A method-of-moments formulation for describing hydrodynamic dispersion of analyte streams in free-flow zone electrophoresis

In this work, a method-of-moments formulation has been presented for estimating the dispersion of analyte streams as they migrate through a free-flow zone electrophoresis (FFZE) channel under laminar flow conditions. The current analysis considers parallel-plate based FFZE systems with an applied pressure-gradient along the channel length for sample and carrier electrolyte transport, and an external electric field in the transverse direction for enabling the electrophoretic separation. A closed-form expression has been derived using this mathematical approach for describing the spatial variance of sample streams as a function of their position in the separation chamber at steady state. This expression predicts that the hydrodynamic dispersion component in an FFZE assay scales as Pex2 where Pex denotes the Péclet number based on the analyte's transverse electrophoretic migration velocity rather than its longitudinal pressure-driven flow speed as expected in transport processes induced by a pressure-gradient. Interestingly however, the coefficient multiplying this dimensionless group, i.e., 1/210, is identically equal to the constant preceding the square of the relevant Péclet number in the latter case (i.e., Péclet number based on the longitudinal flow speed). It must be noted that while the mathematical analysis reported in this work is only valid for FFZE systems in the absence of any unwanted Joule heating, pressure-driven cross-flow and/or differences in the electrical conductivity between the sample and carrier electrolyte, it can also be applied to numerically estimate the effect of these factors on the separation resolution of the assay.