form, while the inertia-driven force (\[eq:fmre\_st\]) in a volume integral form. The overall agreement in the inertia-driven migration velocity indicates that capturing the bulk velocity distributions is important for predicting the migration velocity and can be robustly attained by the mirror image technique over the wide range of $\kappa$. The wide range agreement with the theories ([@vas1976; @mag2003]) was also experimentally demonstrated for the sedimenting rigid particle in a range of $0.1<{\rm Re}< 1$ by [@tak2004] as long as the wall is placed in the Stokes expansion region. Contrastingly, as shown in figure \[fig:migvel\_comp\_exp\], the larger discrepancy between the deformation-induced migration velocities of the simulation and the theory with increasing $\kappa$ indicates that the migration velocity is sensitive to the local effect leading to the additional narrow-gap repulsive force, which may not be covered by the mirror image technique.

Interfacial deformation
-----------------------

To demonstrate the narrow-gap effect, we investigate the bubble deformation. We here examine the scaled interfacial deflection $\hat{f}^{({\rm Ca})}(\theta)=f(\theta,\phi)/({\rm Ca}\ \cos\phi)$. In the experiment, we estimated $f(\theta,\phi)$ taking a circumference of the bubble on the plane $x_2=0$. Figure \[fig:scale\_deform\] shows the angular profile of the deflection $-\hat{f}^{({\rm Ca})}$ for various $\kappa (=(1+\varepsilon)^{-1})$. As shown in figure \[fig:scale\_deform\](a) for 