Experimental and theoretical scaling laws for transverse diffusive broadening in two-phase laminar flows in microchannels

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Abstract
This letter quantifies both experimentally and theoretically the diffusion of low-molecular-weight species across the interface between two aqueous solutions in pressure-driven laminar flow in microchannels at high Péclet numbers. Confocal fluorescent microscopy was used to visualize a fluorescent product formed by reaction between chemical species carried separately by the two solutions. At steady state, the width of the reaction–diffusion zone at the interface adjacent to the wall of the channel and transverse to the direction of flow scales as the one-third power of both the axial distance down the channel (from the point where the two streams join) and the average velocity of the flow, instead of the more familiar one-half power scaling which was measured in the middle of the channel. A quantitative description of reaction–diffusion processes near the walls of the channel, such as described in this letter, is required for the rational use of laminar flows for performing spatially resolved surface chemistry and biology inside microchannels and for understanding three-dimensional features of mass transport in shearing flows near surfaces.