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Twofluid MarangoniBénard convection with a deformable interface
"... Two immiscible fluid layers that are subjected to a temperature gradient perpendicular to their interface, exhibit a range of behaviors that is considerably richer than for the singlefluid case. We describe a numerical technique for calculating thermallydriven flows in two fluid layers which uses ..."
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Two immiscible fluid layers that are subjected to a temperature gradient perpendicular to their interface, exhibit a range of behaviors that is considerably richer than for the singlefluid case. We describe a numerical technique for calculating thermallydriven flows in two fluid layers which uses a simple technique based on a Landau transformation to map the physical domain into a reference domain, enabling the unknown location of the deformable interface to be determined. The coupled system of nonlinear partial differential equations, comprising mapping, continuity, momentum and energy equations and the appropriate boundary conditions, is solved using the finiteelement method in twodimensional domains. Numerical bifurcation techniques are used to investigate the multiplicity of the solution set. The case of heating from above is considered in some detail and the results of finiteelement computations are compared with linear stability calculations performed on unbounded domains. The principal advantages of the finiteelement approach are the ability to determine the effect of non90 degree contact angles (when the conducting solution no longer exists and traditional linear stability approaches fail), the ability to determine the role of finite aspect ratio domains and the relative volume fractions of the two fluids, and the capability of calculating the nonlinear development of flows beyond the critical temperature gradient.
Pattern Formation in Solutal Convection: Vermiculated Rolls and Isolated Cells
"... Observations of the peculiar behaviour of a drink of liqueur topped with cream led us to perform experiments showing that the instability is a convection phenomenon that arises through destabilizing surfacetension forces. The convection is solutal: driven by gradients of concentration of a solute, ..."
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Observations of the peculiar behaviour of a drink of liqueur topped with cream led us to perform experiments showing that the instability is a convection phenomenon that arises through destabilizing surfacetension forces. The convection is solutal: driven by gradients of concentration of a solute, rather than by heat gradients as in the more commonly studied thermal convection. The convective patterns, vermiculated rolls and isolated cells, are quite unlike the usual planforms. They are associated with an elastic surface film, and the Marangoni number is high, characteristic of solutal convection. We have conducted further experiments that reproduce these patterns in simpler working fluids.
Phase Separation in Binary Fluid Mixtures with Continuously Ramped Temperature
, 2003
"... We consider the demixing of a binary fluid mixture, under gravity, which is steadily driven into a two phase region by slowly ramping the temperature. We assume, as a first approximation, that the system remains spatially isothermal, and examine the interplay of two competing nonlinearities. One of ..."
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We consider the demixing of a binary fluid mixture, under gravity, which is steadily driven into a two phase region by slowly ramping the temperature. We assume, as a first approximation, that the system remains spatially isothermal, and examine the interplay of two competing nonlinearities. One of these arises because the supersaturation is greatest far from the meniscus, creating inversions of the density which can lead to fluid motion; although isothermal, this is somewhat like the Bénard problem (a singlephase fluid heated from below). The other is the intrinsic diffusive instability which results either in nucleation or in spinodal decomposition at large supersaturations. Experimental results on a simple binary mixture show interesting oscillations in heat capacity and optical properties for a wide range of ramp parameters. We argue that these oscillations arise under conditions where both nonlinearities are important.
Numerical simulation of the Marangoni e ect on mass transfer to single slowly moving drops
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