(458e) Predicting Electrohydrodynamic Flow Rates in Capillaries: Effect of Geometry and Electrostatic Potential

Electrokinetic-based methods are used in a variety of applications including drug delivery and separation of biomolecules, among others. Many of these applications feature a fibrous or a porous medium that can be modeled by using capillary bundle models to predict the behavior of the flow rates within the particular system. It is often assumed that, within these bundles, capillaries of idealized geometries exist, including rectangular, cylindrical, and annular. Predicting flows in capillaries may be accomplished by applying the principles of electrokinetics in conjunction with hydrodynamics. In this project, capillaries of rectangular and cylindrical geometries are examined, for which velocity profiles are determined and parametrically studied. Afterwards, the flow rates are computed. In order to gain a deeper understanding of how these predictions differ according to the geometries used, the two situations described below are studied.

First, analytical velocity profiles are determined for all three geometries. Specifically, velocity profiles with a 1D spatial dependence are described. From these velocity profiles, volumetric flowrates can be computed for each geometry. Finally, the rectangular geometry capillary can be compared to the cylindrical and annular geometry capillaries through a geometrical analysis relating the cross sectional areas of the three different geometries.

The presentation will describe details of the two cases identified above (i.e. rectangular vs. cylinrical and rectangular vs. annular). The analysis will be illustrated with dimensionless functions of the volumetric flow rates for both geometries, and quantitative comparisons of the prediction of the two analyses will be discussed. These flow rates are useful to predict the optimal time for many applications, including drug delivery and separations and assess the potential error made by choosing a given geometry over another.

In the future and in order to see how the limits identified for the 1D case (see above) are affected, 2D spatial-dependence velocity profiles will be identified. This case will be solved numerically for the velocity profiles and values of the flow rate can be computed afterwards.