Mechanical mobility
= Mechanical mobility
{title2=$\mu_{\mathrm{mech}}=v_{\mathrm{drift}}/F=1/\zeta$}
Mechanical mobility relates a steady drift <velocity> to a weak applied mechanical <force>. For isotropic <linear drag> $-\zeta\mathbf v$, terminal force balance gives $\mathbf v_{\mathrm{drift}}=\mu_{\mathrm{mech}}\mathbf F$ with $\mu_{\mathrm{mech}}=1/\zeta$, in units $\mathrm{s\,kg^{-1}}$. For a sphere obeying <Stokes's law>, it is $1/(6\pi\eta R)$. The corresponding translational <hydrodynamic mobility matrix> is $\mu_{\mathrm{mech}}I$. The <Stokes–Einstein relation> reads $D=k_BT\mu_{\mathrm{mech}}$, and the <velocity relaxation time> is $m\mu_{\mathrm{mech}}$. In the bare-force spherical model, a particle with <electric charge> $q$ has <electrophoretic mobility> $\mu_{\mathrm{ep}}=q\mu_{\mathrm{mech}}$; ionic-atmosphere effects can modify that simple model.