We examine the mean flux across a homogeneous membrane of a charged tracer subject to an alternating, symmetric voltage waveform. The analysis is based on the Nernst-Planck flux equation, with electric field subject to time dependence only. For low frequency electric fields the quasi steady-state flux can be approximated using the Goldman model, which has exact analytical solutions for tracer c...

A theoretical and a mathematical model is presented to determine the entropy generation on electro-kinetically modulated peristaltic propulsion on the magnetized nanofluid flow through a microchannel with joule heating. The mathematical modeling is based on the energy, momentum, continuity, and entropy equation in the Cartesian coordinate system. The effects of viscous dissipation, heat absorpt...

We consider the limit of vanishing Debye length for ionic diffusion in fluids, described by Nernst–Planck–Navier–Stokes system. In asymptotically stable cases blocking (vanishing normal flux) and uniform selective (special Dirichlet) boundary conditions concentrations, we prove that charge density $$\rho $$ converges time to zero interior domain, ( $$\epsilon \rightarrow 0$$ ). The order limits...

We consider ionic electrodiffusion in fluids, described by the Nernst–Planck–Navier–Stokes system. prove that system has global smooth solutions for arbitrary data bounded domains with a boundary three space dimensions, following situations. consider: positive Dirichlet conditions concentrations, potential, initial and regular divergence-free velocities. Global regularity holds any positive, po...

The present study is focused on micromixing enhancement techniques for electroosmotic flows in a modulated microchannel with modified topology by utilizing heated blocks the surface of microchannel. carry higher temperatures as compared to other portions channel wall, resulting sharp variation temperature fluid. species transport governed Nernst–Planck equation form adding thermo-electrochemica...

We carry out the extended symmetry analysis of an ultraparabolic Fokker-Planck equation with three independent variables, which is also called Kolmogorov and singled within class such equations by its remarkable properties. In particular, essential Lie invariance algebra eight-dimensional, maximum dimension above class. compute complete point pseudogroup using direct method, analyze structure s...

In its most widespread, classical formulation, the Nernst–Planck– Poisson system for ion transport in electrolytes fails to take into account finite ion sizes. As a consequence, it predicts unphysically high ion concentrations near electrode surfaces. Historical and recent approaches to an approriate modification of the model are able to fix this problem. Several appropriate formulations are co...

We test the validity of the mean-field approximation in Poisson-Nernst-Planck theory by contrasting its predictions with those of Brownian dynamics simulations in schematic cylindrical channels and in a realistic potassium channel. Equivalence of the two theories in bulk situations is demonstrated in a control study. In simple cylindrical channels, considerable differences are found between the...