Transient molecular diffusion in microfluidic channels: Modeling and experimental verification of the results

Almost all microfluidic devices operate at non-equilibrium transient conditions. Quantitative predictions regarding fluid flow within the components of such devices at the assumed conditions are a prerequisite for their systematic design. Here, we present a mathematical model for the transient dynamics of a target molecule (TM) diffusing along a microfluidic channel driven by a time-varying concentration gradient, and experimentally verify its predictions on a number of case studies. The model is the outcome of coupling the free molecular diffusion equation and Langmuir surface adsorption isotherm, both of which hold the specific geometrical and operational features of the microfluidic system at isothermal and isobar conditions. The TM flux fluctuations, caused by a sudden change in the imposed boundary conditions, are predicted to be highly uneven along the microchannel for a long time after the event. In complicated cases, such as a pulse train TM concentration modulation at the inlet of a background gas-filled microfluidic channel, the model correctly predicts the experimental results in both “diffuse-in” and “diffuse-out” conditions.