Mathematical Modeling of the Thermocapillary Fluid Flows in a Thin Layer with Evaporation

Numerical Investigation of the Liquid Film Flows with Evaporation at Thermocapillary Interface

“…The influences of various effects on the flow character are investigated analytically, numerically and experimentally [1][2][3][4][5][6]. Evaporation at the interface should be taken into account in the modeling of such processes [1][2][3][7][8][9]. A number of works are devoted to the numerical study of flow of evaporating thin liquid layers [2][3][4].…”

The Liquid Film Flow with Evaporation: Numerical Modelling

“…Great attention is paid to the thin liquid films. The mathematical models of the flows in the thin layer approximation and their numerical study are presented in [1][2][3][4][5][7][8][9][10]. Special attention while modelling of the flows with interfaces should be given to the formulation of the boundary conditions [11][12][13].…”

“…The mathematical modelling is based on the long-wave approximation of the Oberbeck-Boussinesq convection equations and the generalized kinematic, dynamic and energetic conditions at the interface [11][12][13]. The evolution equation, determining the liquid layer thickness, is obtained when the effects of gravity, evaporation, capillarity, thermocapillarity and additional tangential stresses from the gas medium are taken into account (see [7][8][9]). …”

Mathematical Modelling of the Evaporating Liquid Films on the Basis of the Generalized Interface Conditions

“…The effects of evaporation on the nonlinear stability of uniformly heated films have been investigated experimentally, numerically and analytically in many papers [1][2][3][4][5][9][10][11]. In this paper we present new mathematical models of flows of the thin evaporating liquid layers on the basis of the long-wave approach (see also [9][10][11]).…”

“…In this paper we present new mathematical models of flows of the thin evaporating liquid layers on the basis of the long-wave approach (see also [9][10][11]). These models are constructed on the basis of the NavierStokes equations or their Boussinesq approximation and generalized kinematic, dynamic and energetic interface conditions.…”