Rising and migration dynamics of an air bubble close to a wall in an elastoviscoplastic fluid

Abstract

We investigate the buoyancy-driven motion of an air bubble rising near a vertical solid wall in an elastoviscoplastic (EVP) fluid using three-dimensional direct numerical simulations. The EVP rheology is modelled via the Saramito-Herschel-Bulkley equation, capturing viscous, elastic, and plastic behaviour. Validation against prior experimental and numerical results for unbounded domains shows excellent agreement. The nearby wall induces a lateral migration to the bubble, with the velocity depending on wall distance, bubble volume, and fluid rheology. For larger bubbles, where inertia dominates, the lateral velocity is consistently positive, indicating persistent wall repulsion, and decreases with increasing wall distance. At long times, both lateral and vertical velocities collapse onto a master curve, depending only on the instantaneous wall distance. In contrast, smaller bubbles, dominated by elastic effects, exhibit a non-monotonic lateral velocity: positive near the wall but negative at larger distances, indicating the existence of an equilibrium lateral position. A parametric study highlights the role of deformability in modulating migration dynamics. More deformable bubbles show enhanced repulsion and rising velocities that depend on terminal shape: large, oblate bubbles rise more slowly due to increased cross section in the direction of flow, while smaller teardrop-shaped bubbles rise more efficiently. Increasing the yield stress strengthens the elastic response, shifting the lateral equilibrium distance closer to the wall. Conversely, decreasing the elastic modulus (softening the medium) increases the terminal velocity and enhances wall repulsion. Finally, variations in initial bubble shape and orientation affect transient deformation but have negligible influence on long-term migration or terminal state.