this problem. As a possible factor causing the inconsistency, we raise a difference between the bubble deformation levels of the experiment and the present analysis. As stated in §\[sec:abe\_lub\], the infinitesimal deformation assumption in the lubrication limit is justified only for the case that $\delta(=\varepsilon^{-3/2}{\rm Ca})\ll 1$. Beyond this limitation, unexplored hydrodynamic ingredients possibly become important on the bubble migration. For the experimental data shown in figure \[fig:migvel\_comp\_exp\] and figure \[fig:migvel\_comp\_lub\], the maximum value of $\delta$ is $0.74$, which is less than but comparable to unity. Therefore, the bubble deformation is finite rather than infinitesimal, and is likely to induce the higher-order force, which is possibly comparable to or stronger than the leading migration force evaluated with the infinitesimal deformation theories. From the theoretical viewpoint, a tiny bubble experiment, which results in a tiny capillary number and thus a tiny deformation, is favorable for comparative study. However, such an experiment has often resulted in an undetectably low migration velocity and made an accurate measurement difficult. To overcome such a dilemma, the highly accurate boundary element computations (e.g. [@wan2006; @dim2007]) for various deformation levels would be helpful to complement the infinitesimal deformation theories.

We thank Shu Takagi for fruitful discussion.

Finite-difference 