ratio in complex geometries. (26th November 2020)

• Record Type: Journal Article
• Authors: Guo, Zhenlin; Yu, Fei; Lin, Ping; Wise, Steven; Lowengrub, John
• Is Part Of: Journal of fluid mechanics. Volume 907(2021)
• Publication Date: 2020-11-26
• Subjects: multiphase flow, -- contact lines, -- computational methods; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2020.790
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract: 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.