the wide-gap theory revealed in [@tak2009]. However, although the quantitative agreement between the interfacial deflections of the experiment and the simulation is shown in figures \[fig:scale\_deform\] and \[fig:deformationr\_kap\], the migration velocity in the experiment is still considerably higher than the simulated one. Its cause is not clear at this moment, and further joint researches among theory, numerics and experiment are needed to resolve this discrepancy problem.

Conclusion
==========

We numerically and theoretically investigated deformation-induced lateral migration of a bubble slowly rising near a vertical plane wall in a stagnant liquid. We focused on a situation with a short clearance $c$ between the bubble interface and the wall. We demonstrated that the wide-gap theory ([@mag2003]), which considers the $n=2$ deformation mode, describes the deformation-induced lift force as long as the bubble-wall gap is sufficiently wide ($a/(a+c)\ll 1$, here $a$ is the bubble radius). For the narrow-gap case with the clearance parameter $\varepsilon(= c/a)$ smaller than unity, we found that the higher-order $n\geq 3$ deformation modes crucially enhance the migration velocity, and the lubrication effect ([@hod2004]) appears to induce the migration velocity, which scales asymptotically like $V_{B3}\rightarrow {\rm Ca}\ \varepsilon^{-1}V_{B1}/25$ as $\varepsilon\rightarrow 0$. This contrasts with the case of the inertia-driven migration, 