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Deformation-induced lateral migration of a bubble slowly rising near avertical plane wall in a stagnant liquid is numerically and theoreticallyinvestigated. In particular, our focus is set on a situation with a shortclearance $c$ between the bubble interface and the wall. Motivated by the factthat numerically and experimentally measured migration velocities areconsiderably higher than the velocity estimated by the available analyticalsolution using the Fax\'{e}n mirror image technique for $a/(a+c)\ll 1$ (here$a$ is the bubble radius), when the clearance parameter $\varepsilon(= c/a)$ iscomparable to or smaller than unity, the numerical analysis based on theboundary-fitted finite-difference approach solving the Stokes equation isperformed to complement the experiment. The migration velocity is found to bemore affected by the high-order deformation modes with decreasing$\varepsilon$. The numerical simulations are compared with a theoreticalmigration velocity obtained from a lubrication study of a nearly sphericaldrop, which describes the role of the squeezing flow within the bubble-wallgap. The numerical and lubrication analyses consistently demonstrate that when$\varepsilon\leq 1$, the lubrication effect makes the migration velocityasymptotically $\mu V_{B1}^2/(25\varepsilon \gamma)$ (here, $V_{B1}$, $\mu$,and $\gamma$ denote the rising velocity, the dynamic viscosity of liquid, andthe surface tension, respectively).

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