## Project Details

### Description

A systematic study of electric field effects on nonlinear free surface flows is proposed. Applications can be found in coating and cooling problems where liquid films are used to enhance heat or mass transfer, and fluid management in microfluidics devices (for example lithographically induced self-assembly technologies). Highly viscous flows are considered because inertia is absent in many important applications. The problems are nonlinear and mathematically challenging because they require the simultaneous solution of the equations of fluid mechanics and of the Maxwell equations. Two basic mathematical approaches are developed. The first is a fully nonlinear numerical method based on a boundary integral equation formulation. This leads to a large system of integral equations which describe the motion and the electric field in each fluid. These equations are coupled by nonlinear boundary conditions and a stable numerical method is derived. The second approach is an asymptotic method based on long wave approximations. It leads to simpler partial differential equations whose range of validity is determined by comparing solutions with those obtained by the first approach. Analysis and computations will be used to solve for the spatio-temporal evolution of electrified coating flows over flat and variable substrates as well as the evolution of microfluidic layers under the action of electric fields in the presence of topographically structured electrodes. Of major interest is the use of electric fields to manipulate the interfacial evolution and possible robust coherent structures such as nonlinear steady- or large-time states.

In the high-tech world of ever decreasing machinery sizes and their components, it is vitally important to be able to construct models and study fundamental aspects of different processes. A mathematical model that can be put on a computer and solved, provides us with a rare opportunity to perform numerical experiments rather than laboratory experiments which can be both time consuming and expensive. The mathematical/computational model becomes an exploratory tool to refine the design of existing processes and at the same time to probe new regimes efficiently. It is important to produce valid mathematical models and resolve them accurately using computers. The present study develops and studies such models with applications in coating of microelectronic components and the production of micro- and nano-sized structures in microelectronics applications. Many components are coated with a liquid which solidifies to form the desired surface (e.g. DVD disks). Any waves that form at the liquid surface and then get inherited in the final product after solidification, produce defects and degrade performance. This study examines, theoretically, ways to control such features. It also examines models that describe the formation of nano-sized features on microelectronic devices that can be used to produce micro-chips. The goal is to study and produce a theoretical protocol to control the waves that form during the liquid phase and before solidification.

Status | Finished |
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Effective start/end date | 8/15/07 → 7/31/12 |

### Funding

- National Science Foundation: $248,199.00