Simulation and theory of open-tube dispersion in short and long capillaries with slip boundaries and retention

Abstract

Using random walk techniques, high resolution simulations of zone shape are conducted in open capillary tubes for short and long tube conditions. Finite size solutes are used as tracers in this treatment. Slip flow boundary conditions and wall retention are utilized as needed. These simulations are able to reproduce previous work in short and long tubes. For the short tube case where dispersion does not asymptotically approach the classic Taylor-Aris and Golay solutions, the effect of slip flow boundaries in the transient region shows zone shapes with abbreviated tails where the larger slip flow values cause zone compression. The use of slip flow to lower dispersion in capillary-based, wall-coated separations is shown to favor long tube behavior. This is because slip flow is relevant for cases where slip lengths are fractions of small capillary tube diameters. Incorporating slip flow into transport in capillaries favors a very small capillary radius where the cross-sectional diffusion length is very small and sampling times are fast. The purely convective zone shape with slip flow boundaries is derived analytically. Applications for this type of separation, guided by both analytical theory and simulation, show the potential for nano-sized capillary tubes less than 1 μm in diameter and favor very fast isocratic separations. Using long tube retention theory with slip boundaries shows that the dispersion-reducing region is most important in the range 0 ≤ k′ ≤ 1, a relatively small retention window. Further discussion of the gradient elution technique and dispersion in packed beds suggests that the general usage of slip flow boundaries is restricted in liquid phase separation systems.