Dynamic Stern layers in charge-regulating electrokinetic systems : three regimes from an analytical approach

摘要: We present analytical solutions for the electrokinetic equations at a charged surface with both non-zero Stern-layer conductance and finite chemical reaction rates. have recently studied same system numerically [B.L. Werkhoven et al., Phys. Rev. Lett. 120, 264502 (2018)], shown that an applied pressure drop across leads to non-trivial, laterally heterogeneous charge distribution steady state. In this work, we linearise governing find closed expressions profile generated streaming electric field. The main results of our calculations are identification three important length time scales govern distribution, consequently classification systems into distinct regimes. can be associated (i) reaction, (ii) diffusion in Stern layer, (iii) conduction where dominating (smallest) scale characterises regime. reaction-dominated regime, constant edge effect recover Helmholtz–Smoluchowski equation. other two regimes, heterogeneity extends over entire surface, either linearly (diffusion-dominated regime) or nonlinearly (conduction-dominated regime).