Buoyant-thermocapillary instabilities in extended liquid layers subjected to a horizontal temperature gradient

Abstract

We report experiments on buoyant-thermocapillary instabilities in differentially heated liquid layers. The results are obtained for a fluid of Prandtl number 10 in a rectangular geometry with different aspect ratios. Depending on the height of liquid and on the aspect ratios, the two-dimensional basic flow destabilizes into oblique traveling waves or longitudinal stationary rolls, respectively, for small and large fluid heights. Temperature measurements and space-time recordings reveal the waves to correspond to the hydrothermal waves predicted by the linear stability analysis of Smith and Davis ͓J. Fluid Mech. 132, 119 ͑1983͔͒. Moreover, the transition between traveling and stationary modes agrees with the work by Mercier and Normand ͓Phys. Fluids 8, 1433 ͑1996͔͒ even if the exact characteristics of longitudinal rolls differ from theoretical predictions. A discussion about the relevant nondimensional parameters is included. In the stability domain of the waves, two types of sources have been evidenced. For larger heights, the source is a line and generally evolves towards one end of the container leaving a single wave whereas for smaller heights, the source looks like a point and emits a circular wave which becomes almost planar farther from the source in both directions.

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

“…The exact characteristics of the waves depend strongly on these parameters and on the aspect ratios of the containers [18,24,42]. For the hydrothermal waves instability considered here, only Ma and Bo are relevant.…”

“…The rectangular channel ( Fig. 1) is 10 mm wide and 250 mm long [13,18]. Plexiglas blocks are inserted in the channel to reduce the length to L b = 180 mm, i.e., aspect ratio Γ = L b /h ≃ 100; this allows us to view the whole cell through a 200 mm diameter lens.…”

“…Both geometries consist of a channel with a glass bottom and vertical copper walls filled with a thin layer of silicon oil of viscosity ν = 0.65cSt and Prandtl number P = 10 (see [18] for characteristics of the fluid). The fluid surface is free and a Plexiglas plate is inserted a few millimeters above the surface of the fluid to reduce evaporation.…”

“…Wave systems have been studied in binary-fluid convection (subcritical traveling waves bifurcation) [4][5][6], oscillatory instability in low Prandtl number convection [7,8], oscillatory rotating convection [9], cylinder wake [10], Taylor dean vortices. [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].…”

“…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].…”