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The majority of studies considering thermocapillary convection in multilayer systems assume the interface is rigid (non-deformable) and the fluids are stationary. Motivated by the potential of using thermally generated convection patterns in moving droplets for mixing, this paper re-examines the Marangoni-Benard instability for a three-layer system with deformable interfaces undergoing Poiseuille flow. Taking into account the deformability of the interface reveals new physics. Linear stability analysis shows that at small wave numbers a deformable interface is of the orders of magnitude less stable than a non-deformable interface. At large wave numbers, both a rigid and a deformable interface have the same stability. Furthermore, a base planar Poiseuille flow affects the linear stability of the system and the type of instability when the interface is allowed to deform. Flow stabilizes an already unstable system and works to destabilize a stable system. Lastly, the dependence of the linear stability of the system on viscosity ratio, depth ratio, and Prandtl number, Pr, experimentally adjustable parameters, is discussed. Whereas Pr has little effect on the stability of the system, we show that a small viscosity ratio and a large depth ratio are advantageous in making the system unstable.

The instability of an evaporating binary mixture underlying its own vapor in an enclosed container is investigated. The fluid dynamics of both liquid and vapor phases, in the absence of gravity, are taken into account as also a deflecting interface. It is concluded from calculations, exemplified by a low weight alcohol mixture, that unlike single component systems a non-dilute binary mixture can become unstable only when it is heated from the vapor side. This instability is caused by solutal Marangoni convection that is triggered in the presence of phase change.

Multi-component mixtures undergoing phase change in the presence of gravity depict instabilities whose physical origins depend upon the heating arrangement. Calculations on evaporative instability in closed systems using the example of low weight alcohols predict that cellular patterns would occur when the system is heated from above provided that the liquid depths are small compared to the vapor depths. The cellular patterns give way to long wavelength modes when the liquid depths are large because the solutal convection is dominant. When heated from below, cellular patterns can always be obtained regardless of the phase depths. Moreover, for this heating arrangement the physics shows thermal dominance at large wave numbers and solutal dominance at small wave numbers.

Motivated by the destabilization of a two-fluid layer flowing in a microchannel for efficient mixing or droplet formation, we study quantitatively the linear stability of the interface between two liquids subjected to an electric field parallel or normal to the flat interface. In the case of fast electric charge relaxation times, the equations for the perturbation can be significantly reduced [A. K. Uguz, O. Ozen, and N. Aubry, Phys. Fluids 20, 031702 (2008)]. Using a simple argument and without solving the equations, Uguz et al. determined the range of parameters over which the electric field is destabilizing, which is narrower for the parallel compared to the normal electric field. However, the argument of Uguz et al. was not amenable to the calculation of growth rates and neutral stability curves. In this paper, by solving the equations, we not only confirm the previous findings but also determine the quantitative linear stability properties, namely, the growth rates and neutral stability curves. Depen...

The application of an electric field to a two-fluid layer in channel flow has been shown to be an effective way to destabilize microscale interfacial flows. Here, we perform a linear stability analysis of a flat interface between two leaky dielectric liquids flowing in a channel while also subjected to an electric field parallel to the interface. It is shown that the analysis simplifies for fast electric charge relaxation times, in which case conditions for the electric field to be either stabilizing or destabilizing are derived analytically. These results are compared to those previously obtained for a normal electric field.

The breakup point of an elliptical liquid bridge was investigated experimentally in a Plateau chamber using two density-matched liquids. The objective was to show that a liquid bridge with elliptical end plates is more stable than a companion circular bridge whose end plates are of the same area as the ellipses. The volume in the elliptical liquid bridge was fixed to be the same as the volume of the hypothetical companion cylindrical bridge at its theoretical critical point. The end plates were parallel and oriented so that they were not twisted with respect to one another. Using two different sizes of ellipses whose semimajor axes were slightly deviated from the radii of the companion circles, it was found that the elliptical liquid bridge breakup point was nearly 3% longer than the corresponding circular bridge. This demonstrated that a deviation from the circular geometry offers greater stability.

Liquid bridges are usually encapsulated with another liquid in float-zone crystal growth processes to ensure the containment of volatile components. This paper is concerned with the stability of an inviscid liquid bridge that is off-centered with respect to its encapsulant. Perturbation theory is used to study the stability of such a bridge subject to inertial disturbances. It is concluded that while the off-centered nature does not change the neutral point it does affect the rate of growth and decay of the disturbances causing the unstable regions to become less unstable and stable regions to become less stable. Limiting conditions are considered in order to provide a better understanding of the physics of off-centering.