3 results
Motion onset in simple yield stress fluids
- K.D. Jadhav, P. Rossi, I. Karimfazli
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- Journal:
- Journal of Fluid Mechanics / Volume 912 / 10 April 2021
- Published online by Cambridge University Press:
- 05 February 2021, A10
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We present an experimental investigation of motion onset in simple yield stress fluids. In this context, motion onset refers to the transition from the motionless steady state to a steady flow, as well as the development of motion in a fluid initially at rest. We consider the natural convection of carbopol microgels in a square cavity with differentially heated sidewalls. We use particle image velocimetry and thermometry to reveal the evolution of both temperature and velocity fields. It is a hallmark of yield stress fluids that a critical ratio of the yield stress and buoyancy stresses exists above which the steady state is motionless. We observe this critical behaviour in our experiments. Contrary to the theoretical predictions, however, systematic motion is evident at the onset of all experiments, even when the steady state is motionless. Above the critical limit, extremely slow motion is observed immediately after the onset of the experiment. This is followed by very slow decay to rest, reminiscent of creep behaviour. Below the critical limit, the initial slow dynamics is followed by flow development patterns similar to theoretical predictions based on the Bingham model. We show that motion onset in carbopol microgels is dominated by subyield motion and fluidization, key processes that are not captured by viscoplastic models.
Thermal plumes in viscoplastic fluids: flow onset and development
- I. Karimfazli, I. A. Frigaard, A. Wachs
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- Journal of Fluid Mechanics / Volume 787 / 25 January 2016
- Published online by Cambridge University Press:
- 18 December 2015, pp. 474-507
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The purely conductive state in configurations such as the Rayleigh–Bénard one is linearly stable for yield stress fluids at all Rayleigh numbers, $Ra$. However, on changing to localized heater configurations the static background state exists only if the yield stress is sufficiently large. Otherwise, thermal plumes may be induced in a stationary viscoplastic fluid layer, as illustrated in the recent experimental study of Davaille et al. (J. Non-Newtonian Fluid Mech., vol. 193, 2013, 144–153). 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 start time $t_{s}$ that increases with the dimensionless ratio of yield stress to buoyancy stress, denoted $B$. We provide a precise mathematical definition of $t_{s}$ and approximately evaluate this for different values of $B$, using both computational and semianalytical methods. For sufficiently large $B\geqslant B_{cr}$, the fluid is unable to yield. For the flow studied, $B_{cr}\approx 0.00307$. The critical value $B_{cr}$ and the start time $t_{s}$, for $B<B_{cr}$, are wholly independent of $Ra$ and $Pr$. For $B<B_{cr}$, yielding starts at $t=t_{s}$. The flow develops into either a weakly or a 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, for progressively larger $Ra$ we observe an increasing number of distinct plume heads and a tendency for plumes to develop as short-lived pulses. Over a certain range of $(Ra,B)$ the flow becomes temporarily frozen between two consecutive pulses. Such characteristics are distinctly reminiscent of the experimental work of Davaille et al. (J. Non-Newtonian Fluid Mech., vol. 193, 2013, 144–153). The yield stress plays a multifaceted role here as it affects plume temperature, size and velocity through different mechanisms. On the one hand, increasing $B$ tends to increase the maximum temperature of the plume heads. On the other hand, for larger $B\rightarrow B_{cr}$, the plume never starts.
A novel heat transfer switch using the yield stress
- I. Karimfazli, I. A. Frigaard, A. Wachs
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- Journal:
- Journal of Fluid Mechanics / Volume 783 / 25 November 2015
- Published online by Cambridge University Press:
- 26 October 2015, pp. 526-566
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We explore the feasibility of a novel method for the regulation of heat transfer across a cavity, by using a controllable yield stress in order to suppress the convective heat transfer. Practically, this type of control can be actuated with electro-rheological or magneto-rheological fluids. We demonstrate that above a given critical yield stress value only static steady regimes are possible, i.e. a purely conductive unyielded fluid fills the cavity. We show that this limit is governed by a balance of yield stress and buoyancy stresses, here described by $B$. With proper formulation the critical state can be described as a function of the domain geometry, and is independent of other dimensionless flow parameters (Rayleigh number, $\mathit{Ra}$, and Prandtl number, $\mathit{Pr}$). On the theoretical side, we examine the conditional stability of the static regime. We derive conservative conditions on disturbance energy to ensure that perturbations from a static regime decay to zero. Assuming stability, we show that the kinetic energy of the perturbed field decays to zero in a finite time, and give estimates for the stopping time, $t_{0}$. This allows us to predict the response of the system in suppressing advective heat transfer. The unconditional stability is also considered for the first time, illustrating the role of yield stress. We focus on the hydrodynamic characteristics of Bingham fluids in transition between conductive and convective limits. We use computational simulations to resolve the Navier–Stokes and energy equations for different yield stresses, and for different imposed controls. 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 until the fluid yields and the flow restarts. We provide estimates of the hydrodynamic timescales of the problem and examples of flow transitions. In total, the theoretical and computational results establish that this methodology is feasible as a control, at least from a hydrodynamic perspective.