migration force and velocity through coupling two flow fields around a spherical bubble translating parallel and perpendicular to the wall. In the subsequent developments, the basic equations and the involved variables are nondimensionalized using $a$, $V_{B1}$ and $\mu$. We suppose that the bubble quasi-steadily rises near an infinite flat plate in a stagnant incompressible liquid, and both the Reynolds and capillary numbers are sufficiently smaller than unity. Hence, the system is described by the steady Stokes equation for solenoidal velocity vectors, i.e. $$\nabla\cdot{\bm U}=\nabla\cdot{\bm u}=0,
\ \ \ -\infty<x_1<\infty,\ -\infty<x_2<\infty,\ -1-\varepsilon\le x_3<\infty,
\label{eq:cont_st}$$ $$\nabla\cdot{\bm \Sigma}=\nabla\cdot{\bm \sigma}=0,
\ \ \ -\infty<x_1<\infty,\ -\infty<x_2<\infty,\ -1-\varepsilon\le x_3<\infty,
\label{eq:mom_st}$$ where $({\bm U},{\bm \Sigma})$ and $({\bm u},{\bm \sigma})$ are the velocity and stress fields for the bubble translating respectively parallel and perpendicular at a speed of unity to the wall. The ${\rm Ca}$ dependence of the interfacial deflection is given by $f(\theta,\phi;{\rm Ca})\ ={\rm Ca}f^{({\rm Ca})}(\theta,\phi)$. The bubble deformation obeys the Laplace law for the infinitesimal deflection $|f|\ll 1$ with ${\rm Ca}\ll 1$, $$\left(\nabla_s^2+2\right)f^{({\rm Ca})}=
-{\bm n}\cdot{\bm\Sigma}\cdot{\bm n}
+3x_1 \langle x_1{\bm n}\cdot{\bm \Sigma}\cdot{\bm n}\rangle_{S_B}
\ \ {\rm at}\ \ \sqrt{x_1^2+x_2^2+x_3^2}=1,
\label{eq:laplace_law}$$ where ${\bm n}$ represents the normal unit vector pointing outwards the liquid, $\nabla_s(=\nabla-{\bm n}({\bm n}\cdot\nabla))$ 