Analytical solutions for the rate of DNA hybridization in a microchannel in the presence of pressure-driven and electroosmotic flows

Abstract

The present study develops closed-form expressions depicting the rate of DNA hybridization in the presence of electroosmotic and pressure-driven flows in a microchannel. The model assumes a diffusion-reaction mechanism of DNA hybridization using second-order hybridization kinetics. Analytical solutions of the pertinent partial differential equation of species conservation are established under time dependant reactive boundary conditions at the channel walls, describing the concentration variation in the presence of both advection and diffusion fluxes. From the analytical solutions, it is revealed that a saturation state of the hybridization reaction is obtained faster in a pure electroosmotic flow, as compared to the case of a pressure-driven flow. A further assessment of the present solutions also reveals very good agreements with full-scale numerical solutions.