Helmholtz-Smoluchowski electro-osmotic velocity
= Helmholtz-Smoluchowski electro-osmotic velocity
{c}
{title2=$U=-\varepsilon\zeta E/\eta$}
In a half-space with no <pressure> gradient, Stokes balance and Poisson electrostatics give $\eta v\prime\prime=\varepsilon E\psi\prime\prime$. No slip at the wall and zero bulk shear imply $v=\varepsilon E(\psi-\zeta)/\eta$. The bulk <velocity> is $U=-\varepsilon\zeta E/\eta$; it is not the fluid speed at the no-slip wall.