CAREER: Mathematical Modeling of Microfluidic Dynamics and Transport

Duke University, Durham NC

Investigators

Abstract

This project will investigate mathematical problems in the fluid dynamics of thin viscous films spreading on solid surfaces. The basic mathematical models for such lubrication flows with strong surface tension effects are fourth-order nonlinear partial differential equations. These equations yield certain singular behaviors that make them problematic. In this work, these difficulties are overcome through the use of physically-motivated generalized models that include interaction forces between the liquid film and the solid substrate. These so-called disjoining-pressure or ``dewetting-film'' models will be used as the basis for the study of an array of interconnected problems. The goals of this research project are: (i) to mathematically establish that dewetting film models can provide faithful representations of the important physical effects in coating flows, and (ii) to extend this basic research to the design of microfluidic devices. These goals will be carried out using a combined computational and analytic study of the nonlinear partial differential equations for the dewetting models. Applying numerical simulations and similarity solutions to the two-dimensional version of the models, the dynamics of flows in structured geometries will be obtained; this work will be combined with a study of mechanisms used to drive thin film fluid flows and their stability. This project focuses on mathematical models for describing the motion of drops of fluids on solid surfaces. The impact of this work lies in its role as basic research supporting advances in biomedical engineering and microfluidic technology. A major focus of this project is the use surface-tension effects for active transport of liquids. Using carefully controlled changes in the local environment, we can create surface tension forces to manipulate fluid droplets in any desired manner. This approach is a key element used in the designs of microfluidic devices for the next generation of biomedical research tools. The project will also examine how material properties of the solid surfaces influence the motion of more complicated fluids. This work will serve as the basis for understanding the important physical factors in the formulation of drug delivery bio-gels used in physiological coating flows and other biologically-motivated fluid flow problems.