Numerical Methods And Analysis For Induced-Charge Electrokinetic Flow With Deformable Interfaces

This project is an investigation of fundamental problems from fluid dynamics that arise in biology and microtechnology. Its focus is on the development of new mathematical models and efficient numerical methods to study the manipulation by electric fields of the shape and position of cells, vesicles, and drops in electrolytic fluids. These so-called 'electrokinetic techniques' are among the most common methods for manipulating particles and fluids in micro-scale devices and biological applications. For example, electric fields are applied to induce shape changes in cells and vesicles, and this is used to infer membrane properties. Electric fields are also used to form transient pores in membranes, which is an important technique to load cells with molecules for drug delivery or gene therapy. Impacts of the proposed research include the development of new mathematical models and numerical methods that will be of benefit to scientists and engineers studying electrokinetic phenomena in biology and engineering. An additional impact of this project will be the education and involvement of graduate students. The interdisciplinary training they receive will be valuable prEnvironmental Protection Agencyration for a range of careers in mathematics and science.

During the interfacial flow of an ionic fluid that is driven by an electric field, a screening cloud of ions develops at the interface and forms an electrochemical double layer or 'Debye layer'. The electric field both acts on the ion cloud it induces and drives both it and the surrounding fluid into motion. This is known as 'induced-charge electrokinetic flow', and it is an important phenomenon in applications. We address a significant difficulty in the numerical computation of such flows in the practically important limit of thin double layers, by developing a fast and accurate hybrid or multiscale numerical method that incorporates an asymptotic analysis of the layer's dynamics into a novel boundary integral formulation of the interfacial free boundary problem. A central theme of the current project is the development of a hybrid method for electrokinetic flow about a membrane. The algorithm will incorporate an analysis of the high-wavenumber or small-scale component of the elastic and electrostatic stresses on a membrane into a nonstiff method that is capable of handling the multiple time and space scales inherent in the problem. The method will be used to study canonical problems in the electrodeformation of drops, vesicles, and cells, and to examine vesicle manufacture by electroformation and coalescence by electrofusion. The numerical investigations will be complemented by analytical studies that will be used to justify existing reduced or 'lumped parameter' models for electrohydrodynamic flow, and to derive new models. The investigators also propose to develop a hybrid method for problems with ionic surfactant, which combines features of both electrokinetic flow and soluble surfactant.