Speaker
Description
The motion of elongated bubbles and ganglia in is frequently encountered in porous media. Although the study of confined bubbles is a canonical problem in fluid mechanics, a fundamental understanding of the problem is still an open issue when the fluids exhibit non-Newtonian behavior. Examples are biological solutions, emulsions, and polymers that behave like shear-thinning fluids, and their effective viscosity is a function of the imposed shear rate.
In this talk, we investigate the dynamics of elongated bubbles that move in an inelastic shear-thinning fluid that obeys the Carreau-Yasuda viscosity model by means of numerical simulations. We focus on regimes where inertia and buoyancy are negligible to assess the effect of the fluid rheology on bubble characteristics up to finite capillary numbers. First, we compare the results with the scaling laws obtained by lubrication theory by analyzing the trends of the film thickness and bubble speed. Then, we show the existence of a general scaling law for the effective viscosity that embeds both the zero-shear rate and shear-thinning effects and holds up to finite capillary numbers. Interestingly, the shape of the bubble is strongly influenced by the fluid rheology, which competes with the capillary number. Finally, the analysis of the viscosity fields shows an interplay between the zero-shear rate and shear thinning effects in different regions of the bubble, including the presence of recirculating vortexes that form ahead and behind the bubble.
These results clarify the effect of fluid rheology on bubble characteristics, and, although the motivation of our work is oriented toward understanding the dynamics of a single Taylor bubble, the scaling laws obtained may serve as a base for constructing more sophisticated models for trains of bubbles. We conclude by showing that the existence of a master curve for effective viscosity appears to be typical of a more general class of problems, including capillary imbibition (when a shear-thinning fluid invades a single pore) and flow in ducts with complex geometry.
| References | Steinik, C., Picchi, D., Lavalle, G., Poesio, P., (2024). Capillary imbibition of shear-thinning fluids: From Lucas-Washburn to oscillatory regimes. Physical Review Fluids, 9, 023305 Barmak, I., Picchi, D., Gelfgat, A., Brauner, N., (2024). Flow of a shear-thinning fluid in a rectangular duct. Physical Review Fluids 9, 023303 Aquino, A., Picchi, D., Poesio, P., Dynamics of a Taylor bubble through a shear-thinning fluid up to finite capillary numbers, Journal of Non-Newtonian Fluid Mechanics, 105003, Picchi, D., Ullmann, A., Brauner, N., Poesio, P., (2021) Motion of a confined bubble in a shear-thinning liquid, Journal of Fluid Mechanics, 918, A7. |
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| Country | Italy |
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