A formula (13) is the same form as Fick's law, in which the term RTLi/ci represents the diffusion coefficient (Di), thus, Integrating over the thickness of the membrane (l) then gives. Convection prevails in a porous medium rather than dense membranes. A flux of mass caused by hydrostatic pressure gradient (dP/dx) is described by the Hagen-Poiseuille law: A flux of individual components caused by concentration gradient (dC/dx) is described by Fick's law: and a flux of electrical charges caused by an electrical potential gradient (dφ/dx) is described by Ohm's law: where J is the flux, Lp hydrodynamic permeability, P is the pressure, D the diffusion coefficient, C the concentration, κ the electrical conductivity, φ the electrical potential, and the subscripts v, i, and e denote volume, individual component, and electrical charges, respectively. Assuming the channel height, h, is always less than or equal to width, w, the resulting approximation is, where h is viscosity and C is a correction factor that takes into account the relative aspect ratio of each channel. This is the currently selected item. Using the above equations, the software determines and applies the appropriate pressure. Diffusion governs in the homogeneously dense RO and ion-exchange membranes, in which electroneutrality of an aqueous solution is sustained due to transport of the ions such as cations and anions in the same direction with the equivalent magnitude. Consider a liquid of co-efficient of viscosity η flowing, steadily through a horizontal capillary tube of length / and radius r. If P is the pressure difference across the ends of the tube, then the volume V of the liquid flowing per second through the tube depends on n. r and the pressure gradient (P/∫). 6 and 7. Convective flow is transport of the solute with solvent molecules caused by mechanical force such as a hydrostatic pressure difference across the membrane interfaces (i.e., feed and permeates side). Stay tuned with BYJU’S for more such interesting articles. For flow at low Reynolds numbers, the Navier–Stokes equation was simplified to. Hence, based on the properties of a real membrane, the flux for each component (i) through the NF membrane is determined by the Extended Nernst-Plank equation (ENP) in terms of diffusion, electromigration, and convection . It is an equivalent of the Hagen-Poiseuille law for a turbulent regime of flow. ScienceDirect ® is a registered trademark of Elsevier B.V. ScienceDirect ® is a registered trademark of Elsevier B.V. URL: https://www.sciencedirect.com/science/article/pii/B9780128142387000234, URL: https://www.sciencedirect.com/science/article/pii/B9781927885215500096, URL: https://www.sciencedirect.com/science/article/pii/B9780128137222000182, URL: https://www.sciencedirect.com/science/article/pii/S0167892297800697, URL: https://www.sciencedirect.com/science/article/pii/B9781455731411500174, URL: https://www.sciencedirect.com/science/article/pii/B9780080925912500145, URL: https://www.sciencedirect.com/science/article/pii/B978185617458950004X, URL: https://www.sciencedirect.com/science/article/pii/B9780444530219500026, URL: https://www.sciencedirect.com/science/article/pii/B9781437734591000156, URL: https://www.sciencedirect.com/science/article/pii/B9780128139264000380, Biermann's Handbook of Pulp and Paper (Third Edition), Prof. Dr.Alexander Ya.