is the nabla operator along the tangential directions on the bubble surface, $\langle ...\rangle_{S_B}$ is the area average taken over the bubble surface, and $x_1$ is the coordinates in the upward direction from the origin at the bubble centroid. Kinematic and free-slip conditions are imposed on the bubble surface, i.e. $$\left.
\begin{array}{rl}
{\bm n}\cdot{\bm U}&=0,\\
({\bm n}\cdot{\bm\Sigma})\times{\bm n}&=0,\\
{\bm n}\cdot{\bm u}&=0,\\
({\bm n}\cdot{\bm\sigma})\times{\bm n}&=0,\\
\end{array}
\right\}
\ \ {\rm at}\ \ \sqrt{x_1^2+x_2^2+x_3^2}=1,
\label{eq:bc_bubsurf_st}$$ where we take the reference frames viewed from the bubble. On the plane wall, we impose the no-slip condition $$\left.
\begin{array}{rl}
{\bm U}&=-{\bm e}_1,\\
{\bm u}&={\bm e}_3,
\end{array}
\right\}
\ \ {\rm at}\ \ x_3=-1-\varepsilon.
\label{eq:wall_st}$$ Sufficiently far from the bubble, the velocity vectors approach the uniform velocities $$\left.
\begin{array}{rl}
{\bm U}&\rightarrow -{\bm e}_1,\\
{\bm u}&\rightarrow {\bm e}_3,\\
\end{array}
\right\}
\ \ {\rm as}\ \ \sqrt{x_1^2+x_2^2+x_3^2}\rightarrow \infty.
\label{eq:far_st}$$ Thanks to the reciprocal theorem ([@lea1980]; (35) of [@mag2003]), the deformation-induced lateral force $F_M={\rm Ca}F_M^{({\rm Ca})}$ to cancel the migration velocity and to maintain the wall-parallel motion is expressed as $$F_{M}^{({\rm Ca})}=
\oint_{S_B}\!\!\!\!\!{\rm d}^2{\bm x}\ 
{\cal L}(f^{({\rm Ca})}),
\label{eq:fmca_st}$$ where $S_B$ denotes the bubble surface, and the operator ${\cal L}$ is given by $$\begin{split}
&{\cal L}=
{\bm n}\!\cdot{\bm \sigma}\!\cdot{\bm 