Instabilities of shallow dynamic thermocapillary liquid layers

Abstract

Results of experiments with thermocapillary flow in shallow liquid layers heated from the side are presented. The fluid has Prandtl number 17 and the main configuration investigated is an annular gap to avoid side-wall effects. The liquid depth d was d≤3.00 mm to have negligible buoyancy effects. Various instabilities have been observed. At a Marangoni number M≂6⋅102, a transition to steady multicellular flow occurred. The convection cells are longitudinal rolls embedded in the main flow all rotating in the same direction. At M≂3⋅103, a transition of the steady multicellular flow to time-dependent flow states (t) was observed. Two different t-flow states have been identified by thermocouple measurements and by visualization of the dynamic-free surface deformations of oscillatory flow. Both t states can be described by disturbances in the form of traveling waves. A short-wavelength t state with small surface deformations and with waves traveling in azimuthal direction is the preferred mode for d≤1.4 mm. A long-wavelength t state with larger surface deformations and with waves traveling in radial and in azimuthal directions is preferred for d≥1.4 mm. The stability diagram, wavelength, frequency, and phase speed of both t states are presented and the findings in comparison to an already existing theory by Smith and Davis [J. Fluid Mech. 132, 119, 145 (1983)] are discussed.

Hydrothermal waves and corotating rolls in laterally heated convection in simple liquids

“…On the experimental side, Schwabe et al [11] observed oscillatory motions in half zones. Villers and Platten [12] reported oscillatory motions in experiments and numerical simulations in a shallow layer of acetone ðPr ¼ 4:2Þ in a rectangular container submitted to a horizontal temperature gradient along the larger extension.…”

“…In these theoretical works, the layer is assumed to be of infinite horizontal extension and therefore only intrinsic perturbations are considered. However, numerical simulations [6] and experiments [11][12][13][14] show that a pattern of corotating stationary rolls transverse to the basic flow may appear in the liquid. This apparent contradiction is resolved taking into account that the boundary layer on the hot sidewall constitutes a finite perturbation that, depending on the sign of the attenuation rate of the perturbation, may spatially fade, that is, remain localised, or become amplified spreading throughout the layer.…”

“…As quoted in [20], important discrepancies regarding either the convective threshold or the critical wavenumber still remain. Moreover, Schwabe et al [11], Burguete et al [20], Garnier [21], Garnier et al [22,23] find two wave regimes, one for very thin layers (typically h < 1:4 mm) and another for thicker layers. Finally, Shetsova et al [24] investigated numerically a finite two-dimensional cavity heated from the side, and analysed the interplay between the steady cell created near the hot wall and the hydrothermal waves.…”

An experimental research on surface oscillation of buoyant-thermocapillary convection in open cylindrical annuli

“…Then, the flow would become unstable when the temperature difference was increased and the hydrothermal waves would first occur, followed by more complicated oscillatory flows. They also discovered that the LWI had a longer nondimensional wavelength, even one order of magnitude larger than the SWI [7], and two new convective structures in the case of larger dynamic Bond number [8]. Shi et al [9] did a 3-D numerical simulation of an 1 mm deep model with finite volume method and Li et al [10][11][12] did a theoretic calculation on double layers thermocapillary convection using approximate algorithm and got temperature configuration as well as velocity distribution in the main flow region.…”

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

“…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].…”