Onset of convection in two layers of a binary liquid

Abstract

We perform linear stability calculations for horizontal bilayers of a two-component fluid that can undergo a phase transformation, taking into account both buoyancy effects and thermocapillary effects in the presence of a vertical temperature gradient. Critical values for the applied temperature difference across the system that is necessary to produce instability are obtained by a linear stability analysis, using both numerical computations and small wavenumber approximations. Thermophysical properties are taken from the aluminum–indium monotectic system, which includes a liquid–liquid miscibility gap. In addition to buoyant and thermocapillary modes of instability, we find an oscillatory phase-change instability due to the combined effects of solute diffusion and fluid flow that persists at small wavenumbers. This mode is sensitive to the ratio of the layer depths, and for certain layer depths can occur for heating from either above or below.

Onset of morphological instability in two binary liquid layers

“…The two phases are separated by a deformable interphase boundary with a temperature-dependent surface energy that can give rise to Marangoni convection in addition to Rayleigh-Benard convection. In the previous paper, 5 we found a mode of instability even in the absence of buoyancy and thermocapillarity, which is therefore a phasechange mode of instability reminiscent of the familiar morphological instability in two-phase systems subject to transport by diffusion and heat flow. 6 This mode was examined for the aluminum-indium system, sufficiently far from the critical point that the usual transport equations are valid with a sharp interface model.…”

“…We computed the solution numerically using two methods as described previously. 4,5 A matrix collocation procedure, based on a pseudospectral Chebyshev discretization of the solution, 10 provides an approximate set of growth rates for a given wavenumber and value of G. In a complementary shooting procedure, a single growth rate is obtained by using the two-point boundary value solver BVSUP. 11 The resulting modes would take the form of a set of convection rolls on either side of a sinusoidally distorted interface in a twodimensional geometry.…”

“…As in our previous work, 5 we have ignored pressure perturbations in Eqs. ͑25͒ and ͑26͒ since their effects are negligible for the wavenumbers considered here.…”

“…The stability of a fluid-fluid interface is important in a number of scientific and technological applications. [1][2][3][4] In previous work, 5 we have considered the linear stability of a two-phase binary liquid confined between differentially heated horizontal parallel plates in a layer geometry and subject to the effects of buoyancy and thermocapillarity. The two liquid phases are not considered to be immiscible, but are in thermodynamic equilibrium.…”

“…The new term proportional to c 1 requires the careful retention of O͑a 2 ͒ terms that were neglected previously. 5 The outline of the paper is as follows. In Sec.…”