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\subsubsection{Diffusio-phoresis}  For {\it charged} interactions, the mobility $\mu\propto 1/c$. This leads to diffusio-phoretic velocity $V = D\nabla\log c$. This arises from the balance of osmotic and viscous forces in the Debye layer. The diffusion coefficient $D \sim T/\eta\ell_{\rm B}$, where $\ell_{\rm B}$ is the Bjerrum length (ratio of electrostatic to thermal energy). Derivation of DP velocity done in \citet{http://adsabs.harvard.edu/abs/1989AnRFM..21...61A}, page 14ish.