Diffusion-induced bubble growth and collapse in yield stress fluids

The dynamics of diffusion-induced bubble growth and collapse in yield stress fluids are investigated. A properly formulated model, which requires a rheological constitutive equation that allows for elastic deformation before yielding, is developed that includes as special cases bubble growth and collapse in Newtonian liquids and elastic solids. The model describes bubble growth (collapse) driven by mass diffusion from (to) the medium surrounding the bubble where mass and momentum transport are coupled through the boundary condition at the bubble-medium interface. During the initial stage of the process, the entire medium behaves like an elastic solid; when the yield stress is reached, the medium has both yielded and un-yielded regions separated by a time-dependent yield surface. Bubble growth and collapse dynamics are examined as function of the parameter N_σ=σ/G, the yield stress σ normalized by the elastic modulus G. For bubble growth (collapse), the rate of growth (collapse) in a yield stress fluid is reduced relative to the Newtonian case and decreases with increasing N_σ until the elastic case is reached.