Comparison of approximate and exact description of isoviscous flow velocity profile formed in rectangular cross-section channel for field-flow fractionation

Summary

The shape of the velocity profile established in a carrier liquid flowing in a duct of rectangular cross-section under conditions of isoviscous flow is well known and can be calculated by using an approximate or the exact solution of Navier-Stokes equation. The series evaluated when applying the exact solution were found to converge very rapidly. Consequently, computing can be substantially shortened without loss of accuracy by summing only the first three terms of the series. A fair agreement between the approximate solution of Takahashi and Gill and the exact solution was obtained for all practically applicable aspect ratios of the separation channels used in field-flow fractionation. This conclusion is of interest when calculating various separation parameters in three-dimensional channels for field-flow fractionation.