Hydrodynamic interaction between coaxially rising bubbles in elastoviscoplastic materials: Equal bubbles

We consider the buoyancy-driven rise and interaction between two coaxially placed bubbles of equal size and constant volume that are initially stationary inside an elastoviscoplastic material. We simulate the material using the Saramito extension of the Herschel-Bulkley constitutive model, and we fit its properties to a 0.1% aqueous Carbopol solution. The interplay between plasticity, viscoelasticity, and inertia is investigated. We observe that a "bridge" of shear stresses develops, which connects the leading and the trailing bubble, decreasing the drag force on the latter and initiating their approach. The solidlike behavior of the material preserves stresses generated by the passage of the leading bubble and makes the material "softer" for the trailing bubble. At the same time the normal stresses primarily extend the bubbles, but their finite distance eventually causes the leading bubble to adopt a hydrodynamically less favorable shape that slows it down, further promoting the approach. Moreover, we examine the effect of the geometric characteristics and the material properties. Increasing the initial distance between the bubbles delays their approach, which, however, is inevitable. Increasing the radius results in a transition from the elastoplastic to a mixed elastoplastic-inertial regime and a delayed approach. Increasing elasticity or the shear and extension thinning of the material decreases the approach time. On the contrary, an increased viscosity delays their approach. Finally, varying the yield stress induces a nonmonotonic effect. Sufficiently small values of yield stress delay the approach compared to intermediate values, because it reduces the elastic response. Raising the yield stress slightly above the entrapment conditions of a single bubble, the bubbles still interact and move.