Nemst-Plank equation

For electrically charged membranes and when ionic solutes are present in the feed liquid, transport for each species should be appropriately described by the general Nemst-Plank equation ... 

The molar flux of species i can be calculated using Nemst-Plank equation [15]... 

Since there is no the radial flux of ions at the surface of the capillary, we have u = 0. From the Nemst-Plank equation (5.85), there follows ... 

Transport through nanofiltration membranes is controlled primarily by electrostatic and steric interactions. The extended Nemst-Plank equation commonly is used with Donnan and steric partitioning to predict transport rates based on effective membrane charge density, pore radius, and thickness to porosity ratio [131-132]. Inclusion of solute-pore hydrodynamic interactions and a pore size distribution improves the predictive and correlative capabilities of the models [133]. 

The extended Nemst-Plank equation is applied for charged solutes and can be written as [31,39,40] ... 

Instead of the Nemst-Plank equation for the flux of ionic transportation, the equilibrium Poisson equation can be selected as the starting point for describing the electrical potential because the time required for cellular motion, electrophoresis, coagulation, and deposition is much longer than the diffusion equihbrium of ionic profile in interacting double layers [70-72]. The spatial variation in the electrostatic potential can be described by the Poisson equation... 

This model has been successfully used by Chin and Sabde [25] for crevice cathodic protection using numerical analysis based on the dilute solution theory and reduction reaction of dissolved oxygen and Aa+, Cl, and OH ions at the crevice surface. Hence, the Nemst-Plank equation, eq. (4.2), can be generalized as a differentiable and continues scalar diffusion molar flux function... 

Consider now a negatively charged cation-permeable membrane. If it behaves ideally and allows no anions and water to go through, by the Nemst-Plank equation for the cations (i =1), at the membrane-solution interface,... 

Nemst-Plank equation, drag coefficient, or Stefan-Maxwell erpiation Ohm s law... 

In the model to be presented, the Nemst-Plank relations are applied to multicomponent systems and two nonlinear differential equations have to be solved simultaneously. 

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