My PhD research focuses on buoyancy driven flow of yield stress fluids. These fluids are quite commonplace in industry and in nature. A few examples are heavy oil, toothpaste, lava lakes, planetary mantles, molten chocolate and sewage sludge(!).
The key characteristic of yield-stress fluids is the dual nature of their mechanical behavior: when subject to a shear stress less than a certain value (the yield stress) they seem to behave like solids, undergoing a deformation of finite magnitude. On the other hand, when the applied shear exceeds the yield stress, the material flows as expected from a fluid, exhibiting a sustained strain rate, albeit nonlinearly related to the shear stress. Starting with a very simple geometry and by gradually incorporating more (geometric) variables, I have tried to explore the various mechanisms through which the yield stress affects the hydrodynamics of buoyancy driven flows.
- a stratified vertical channel
We analyze the 1D flow of a Bingham fluid between two differentially heated vertical plates, in the presence of a stabilizing vertical temperature gradient, imposed at the walls. We show that flow onset is governed by a balance of yield stress and buoyancy stress. For sufficiently large stratification and decreasing yield stress, we show that in principle, an arbitrarily large number of plugs can be found in the finite width channel!
- a square cavity with differentially heated sidewalls
Here we examine the conditional and unconditional stability of the static regime . We also explore effect of the yield stress on transition between conductive and convective states. We show that depending on the initial conditions, a yield stress less than the critical value can result in temporary arrest of the flow. The temperature then develops conductively till the fluid yields and the flow restarts.
- a square cavity with localized heating on the bottom wall (accepted)
The purely conductive state in configurations such as the Rayleigh-Benard is linearly stable for yield stress fluids regardless of the relative strength of buoyancy and viscous stresses. However, on changing to localised heater configurations the static background state exists only if the yield stress is sufficiently large. Otherwise, thermal plumes may be induced in a stationary visco-plastic fluid layer, as illustrated in the recent experimental study of Davaille et al. (2013). Here we study an analogous problem both analytically and computationally, from the perspective of an ideal yield stress fluid (Bingham fluid) that is initially stationary in a locally heated rectangular tank.
We show that for a non-zero yield stress the onset of flow waits for a finite time that increases with the yield stress. Once the flow starts, it develops into either a weakly or strongly convective flow. In the former case the passage to a steady state is relatively smooth and monotone, resulting eventually in a steady convective plume above the heater, rising and impinging on the upper wall, then recirculating steadily around the tank. With strongly convecting flows, we observe an increasing number of distinct plume heads and a tendency for plumes to develop as short-lived pulses.