Parametric investigation of the Nernst–Planck model and Maxwell’s equations for a viscous fluid between squeezing plates

The Poisson–Boltzmann equation is derived from the assumption of thermodynamic equilibrium where the ionic distribution is not affected by fluid flow. Although this is a reasonable assumption for steady electroosmotic flow through straight micro-channels, there are some important cases where convective transport of ions has nontrivial effects. In these cases, it is necessary to adopt the Nernst–Planck equation instead of the Poisson–Boltzmann equation to model the internal electric field. The modeled system of equations is transformed by similarity transformation to derive the equations of flow field, electric potential, electrokinetic force, entropy generation, and energy equation. The Parametric Continuation Method (PCM) is used to solve the system of ordinary differential equations. It is concluded that decrease in the mass diffusion decreases the anion distribution from lower to upper plate. The Batchelor number decreases the strength of magnetic field. Entropy generation and the Bejan number are maximum near the two plates because of the maximum disorderness due to plate movements and have minimum value in the fluid’s center. Also the Eckert number increases viscous heating, which causes the entropy production in the vicinity of the two plates to increase.