A semi-analytical model for species transport in combined electroosmotic and pressure driven microflows with surface adsorption-desorption reactions

We derive semi-analytical solutions for solutal concentration distribution in microfluidic channels under the combined action of pressure-driven and electroosmotic transport, considering the effects of adsorption-desorption reactions at the substrate-fluid interface. Within the pertinence of common bio-microfluidic applications, we obtain the spatio-temporal evolution of analyte concentration by solving the corresponding eigen value problems on species transport with non self-adjoint operators, yielding non-orthogonal eigen functions. We analyze the implications of the relative strengths of the pressure-driven and electroosmotic flow components towards dictating the strongly interconnected reaction-advection-diffusion transport. We also discuss various interesting limiting cases, including the situations in which the solutal concentration band effectively propagates in the microchannel as a shock front. For such cases, we obtain the propagation velocity of the band as an explicit function of the relative strengths of the respective flow actuation mechanisms and the other significant parameters pertinent to the surface reactions.