Science and engineering of enrichment, separation, detection, and extraction of chemical species in a liquid sample have had a significant impact on our society. It has a wide ranges of applications in environment, biotechnology, oil industry, and public health. Some of the examples include, but not limited to, heavy metal detection, DNA analysis, sea water desalination, and hemodialysis.

For last decades, there have been a growing interest in a electrokinetic methods for enrichment or separation using a perm-selective membrane or a reactive electrode. The method applies an electric current across the perm-selective membrane or the electrode, then, leverages the unique electric field formation nearby to manipulate target analytes in the electrolytes. The methods prevents direct contacts between the target analytes and the membrane. Therefore, the membrane is more robust on fouling. In addition, the fabrication is easy allowing convenient testing of new ideas for various applications.

The electrokientics is a complex multi-physic dealing with fluid flow, electro-dynamics, and mass transport, which controls diffusion, convection, and electro-migration of the species in the electrolytes. This system can be modelled by Navier-Stokes and Poisson-Nernst-Planck equations, which has no analytic solutions except for extremely simplified case. On the other hand, most experimental methods are limited to the current measurement or visualizing concentrations. Therefore, only limited amount of information is accessible making understanding the enrichment/separation system challenging.

The research directions in this work are divided into two: First, extend the current capabilities of enrichment/separation by introducing unconventional ways of using the perm-selective membrane or the reactive electrode. Second, develop a numerical framework to solve Navier-Stokes and Poisson-Nernst-Planck equations to simulate charged species transport in electrokinetic separation/enrichment system.

To achieve the first goal, the enrichment efficiency was improved by introducing packed bed silver particles on the conventional planar gold electrode. Separately, the perm-selective membrane based electrokinetic system was incorporated into the droplet microfluidics. It was shown that the proposed method can concentrate, separate, and inject ions into the droplets. Then, the method was tested for a cell lysis and enzymatic assay in the microdroplets. For the second goal, highly paralleled finite element method based numerical method was developed. To minimize numerical instabilities and improve the accuracy, variational multiscale method along with Dirichlet to Neumann boundary condition transition were applied. The numerical results showed high efficiency and accuracy in boundary flux calculation. In addition, the numerical results provided detailed information on spatio-temporal electrokinetic instabilities.

The results in this work is significant, as it proposed a new method of handling analytes in microdroplets, which has many potential applications. The numerical plate form successfully simulates the charged transport in electrolytes, and provides design suggestions and insights to the experimental part of the study.