Instabilities of dynamic thermocapillary liquid layers. Part 1. Convective instabilities

Abstract

A planar liquid layer is bounded below by a rigid plate and above by an interface with a passive gas. A steady shear flow is set up by imposing a temperature gradient along the layer and driving the motion by thermocapillarity. This dynamic state is susceptible to two types of thermal-convective instabilities: (i) stationary longitudinal rolls, which involve the classical Marangoni instability studied by Pearson; and (ii) unsteady hydrothermal waves, which involve a new mechanism of instability deriving its energy from the horizontal temperature gradients. Thermal stability characteristics for liquid layers with and without return-flow profiles are presented as functions of the Prandtl number of the liquid and the Biot number of the interface. Comparisons are made with available experimental observations.

Nonlinear dynamics of waves and modulated waves in 1D thermocapillary flows. II. Convective/absolute transitions

“…The existence of hydrothermal waves in a fluid layer subjected to a horizontal temperature gradient has been predicted on the basis of a linear stability analysis by Smith and Davis [23], and studied numerically in conditions close to our experimental situation by Mercier and Normand [40]. Hydrothermal waves have been detected and characterized in several experiments [13,18,24,25,41].…”

“…[11,12] Among these different waves systems, thermocapillary flows and in particular hydrothermal waves [13][14][15][16][17][18] or hot wire waves [19][20][21][22] appear as a very simple tool, owing to their supercritical bifurcation. They correspond to the first instability of a thin liquid layer with a free surface subjected to a horizontal temperature gradient [23]. Different experimental configurations have been used to study those traveling waves: rectangular cells with different aspect ratios [13,24,25,18,15], annular cells [26,14], cylindrical cells [27,17] and linear hot wire under the surface of a liquid [19][20][21][22].…”

Linear instability analysis of thermocapillary convection in a bilayer system

“…the thermal Couette flow. Particula rly, Smith and Davis [4] found that for this linear base flow, when it was subjected to spanwise disturbance s, convection may occur in the form of stationary longitudina l rolls, or in the form of hydrothe rmal waves. The hydrothermal wave only occurs when the Prandtl number is small.…”

“…Linear stability analysis of Pearson predicts the threshold value of Marango ni number, Ma = 79.6, which coincides with experiments. Smith and Davis [4,5] and Davis [6] considered thermocapillary instabilities in a single layer system with a non-deformabl e interface. Sen and Davis [7] studied steady thermocapi llary flows in two-dimensi onal slots.…”

“…Sen and Davis [7] studied steady thermocapi llary flows in two-dimensi onal slots. In [4][5][6][7], the flow system was subjected to a constant horizontal temperature gradient along the interface resulted in a linearly distribut ed horizontal flow, i.e. the thermal Couette flow.…”