Mass transfer effects during bubble mobilisation in yield stress fluids via pressure reduction

Recent experiments by Daneshi & Frigaard ( J. Fluid Mech. , vol. 957, 2023, p. A16) examined the response of an initially spherical, stationary bubble in an elastic yield-stress material to stepwise ambient-pressure variations under two protocols. In the first protocol, pressure decreases and the bubble swells, elongates, and mobilises. In the second protocol, pressure decreases then increases; the bubble stays stationary, but its volume shows hysteresis between the two phases. This hysteresis was attributed to elastic non-recoverable strain. In the present study, we numerically investigate these two protocols, accounting for elasticity, residual stresses and nonlinear viscoelastic deformation before yielding, using the Saramito–Herschel–Bulkley model. In the first protocol, assuming constant bubble mass yields clear deviations from experiments in ( a ) the bubble radius evolution, ( b ) the pressure–volume product at different pressures and ( c ) the bubble mobilisation. These deviations are resolved by including mass transfer of gas from the surrounding material, which increases bubble mass. This is caused by the pressure reduction, which decreases the gas concentration at the bubble interface below the ambient value, generating a mass influx. In the second protocol, we demonstrate that hysteresis can be predicted only when mass transfer is included. Finally, we propose a simplified model to predict the bubble dynamics during either pressure protocol, which can also be used to extract the mass-transfer properties of gas–fluid systems in yield stress materials.