|Ph.D Student||Podolny Alla|
|Subject||Marangoni Convection in Binary Liquids and Nanofluids|
In the Presence of the Soret Effect
|Department||Department of Applied Mathematics||Supervisors||Professor Alexander Oron|
|Professor Emeritus Alexander Nepomniashchy|
This research belongs to the fascinating field of linear and nonlinear instabilities of surface-tension-driven flows. This kind of instabilities is especially important for engineering processes under microgravity conditions. Recently, a new class of fluids, nanofluids, has been successfully applied in heat transfer devices. In some new applications, specifically for heat pipes used for cooling aboard of spacecraft, the Marangoni convection is crucial. In this Ph.D thesis the problems of surface-tension-driven instabilities in binary solutions and nanofluids in the presence of thermodiffusion were solved. We show that the well-posed model for the description of hydrodynamics and heat transfer in nanofluids is identical to the system of equations for a binary mixture with the Soret effect. The research presents a unified theoretical description of Marangoni convection, which can be applied for both binary solutions and nanofluids. At the first stage, we carried out investigation of the long-wave Marangoni instability in a binary-liquid layer with a deformable interface in the limit of a small Biot number. We performed a thorough analysis and found a new, previously unknown distinguished asymptotic limit, and revealed a variety of instability modes, including a new long-wave oscillatory mode that appears in thin layers. At the next stage, the generality of the previous results was essentially extended. We discovered a novel type of long-wave Marangoni instabilities that exists for arbitrary Biot numbers, and developed a linear and non-linear theory of these instabilities. Specifically, we derived a set of long-wave nonlinear evolution equations governing the spatio-temporal dynamics of thin binary-liquid films, and carried out the weakly-nonlinear analysis of the dynamics near the bifurcation point. We also investigated the selection of stable supercritical wave patterns. At the final stage of this Ph.D research, the long-wave instability in the system with poorly conducting boundaries in the case of the combined Marangoni and Rayleigh phenomena in binary solutions and nanofluids was investigated. We found that in the case of small Biot numbers two long-wave regions exist. The dependence of the monotonic and oscillatory thresholds of instability in these regions on both the Soret and dynamic Bond numbers was investigated. The complete linear stability analysis reveals the diversity of instability types in the long-wave region, and a necessity of the development of the nonlinear theory of the discovered phenomena becomes important.