Traction of translating-sphere Papkovich–Neuber potentials (source code)

= Traction of translating-sphere Papkovich–Neuber potentials
{title2=$\sigma n=(6\mu/a)[\beta U+(\alpha-3\beta)(U\cdot n)n]$}

For $\Phi=U+\alpha aU/r$ and $\chi=\beta a^3U\cdot\nabla(1/r)$ in the <Unscaled Papkovich–Neuber representation>, the <Newtonian fluid stress tensor> gives the displayed traction at $r=a$. The $\alpha$ contribution is the <Stokeslet> stress; the $\beta$ contribution is twice the viscosity times the Hessian of its harmonic scalar potential. The prefactor is $6\mu/a$, not $12\mu/a$. The rigid translating-sphere limit is a direct normalization check.