Flow onset for a single bubble in a yield-stress fluid

Abstract

We use computational methods to determine the minimal yield stress required in order to hold static a buoyant bubble in a yield-stress liquid. The static limit is governed by the bubble shape, the dimensionless surface tension ( $\gamma$ ) and the ratio of the yield stress to the buoyancy stress ( $Y$ ). For a given geometry, bubbles are static for $Y > Y_c$ , which we determine for a range of shapes. Given that surface tension is negligible, long prolate bubbles require larger yield stress to hold static compared with oblate bubbles. Non-zero $\gamma$ increases $Y_c$ and for large $\gamma$ the yield-capillary number ( $Y/\gamma$ ) determines the static boundary. In this limit, although bubble shape is important, bubble orientation is not. Two-dimensional planar and axisymmetric bubbles are studied.

Growth and stability of bubbles in a yield stress fluid

“…The blue and red dots represent the numerical results obtained for and , respectively (Pourzahedi et al. 2022). The inset of this panel indicates yield-capillary number against surface tension.…”

“…The current study follows on from a theoretical study by Pourzahedi et al. (2022), that calculated the yield limit as a function of the shape of the bubble and the surface tension of the gel, using ideal viscoplastic fluid models, i.e. inelastic.…”

“…In the theoretical framework of Pourzahedi et al. (2022), the yield limit is calculated for any specified bubble shape. Ideal viscoplastic fluid models do not allow deformation below the yield stress, so this approach is self-consistent.…”

“…From theoretical considerations (Pourzahedi et al. 2022), we expect that the onset of motion is dictated by a balance between the yield stress and the stresses arising from buoyancy and surface tension. This inelastic theory gives rise to the following dimensionless groups: and a scaled surface tension, (the inverse of the Bond number).…”

“…Pourzahedi et al. (2022) performed a comprehensive study of the yield limit for bubbles with fixed elliptical shapes. The thinner and longer the bubble is (i.e.…”