Hydrodynamics rheological impact of an oscillatory electroosmotic flow on a mass transfer process in a microcapillary with a reversible wall reaction

In this work, we carry out a theoretical analysis of the mass transport rate through a long microcapillary, with a reactive wall, connecting two reservoirs with different concentrations of some electro-neutral solute, caused by an oscillatory electroosmotic flow of a Jeffreys fluid. The mass transport enhancement relative to that caused only by molecular diffusion is found to be a function of the following dimensionless parameters: the angular Reynolds number Rω; the Deborah numbers De1 and De2, associated with the relaxation and retardation times, respectively; the Schmidt number Sc; the Damköhler number Da; the partition number σ the tidal displacement ΔZ; and the ratio between the radius of the microcapillary and the Debye length κ. We find that for a viscoelastic fluid, there exists a resonant behavior of the mass transfer rate when the angular Reynolds number assumes specific values. In this context, we evidence that the interaction between the fluid elasticity and the oscillatory character of the flow enhances the mass transfer rate up to several orders of magnitude compared with that caused by an oscillatory electroosmotic flow of a Newtonian fluid. We also found that the microcapillary wall's reactive characteristics, manifested through the Damköhler number and the dimensionless partitioning coefficient, could enhance or diminish the mass transfer rate depending on the interplay of the other dimensionless parameters involved in the analysis.