Modeling electroosmotic and pressure-driven flows in porous microfluidic devices: Zeta potential and porosity changes near the channel walls

Abstract

This work presents analytical solutions for both pressure-driven and electroosmotic flows in microchannels incorporating porous media. Solutions are based on a volume-averaged flow model using a scaling of the Navier-Stokes equations for fluid flow. The general model allows analysis of fluid flow in channels with porous regions bordering open regions and includes viscous forces, permitting consideration of porosity and zeta potential variations near channel walls. To obtain analytical solutions problems are constrained to the linearized Poisson-Boltzmann equation and a variation of Brinkman's equation [Appl. Sci. Res., Sect. A 1, 27 (1947); 1, 81 (1947)]. Cases include one continuous porous medium, two adjacent regions of different porosities, or one open channel adjacent to a porous region, and the porous material may have a different zeta potential than that of the channel walls. Solutions are described for two geometries, including flow between two parallel plates or in a cylinder. The model illustrates the relative importance of porosity and zeta potential in different regions of each channel.

Iontophoresis From a Micropipet into a Porous Medium Depends on the ζ-Potential of the Medium

“…32 Two juxtaposed media with different ζ-potentials create pressure in an electric field. 39 When the hydrogel's ζ-potential magnitude is less than that of the capillary, there is the possibility of transport by pressure-induced flow arising from the larger ζ-potential in the pipette. When the hydraulic permeability is high in the medium with the larger ζ-potential magnitude (pipette), and the hydraulic permeability is low in the medium with the smaller ζ-potential magnitude (hydrogel), pressure-induced fluid flow in the hydrogel is likely to be small.…”

Pressure-driven and electroosmotic non-Newtonian flows through microporous media via lattice Boltzmann method

“…In order to simulate electroosmotic flow driven by the external electricity in porous media at the REV scale, due to the charge of the solid porous material in the channel, it is desirable to remove the charge density's dependence on position at the pore level. An effective charge density eff was obtained which results in the same volume flow in a single pore that would result if the actual charge density had been used [29] …”

Numerical Modeling of Electroosmotic Push–Pull Perfusion and Assessment of Its Application to Quantitative Determination of Enzymatic Activity in the Extracellular Space of Mammalian Tissue

“…EO flow in a porous medium 34–36 can be modeled as a body force resulting in a modified Darcy’s law (Eqn. 1), $$\frac{\eta }{\kappa }u+\nabla P+{\rho }_{\mathit{eff}}\nabla \varphi =0$$where η is the dynamic viscosity (Pa s), κ is the permeability (m 2 ), u is the superficial velocity (m/s), ∇ P is the pressure gradient (Pa/m), ρ eff is the effective charge density of the fluid (C/m 3 ), and ∇ ϕ is the gradient of the electric potential (V/m).…”