On the lateral migration of a slightly deformed bubble rising near a vertical plane wall

Abstract

Deformation-induced lateral migration of a bubble slowly rising near a vertical plane wall in a stagnant liquid is numerically and theoretically investigated. In particular, our focus is set on a situation with a short clearance $c$ between the bubble interface and the wall. Motivated by the fact that numerically and experimentally measured migration velocities are considerably higher than the velocity estimated by the available analytical solution using the Faxén mirror image technique for $a/(a+c)\ll 1$ (here $a$ is the bubble radius), when the clearance parameter $\epsilon (=c/a)$ is comparable to or smaller than unity, the numerical analysis based on the boundary-fitted finite-difference approach solving the Stokes equation is performed to complement the experiment. The migration velocity is found to be more affected by the high-order deformation modes with decreasing $\epsilon$. The numerical simulations are compared with a theoretical migration velocity obtained from a lubrication study of a nearly spherical drop, which describes the role of the squeezing flow within the bubble-wall gap. The numerical and lubrication analyses consistently demonstrate that when $\epsilon \le 1$, the lubrication effect makes the migration velocity asymptotically $\mu V_{B1}^2/(25\epsilon \gamma )$ (here, $V_{B1}$, $\mu$, and $\gamma$ denote the rising velocity, the dynamic viscosity of liquid, and the surface tension, respectively).

24 pages, 9 figures, J. Fluid Mech. (accepted)

References in corpus (4)

• Soft lubrication: the elastohydrodynamics of non-conforming and conforming contacts
• Soft lubrication
• Hydrodynamic lift of vesicles under shear flow in microgravity
• The lift on a tank-treading ellipsoidal cell in a bounded shear flow

Cited by in corpus (3)

• Lift at low Reynolds number
• Bubble rising near a vertical wall: experimental characterization of paths and velocity
• Enhanced axial migration of a deformable capsule in pulsatile channel flows