Analysis of electrokinetic pumping efficiency in capillary tubes

Abstract

A mathematical model for predicting the maximum pumping efficiency and pressure difference generation by an electrokinetic-driven fluid pumping system through a capillary tube is presented in this study. Both the maximum pumping efficiency and optimum pressure difference generation are found to depend on a single variable. This single variable is termed as the figure of merit since it determines the performance of electrokinetic pumping. The figure of merit is found to depend on three dimensionless parameters, the normalized Debye length, zeta potential, and Levine number indicating the nominal ratio of convective current to conductive current. All three parameters can be related to the pH value and concentration of aqueous salt solution by the introduction of concentration-dependent electrical conductivity and pH-dependent zeta potential. By presenting the maximum pumping efficiency and optimum pressure difference generation as functions of pH value, salt concentration, and capillary tube radius, it is found that both maximum pumping efficiency and optimum pressure difference generation increase with the decrease in capillary radius and salt concentration. The optimum pH values at which the maximum pumping efficiency and optimum pressure difference generation occur are found to be in the range between 6 and 9. For the salt concentration of 10(-6) M, pH 6.9, and a capillary tube radius value of 0.5 micro m, the predicted maximum pumping efficiency is 5.4% which is close to the experimental measurement reported in the literature.