= Quadrupolar surfactant distribution on a spherical interface
For radius $a$ and tangential velocity $\mathbf u_s=\mathbf I_s\mathbf A\mathbf x$ with symmetric traceless $\mathbf A$, the <surface divergence> is $-3\mathbf n\cdot\mathbf A\mathbf n$. At small surface <Péclet number> $a^2|\mathbf A|/D_s$, neglecting advection of the concentration perturbation gives
$$
C-C_0=\frac{C_0a^2}{2D_s}\mathbf n\cdot\mathbf A\mathbf n.
$$
The result follows because this quadratic is a degree-two <spherical harmonic> with <surface Laplacian> $-6/a^2$ times itself and zero spherical mean.
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