Dipolar surfactant distribution ($C^{\prime }=B\mathbf{U}\cdot \mathbf{n}$)

Linear steady transport on a translating sphere gives $B=2A{C}_{0}a/(k{a}^2+2D_s)$. The components of its unit normal vector are degree-one spherical harmonics. The condition $2|A|Ua/(k{a}^2+2D_s)\ll 1$ ensures the concentration perturbation is small relative to $C_0$.