Shear dispersion in combined pressure‐driven and electro‐osmotic flows in a capillary tube with a porous wall

Abstract

An analytical expression is derived for the shear dispersion during transport of a neutral nonreacting solute within a coupled system comprised of a capillary tube and a porous medium under the combined effects of pressure‐driven and electro‐osmotic flows. We use the Reynolds decomposition technique to obtain a dispersion coefficient by considering a sufficiently low wall or zeta potential that accounts for the combined flows. The coupled dispersion coefficient depends on the Debye–Hückel parameter, Poiseuille contribution fraction, and Péclet number. The developed model also provides a shear dispersion coefficient for an impervious capillary tube (noncoupled system). The ratio of the coupled (porous wall) and noncoupled (impervious) dispersion coefficients reveals that it is essential to include the transport of chemical species from the tube to the porous medium in several important physical situations. These findings have implications for design of chemical species transport in porous microfluidic networks and separation of emulsions in microchannel‐membrane systems. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3981–3995, 2015

Effect of pore geometry on nanoconfined water transport behavior

“…Considering water slip phenomenon, the boundary condition of water transport through elliptical nanopores can be described by the following equation. [55][56][57] v…”

A reduced‐order model for chemical species transport in a tube with a constant wall concentration

“…[9][10][11][12][13]20,24] A detailed review of these assumptions can be found elsewhere. [12,13] By taking into consideration these assumptions and using Equation (2) and making some rearrangements, Equation (7) reduces to the following:…”

“…Now, we apply three significant assumptions adopted from Taylor [14] and Fischer et al [20] for determination of a dispersion coefficient during dispersive chemical species transport. These assumptions are as follows: the chemical species transport occurs under a quasisteady state condition (@C 0 D =@t D % 0), [9][10][11][12][13][14][20][21][22][23] C 0 D is a slowly varying function, [20] and the longitudinal advection is dominant compared to the longitudinal diffusion (…”

“…Recently, Dejam et al [9][10][11][12][13] presented analytical expressions for dispersion during transport of a chemical species in two different double-porosity systems with two-dimensional linear [9,10,13] and radial [11][12][13] geometries comprised of a channel [9,10,13] or tube [11][12][13] and a porous medium under the combined effects of pressure-driven [9][10][11][12][13] and electroosmotic [10,11,13] flows. Their developed models also provided dispersion coefficients for two-dimensional linear and radial geometrical conduits with a no-flux boundary condition at the walls.…”

“…Webster et al [15] also implemented the same methodology to address effective macroscopic transport parameters between parallel plates with constant concentration boundaries. The presented work can find applications in understanding the chemical reactive transport, [16] describing the transport in a conduit with solute stored in the porous matrix block, [9][10][11][12][13]17] and modelling of non-aqueous phase liquid (NAPL) dissolution. [18] However, the following main features make this study distinct from previous theoretical studies.…”