The effect of phase change on stability of convective flow in a layer of volatile liquid driven by a horizontal temperature gradient

Buoyancy–thermocapillary convection in a layer of volatile liquid driven by a horizontal temperature gradient arises in a variety of situations. Recent studies have shown that the composition of the gas phase, which is typically a mixture of vapour and air, has a noticeable effect on the critical Marangoni number describing the onset of convection as well as on the observed convection pattern. Specifically, as the total pressure or, equivalently, the average concentration of air is decreased, the threshold of the instability leading to the emergence of convective rolls is found to increase rather significantly. We present a linear stability analysis of the problem which shows that this trend can be readily understood by considering the transport of heat and vapour through the gas phase. In particular, we show that transport in the gas phase has a noticeable effect even at atmospheric conditions, when phase change is greatly suppressed.

Conjugated liquid layers driven by the short-wavelength Bénard–Marangoni instability: experiment and numerical simulation

The coupled dynamics of two conjugated liquid layers of disparate thicknesses, which coat a solid substrate and are subjected to a transverse temperature gradient, is investigated. The upper liquid layer evolves under the short-wavelength Bénard–Marangoni instability, whereas the lower, much thinner film undergoes a shear-driven long-wavelength deformation. Although the lubricating film should reduce the viscous stresses acting on the up to one hundred times thicker upper layer by only 10 %, it is found that the critical Marangoni number of marginal stability may be as low as if a stress-free boundary condition were applied at the bottom of the upper layer, i.e. much lower than the classical value of 79.6 known for a single film. Furthermore, it is experimentally verified that the deformation of the liquid–liquid interface, albeit small, has a non-negligible effect on the temperature distribution along the liquid–gas interface of the upper layer. This stabilizes the hexagonal pattern symmetry towards external disturbances and indicates a two-way coupling of the different layers. The experiments also demonstrate how convection patterns formed in a liquid film can be used to pattern a second conjugated film. The experimental findings are verified by a numerical model of the coupled layers.

Marangoni convection in an ewline Oldroyd-B fluid layer with ewline throughflow

The onset of Marangoni convection in a horizontal Oldroyd-B fluid layer in the presence of a vertical throughflow is determined by linear analysis. We find an approximate solution to the corresponding eigenvalue problem using the Galerkin method. The effects of viscoelastic parameters on the critical Marangoni number, wave number, and frequency are discussed. The study also reveals the existence of a critical retardation time for which the oscillatory motion reaches its maximum strength. This study has possible implications in microgravity situations. PACS No.: 47.20.Gv

Be´nard-Marangoni Instability in an Open Vertical Cylinder With Lateral Heating

A linear stability analysis of Rayleigh-Be´nard-Marangoni flow of low Prandtl number fluid contained in an open vertical cylinder is presented. The cylinder is heated laterally and is cooled at top surface by radiation. Governing equations of the flow are solved for axisymmetric base flow using higher order finite difference scheme. Small perturbation was applied to the obtained base flow to determine the critical Marangoni number and Grashof number at which the axisymmetry is broken. The eigenvalue matrix equation is solved using linear fractional transformation with banded matrix structure taken into account. It is found that the thermocapillary effect stabilizes the convective flow driven by buoyancy.

On the instability of a falling film due to localized heating

We analyse the stability of a thin film falling under the influence of gravity down a locally heated plate. Marangoni flow, due to local temperature changes influencing the surface tension, opposes the gravitationally driven Poiseuille flow and forms a horizontal band at the upper edge of the heater. The thickness of the band increases with the surface tension gradient, until an instability forms a rivulet structure periodic in the transverse direction. We study the dependence of the critical Marangoni number, a non-dimensional measure of the surface tension gradient at the onset of instability, on the associated Bond and Biot numbers, non-dimensional measures of the curvature pressure and heat-conductive properties of the film respectively. We develop a model based on long-wave theory to calculate base-state solutions and their linear stability. We obtain dispersion relations, which give us the wavelength and growth rate of the fastest growing mode. The calculated film profile and wavelength of the most unstable mode at the instability threshold are in quantitative agreement with the experimental results. We show via an energy analysis of the most unstable linear eigenmode that the instability is driven by gravity and an interaction between base-state curvature and the perturbation thickness. In the case of non-zero Biot number transverse variations of the temperature profile also contribute to destabilization.

The effects of thermal modulation upon the onset of Marangoni–Bénard convection

The effects of thermal modulation with time on the thermocapillary instability of a thin horizontal fluid layer with a deformable free surface are investigated on the basis of linear stability theory. First, a sinusoidal heating with a mean component is applied at the lower wall, corresponding to boundary conditions either in the form of prescribed temperature or heat flux. For finite-wavelength convection the thermal modulation exerts a strong effect, giving rise to a family of looped regions of instability corresponding to alternating synchronous or subharmonic responses. In the case of prescribed heat flux, the critical curve consists of significantly fewer loops than in the case of prescribed temperature. Thermal modulation with moderate modulation amplitude tends to stabilize the mean basic state, and optimal values of frequency and amplitude of modulation are determined to yield maximum stabilization. However, large-amplitude modulation can be destabilizing. A basic state with zero mean is then considered and the critical Marangoni number is obtained as a function of frequency. The effects of modulation are also investigated in the long-wavelength limit. For the case of prescribed temperature, the modulation does not affect the onset of the long-wavelength mode associated with the mean basic state and a purely oscillating basic state is always stable with respect to long-wavelength disturbances. For the case of prescribed heat flux both at the wall and free surface, by contrast, thermal modulation exerts a significant effect on the onset of convection from a mean basic state and long-wavelength convection can occur even for a purely oscillating basic state. The modulation can be stabilizing or destabilizing, depending on the frequency.