Convective flows in a two-layer system with a temperature gradient along the interface

Abstract

The nonlinear stability of two superposed horizontal liquid layers bounded by two solid planes and subjected to a horizontal temperature gradient, is investigated. Two types of boundary conditions, periodic boundary conditions and heat-insulated lateral walls, are considered. The nonlinear simulations of the wavy convective regimes for a particular set of fluids, are performed. The dependence of the direction of the wave propagation depends on two factors, which are studied, the ratio of the layers thicknesses and the Marangoni number.

Asymptotic solution of thermocapillary convection in two immiscible liquid layers in a shallow annular cavity

“…Therefore, eqs. (84)−(87) are the same as the results obtained by Nepomnyashchy and Simanovskii [17].…”

“…A linear perturbative analysis with respect to two-dimensional and three-dimensional perturbations revealed the existence of three kinds of patterns: wave propagation from the cold to the hot regions or in the opposite direction or still stationary longitudinal rolls. Nepomnyashchy and Simanovskii [17,18] investigated the nonlinear stability of the same two-layer system and concluded that the direction of the wave propagation depended on the ratio of the layers thicknesses and the Marangoni number. Although the existing literatures on square cavities are rich, the investigations concerned with annular cavities are fairly limited.…”

Self-Organized Micropatterning of Thin Viscous Bilayers Under Microgravity

“…Here f (x,y) is a periodic function that describes the topographic patterns decorated on the substrate surface. The evolution equations thus obtained shown below describe the stability, dynamics and morphology of the liquid-air interface (i = 2) and the liquid-liquid interface (i = 1) (Danov et al 1998a, b;Pototsky et al 2006;Nepomnyashchy and Simanovskii 2006a, b, 2007, 2009aFisher and Golovin 2005):…”

“…The effective pressures at the liquid-liquid and liquid-air interfaces are derived from the normal stress balances at the respective interfaces as (Danov et al 1998a, b;Bandyopadhyay et al 2005Bandyopadhyay and Sharma 2006;Pototsky et al 2006;Nepomnyashchy and Simanovskii 2006a, b, 2007, 2009aFisher and Golovin 2005):…”

“…Figure 1 shows the schematic diagram of the bilayers on top of (a) physically heterogeneous and (b) chemically patterned substrate. Detailed theoretical studies into the different features of short and long time instabilities of ultra-thin bilayers have also been recently conducted (Danov et al 1998a, b;Paunov et al 1998;Bandyopadhyay et al 2005Bandyopadhyay and Sharma 2006, 2010Pototsky et al 2004Pototsky et al , 2005Pototsky et al , 2006Nepomnyashchy and Simanovskii 2006a, b, 2007, 2009aMerkt et al 2005;Kumar and Matar 2004;Matar et al 2005;Golovin 2005, 2007).…”