assumptions. To complement the experiment and to gain further insight into the deformation-induced migration, we investigate the migration behavior with attention to shortness of a bubble-wall clearance $c(=d-a)$. As in [@mag2003], using two Stokes flow solutions for a spherical bubble translating parallel and perpendicular to the wall, we apply the Lorentz reciprocal theorem to evaluating the migration velocity. We carry out numerical simulations using a boundary-fitted grid, which can accurately implement the boundary conditions and release the constraint of the sufficiently wide bubble-wall gap in the mirror image technique. In addition, comparisons with a theoretical migration velocity for $\varepsilon\ll 1$ obtained from a lubrication study of a nearly spherical drop moving near a tilted plane ([@hod2004]), in which the secondary flow due to the change in the boundary geometry caused by the bubble deformation is responsible for the wall-normal force, are made to shed more light on the short clearance effect.

Numerical simulation
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General formulation {#sec:gf}
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To clarify the physical mechanism of the repulsive force, we numerically address the bubble migration. In a similar manner to [@mag2003], instead of directly solving the flow field with the deformed bubble, we employ the Lorentz reciprocal theorem to determine the lateral 