Reduced-order model for solute transport in mixed electro-osmotic and pressure-driven flows of viscoelastic fluids in microchannels

The solute transport due to mixed electro-osmotic and pressure-driven flows of viscoelastic fluids in microchannels is studied here. The Reynolds decomposition technique, in combination with the assumptions underlying the Taylor-Aris theory, is used to derive a reduced-order model that yields the dispersion coefficient, which is then solved using the general Duhamel theorem to obtain the cross-sectional average concentration. The dispersion is evaluated for the general case of mixed electro-osmotic and pressure-driven flows of viscoelastic fluids, and for three special cases: combined electro-osmotic and pressure-driven flows of a Newtonian fluid, electro-osmotic flow of a viscoelastic fluid, and pressure-driven flow of a viscoelastic fluid. The dispersion coefficient is characterized by four main nondimensional parameters: the ratio of advection to diffusion (Pe), the inverse of the electric double-layer thickness (κ), the ratio of pressure-driven to electro-osmotic forces (λ), and the fluid viscoelasticity (ɛDe^{2}). As expected, the larger the Peclet number, the greater the dispersion for fixed λ and ɛDe^{2} values. It is generally observed that the dispersion coefficient increases as the fluid viscoelasticity increases, for constant values of the Peclet number and the ratio of pressure-driven to electro-osmotic forces. The results also indicate that the dispersion exhibits nonmonotonic behavior as λ increases from negative to positive values, for fixed Peclet number and fluid viscoelasticity. The dispersion coefficient and the cross-sectional average concentration are examined for special cases and compared with the general case. The developed mathematical model and findings have implications for the design of solute transport in microfluidic systems.