Clouds of bubbles in a viscoplastic fluid

Abstract

Viscoplastic fluids can hold bubbles/particles stationary by balancing the buoyancy stress with the yield stress – the key parameter here is the yield number $Y$ , the ratio of the yield stress to the buoyancy stress. In the present study, we investigate a suspension of bubbles in a yield-stress fluid. More precisely, we compute how much is the gas fraction $\phi$ that could be held trapped in a yield-stress fluid without motion. Here the goal is to shed light on how the bubbles feel their neighbours through the stress field and to compute the critical yield number for a bubble cloud beyond which the flow is suppressed. We perform two-dimensional computations in a full periodic box with randomized positions of the monosized circular bubbles. A large number of configurations are investigated to obtain statistically converged results. We intuitively expect that for higher volume fractions, the critical yield number is larger. Not only here do we establish that this is the case, but also we show that short-range interactions of bubbles increase the critical yield number even more dramatically for bubble clouds. The results show that the critical yield number is a linear function of volume fraction in the dilute regime. An algebraic expression model is given to approximate the critical yield number (semi-empirically) based on the numerical experiment in the studied range of $0\le \phi \le 0.31$ , together with lower and upper estimates.

Bubble-induced entrainment at viscoplastic–Newtonian interfaces

“…At a moderate value of Bo, the bubble experiences breakup as it enters the upper Newtonian fluid, whereas at a high Bo, the bubble undergoes breakup within the viscoplastic fluid layer, with a small portion of it remaining confined within this layer. for cases with capillary number above a Ca c (Chu et al 2019). We also see a breakup/detachment process later in the flow as the bubble rises.…”

“…During the last few decades, many theoretical and computational studies have been performed focused at determining the yield surfaces around moving objects in viscoplastic fluids (Tsamopoulos et al 2008;Sikorski, Tabuteau & de Bruyn 2009;Dimakopoulos, Pavlidis & Tsamopoulos 2013;Lopez, Naccache & de Souza Mendes 2018;Chaparian & Frigaard 2021;Pourzahedi et al 2022;Daneshi & Frigaard 2023;Kordalis et al 2023). Theoretical and computational studies amongst these are often based upon a model of ideal (or simple) viscoplastic fluids, as defined in Frigaard (2019).…”