Stream broadening due to fluid shear across the wider transverse dimension of a free-flow zone electrophoresis channel

While the pressure-gradient applied along the length of a free-flow zone electrophoresis (FFZE) chamber is known to produce a parabolic flow profile for the carrier electrolyte across the narrower channel dimension (typically the channel depth), additional fluid shear can arise across the channel width due to a variety of reasons. Most commonly, any variation in the pressure-drop or channel depth across this wider dimension can lead to a gradient in the liquid flow velocity along it, significantly altering the stream broadening and, thereby, the separation performance of the assay. This article assesses the effect of such fluid shear on stream broadening during the FFZE process by describing a mathematical framework for solving the relevant advection-diffusion equation based on the method-of-moments approach. A closed-form expression for the leading order term describing the additional contribution to the spatial stream variance has been derived considering a small linear gradient in the liquid velocity across the wider transverse dimension of the FFZE chamber. The noted analysis predicts this contribution to be governed by two Peclet numbers that are evaluated based on the axial pressure-driven flow and transverse electrophoretic solute velocities. More importantly, this contribution is shown to vary quadratically with the axial distance traversed by the analyte stream as opposed to the classical linear variation known for all other stream broadening contributions in FFZE systems. The results from the analytic theory have been validated with Monte Carlo simulations, which also establish a time and length scale over which the noted analytical results are applicable.