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Dynamics and rheology of sheared two-dimensional foam

University of British Columbia
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  • Mathematics


Using a shear cell device, we have studied four associated problems in foam by experiments: Bubble-bubble coalescence in sheared two-dimensional foam; lateral migration of a single large bubble in an otherwise monodisperse foam; size segregation of bubbles in sheared bidisperse foam; and the effect of non-Newtonian rheology of foam on lateral migration of bubble. For bubble-bubble coalescence in sheared two-dimensional foam, we observed a threshold of shear rate beyond which coalescence of bubbles happens. The most promising explanation was the model based on the centripetal force with qualitative agreement with experimental results. Next we studied the dynamics of monodisperse foam in the presence of a single bubble whose size is different from the neighboring bubbles. We reported the lateral migration of a larger single bubble away from the wall. We also reported thresholds of shear rate and bubble size ratio beyond which migration occurs. In this study we modified the Chan-Leal model and predicted the experimental trajectories of migrating bubbles. For bidisperse foams, we reported evolution in foam structure to a size segregated structure, in which large bubbles accumulate at the middle of the gap whereas smaller ones close to walls. Then, we adopted a model based on convection-diffusion equation to account for both lateral migration and shear induced diffusion. Finally, we extended the second work by widening the gap of Couette coaxial cylinder geometry. Similar to the second work, we found that large bubble migrates laterally to an equilibrium position close to the inner wall. We believe this new mechanism is the non-Newtonian feature of foam. We characterized our foam by measuring its degree of shear thinning and also estimated its elasticity based on the literature data on foam. Then, we found out for a shear thinning fluid bubble migrated to position even closer to the inner wall than in the foam while a bubble in Boger fluid migrated to a position closer to the outer cylinder. Therefore, for a viscoselastic fluid which has the same feature one would expect to see bubble migration to a position between these two for two fluids.

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