Proc. of APCChE 2015

Mixing of fluids is of great value in many applications. Oscillatory and pulsatile flows can enhance mixing by generating high shear oscillations. Electro-osmosis is a phenomenon where external electric fields induce flow in fluids that are in contact with charged surfaces. It has drawn considerable attention in the field of fluid manipulation, and non-uniform electric fields are expected to be particularly effective for mixing enhancement. Fluid flow is governed by the Navier-Stokes partial differential equation, and an approach for determining the most effective input profile for electro-osmotic mixing is of great value. The nature of electro-osmosis being induced by a set of cylindrical electrodes with a zero net charge means the problem of maximisation of electro-osmotically induced mixing with a fixed input magnitude is a constrained optimisation problem for a distributed parameter system. This paper proposes an approach for relating the voltages between electrodes, and uses constrained optimisation to find the most effective electrode voltage profile for creating electro-osmotically induced mixing. The Navier-Stokes equation is converted into a system of linear equations and the constrained optimisation problem is solved to determine the most effective input profile for inducing electro-osmotic mixing given a predefined electrode configuration, including the magnitude and phase of the voltage between each electrode. The solution to this problem is valuable as it directly provides the voltage input required by the power supplies for the electrodes in order to maximise mixing, and this result can be quickly and systematically generated for any predefined electrode configuration