Derivation of dispersion coefficient in an electro-osmotic flow of a viscoelastic fluid through a porous-walled microchannel

An analytical expression for the dispersion coefficient in an electro-osmotic flow of a viscoelastic fluid (which obeys the simplified Phan-Thien-Tanner rheological model) through a porous-walled microchannel is theoretically developed. The decomposition technique in combination with the assumptions behind the Taylor-Aris theory of the solute species dispersion is used to derive the dispersion coefficient in a porous-walled microchannel. The microchannel-porous medium interaction via the exchange of the solute species between the two media is included in derivation of the dispersion coefficient in a porous-walled microchannel. In other words, the continuity of the solute species concentration and its flux is considered at the interface between the microchannel and the porous medium. The developed dispersion coefficient in a porous-walled microchannel is a function of three parameters, which characterize the Peclet number, the fluid elasticity, and the nondimensional Debye-Flfickel parameter. The proposed model is also capable to deliver the dispersion coefficient in a nonporous-walled microchannel (where a no-flux boundary condition is considered at the walls), which is in agreement with the existing model in literature. (C) 2019 Elsevier Ltd. All rights reserved.