Evaporative instability in binary mixtures

Overview & Synopsis

This study focuses on understanding the physics of the convective flow resulting from evaporative instability in binary mixtures. This problem has wide applications in spin coating, film deposition, heat pipes, etc. where phase change and convection play a very important role in the design process and also final quality of the product. The physical system of interest consists of a liquid mixture underlying its own vapor sandwiched between two conducting plates with insulated sidewalls in a closed container. The conducting plates are used to apply a vertical temperature gradient while there is no applied concentration gradient in the system. Concentration gradients are induced by the different evaporation rate of the components. In this system it is important to understand how the fluid dynamics and the heat and mass transfer interact competitively to form patterns. The main goal of this work is to identify the conditions for the system going from the conductive no-flow state to a convection state when the applied vertical temperature gradient exceeds a certain value called the critical value.In the system convection arises due to three distinct phenomena; evaporation, density gradients, and interfacial tension gradients. These convective forces are opposed by the diffusion effects that try to keep the system in the conductive no-flow state. The onset point depends upon several variables such as the dimensions of the container, thermo-physical properties of both liquid and vapor phases, mass fraction, and the characteristic of the disturbance given to the system. The effects of each of these variables on the onset point are investigated both in the presence and in the absence of gravity. To represent the physics a complete non-linear mathematical model is developed including momentum, energy, and mass balances in both phases with appropriate boundary conditions. The binary mixture is assumed to be made up of two low weight alcohols such as ethanol and sec-butanol. In the modeling equations the density and the interfacial tension are taken to be function of both temperature and concentration. To identify the onset point the non-linear equations are linearized around a known base state. In this case the base state is the conductive no-flow state. The resulting set of linear equations is solved using a spectral Chebyshev collocation method. Four major results arise from this work. First, in a multi-component system in the absence of gravity, an instability arises only when the system is heated from the vapor side as opposed to evaporation in a single-component. The implication is that evaporative processes in thin layers or in micro-gravity are best conducted with heat from the liquid side if instabilities are to be avoided.Second, in the presence of gravity, a multi-component system may become unstable no matter the direction of heating. If thermal buoyancy is negligible then it is shown in this study that heating from the vapor side is the unstable arrangement. Otherwise either heating style can produce an instability. This result means that the applied temperature difference must be kept below a threshold in order to avoid flow instabilities no matter the heating direction.Third, whenever instability occurs in the absence of gravity, patterns will not result in the case of a pure component but may result in the case of multi-components. Likewise, patterns will result when gravity is taken into account provided the aspect ratio of the container lies in a suitable range. As a result, aspect ratios can be chosen to avoid multi-cellular patterns even if convective flow instabilities arise during evaporation.Lastly, oscillations are not ordinarily predicted despite opposing effects of solutaland thermal convection in the evaporation problem.