Onset of Convection in Two Liquid Layers with Phase Change

We perform linear stability calculations for horizontal fluid bilayers that can undergo a phase transformation, taking into account both buoyancy effects and thermocapillary effects in the presence of a vertical temperature gradient. We compare the familiar case of the stability of two immiscible fluids in a bilayer geometry with the less-studied case that the two fluids represent different phases of a single-component material, e.g., the water-steam system. The two cases differ in their interfacial boundary conditions: the condition that the interface is a material surface is replaced by the continuity of mass flux across the interface, together with an assumption of thermodynamic equilibrium that in the linearized equations represents the Clausius-Clapeyron relation relating the interfacial temperature and pressures. For the two-phase case, we find that the entropy difference between the phases plays a crucial role in determining the stability of the system. For small values of the entropy difference between the phases, the two-phase system can be linearly unstable to either heating from above or below. The instability is due to the Marangoni effect in combination with the effects of buoyancy (for heating from below). For larger values of the entropy difference the two-phase system is unstable only for heating from below, and the Marangoni effect is masked by effects of the entropy difference. To help understand the mechanisms driving the instability on heating from below we have performed both long-wavelength and short-wavelength analyses of the two-phase system. The short-wavelength analysis shows that the instability is driven by a coupling between the flow normal to the interface and the latent heat generation at the interface. The mechanism for the large wavelength instability is more complicated, and the detailed form of the expansion is found to depend on the Crispation and Bond numbers as well as the entropy difference. The two-phase system allows a conventional Rayleigh-Taylor instability if the heavier fluid overlies the lighter fluid; applying a temperature gradient allows a stabilization of the interface

Surface Instability of Icicles

Quantitatively-unexplained stationary waves or ridges often encircle icicles. Such waves form when roughly 0.1 mm-thick layers of water flow down the icicle. These waves typically have a wavelength of 1cm approximately independent of external temperature, icicle thickness, and the volumetric rate of water flow. In this paper we show that these waves can not be obtained by naive Mullins-Sekerka instability, but are caused by a quite new surface instability related to the thermal diffusion and hydrodynamic effect of thin water flow.Comment: 11 pages, 5 figures, Late

Non-isothermal model for the direct isotropic/smectic-A liquid crystalline transition

An extension to a high-order model for the direct isotropic/smectic-A liquid crystalline phase transition was derived to take into account thermal effects including anisotropic thermal diffusion and latent heat of phase-ordering. Multi-scale multi-transport simulations of the non-isothermal model were compared to isothermal simulation, showing that the presented model extension corrects the standard Landau-de Gennes prediction from constant growth to diffusion-limited growth, under shallow quench/undercooling conditions. Non-isothermal simulations, where meta-stable nematic pre-ordering precedes smectic-A growth, were also conducted and novel non-monotonic phase-transformation kinetics observed.Comment: First revision: 20 pages, 7 figure

The Effect of Convection on Disorder in Primary Cellular and Dendritic Arrays

Directional solidification studies have been carried out to characterize the spatial disorder in the arrays of cells and dendrites. Different factors that cause array disorder are investigated experimentally and analyzed numerically. In addition to the disorder resulting from the fundamental selection of a range of primary spacings under given experimental conditions, a significant variation in primary spacings is shown to occur in bulk samples due to convection effects, especially at low growth velocities. The effect of convection on array disorder is examined through directional solidification studies in two different alloy systems, Pb-Sn and Al-Cu. A detailed analysis of the spacing distribution is carried out, which shows that the disorder in the spacing distribution is greater in the Al-Cu system than in Pb-Sn system. Numerical models are developed which show that fluid motion can occur in both these systems due to the negative axial density gradient or due the radial temperature gradient which is always present in Bridgman growth. The modes of convection have been found to be significantly different in these systems, due to the solute being heavier than the solvent in the Al-Cu system and lighter than it in the Pb-Sn system. The results of the model have been shown to explain experimental observations of higher disorder and greater solute segregation in a weakly convective Al-Cu system than those in a highly convective Pb-Sn system

Studies on natural immunity in the cat

Dissertation (Ph.D.)--University of Kansas, Bacteriology, 1940