Broadening of analyte streams due to a transverse pressure gradient in free-flow isoelectric focusing

Pressure-driven cross-flows can arise in free-flow isoelectric focusing systems (FFIEF) due to a non-uniform electroosmotic flow velocity along the channel width induced by the pH gradient in this direction. In addition, variations in the channel cross-section as well as unwanted differences in hydrostatic heads at the buffer/sample inlet ports can also lead to such pressure-gradients which besides altering the equilibrium position of the sample zones have a tendency to substantially broaden their widths deteriorating the separations. In this situation, a thorough assessment of stream broadening due to transverse pressure-gradients in FFIEF devices is necessary in order to establish accurate design rules for the assay. The present article describes a mathematical framework to estimate the noted zone dispersion in FFIEF separations based on the method-of-moments approach under laminar flow conditions. A closed-form expression has been derived for the spatial variance of the analyte streams at their equilibrium positions as a function of the various operating parameters governing the assay performance. This expression predicts the normalized stream variance under the chosen conditions to be determined by two dimensionless Péclet numbers evaluated based on the transverse pressure-driven and electrophoretic solute velocities in the separation chamber, respectively. Moreover, the analysis shows that while the stream width can be expected to increase with an increase in the value of the first Péclet number, the opposite trend will be followed with respect to the latter. The noted results have been validated using Monte Carlo simulations that also establish a time/length scale over which the predicted equilibrium stream width is attained in the system.