Molecular diffusive scaling laws in pressure-driven microfluidic channels: deviation from one-dimensional Einstein approximations

This study presents a theoretical analysis of the scaling laws for analyte diffusion in a microfluidic chemical analysis device, the T-sensor. Because the flow is pressure-driven, the velocity profile is non-uniform, inducing a distribution in residence time among analyte molecules. Solutions for concentration distribution are given from the device inlet to a downstream distance where variations in the scaling law become negligible. All data were generated using a custom two-dimensional model that describes convection and diffusion in a system of two fluids running side-by-side in a duct. These results deviate substantially from those expected by simpler calculations, including a one-dimensional model. This study lends a better understanding of the transport of analytes diffusing in microchannels and provides a means for determining whether the complicated effects need to be considered in device design and operation.