Interfacial Convection in Multilayer Systems by A. Nepomnyashchy, I. Simanovskii, J.C. Legros

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Let the vapor (fluid 1) be located in the region z > h(x, y, t), and the liquid (fluid 2) be located in the region z < h(x, y, t). Assume that there is a normal mass flux J(x, y, t) through the interface z = h(x, y, t) due to evaporation. 3)). Both these kinematic conditions are violated in the presence of evaporation. 98) where τ (l) (l = 1, 2) are tangent vectors to the interface. 99) where ρm is the density of fluid m (m = 1, 2). 1)) is modified in the following way: J(v1,i − v2,i ) + (σ1,ik − σ2,ik )nk = −σ 1 1 + R1 R2 ni + ∂σ .

1)) is modified in the following way: J(v1,i − v2,i ) + (σ1,ik − σ2,ik )nk = −σ 1 1 + R1 R2 ni + ∂σ . 101) ∂σ (l) τ = 0. 101) proportional to J 2 corresponds to a “recoil” of molecules crossing the vapor–liquid interface. 5)), has to include also the latent heat of vaporization Lv , the change in molecular kinetic energy from crossing the interface, and the work done by the viscous stresses. , 1988): κ1 ∂T1 ∂T2 − κ2 ∂xi ∂xi ni = JLv + J3 2 1 1 − 2 ρ21 ρ2 −J σ1,ik σ2,ik − ρ1 ρ2 ni nk . 103) Let us discuss now the behavior of the temperature field near the interface.

Verschueren et al. (2001) applied a diffuse-interface model for the computation of a twophase thermocapillary motion in a Hele–Shaw cell. They simulated the creation of a droplet due to the deformational Marangoni instability of a plane interface. Borcia and Bestehorn (2003) used the phase-field approach for the description of the Marangoni instability in a two-layer liquid–gas system. 38 1 Introduction. , 1998). 173) to be added to the viscous stress tensor in the Navier–Stokes equation. Denniston and Yeomans (1999) took into account the latent heat of the phase transformation.