the relatively wide gap $\varepsilon=0.67$, the analytical solution for $\kappa\ll 1$ ([@mag2003]) is consistent with the measured and simulated deflections. Note that the agreement between the theoretical and simulated deflections is confirmed to be better in the wider separation. For the narrower gap ($\varepsilon=0.10$, $0.25$), by contrast, the analytical solution of the deflection magnitude is smaller than the measured one especially in the wall neighborhood ($\theta\sim 0$), which may be related to the considerable underestimation of the migration velocity as shown in figure \[fig:migvel\_comp\_exp\]. Contrastingly, the present simulation quantitatively captures the local near-wall profile of the measured deflection as well as the global magnitude.

To quantify the local effect of such a large discrepancy in $\hat{f}^{({\rm Ca})}$ on the migration velocity, we here describe the deflection in an expansion form $$\hat{f}^{({\rm Ca})}(\theta)=
\sum_{n=2}^\infty
\hat{f}_n^{({\rm Ca})}
P_n^1(\cos\theta),$$ where $P_n^1$ represents the associated Legendre polynomial. Figure \[fig:deformationr\_kap\] shows the modal deflections $\hat{f}_n^{({\rm Ca})}$ for $2\leq n\leq 5$ as a function of $\kappa$. The simulation results are consistent with the measured deflections for all the shown modes. In predicting the bubble migration, the wide-gap theory ([@mag2003]) assumes that the mirror image primarily induces the deformation of the mode $n=2$. The leading-order of the 