One dimensional transport equations for CE systems by asymptotic homogenization

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DESCRIPTION (provided by applicant): Research in the area of Microfluidics has lately been driven by the ultimate goal of creating a micro-total analysis system (mu-TAS) or more colloquially the 'Lab On a Chip'. The Capillary Electrophoresis (CE) channel is an essential component of any such system and much effort is focussed upon improving its design so as to maximize separation efficiency and reproducibility. Numerical solution of the equations describing the physics of the separation process is one of the most important modern tools available to the designer. Computational studies help save time and cost by helping to narrow down the possible design solutions prior to actual fabrication of prototypes. This proposal seeks to combine numerical approaches and asymptotic methods towards the solution of the fluid flow and species transport equations in CE channels so as to reduce the computational cost by many orders of magnitude. It is based on the observation that the physical problems in this class are characterized by a small parameter: the ratio of the characteristic width to the characteristic length of the micro-channel. The presence of this small parameter renders the underlying equations "stiff and hence difficult to solve. One can however take advantage of this stiffness by using "asymptotic homogenization" to essentially reduce the three dimensional problem to one that has only one space dimension with only a very small loss of accuracy. As a proof of concept, a web based computational design tool will be created on which remote users can run computations in real time. This is possible because of the massive reduction of computational effort that results from the replacement of a 3D stiff system of partial differential equations by a 1D non-stiff system. RELEVANCE: An approach is being proposed for reducing by many orders of magnitude the computational effort involved in the numerical simulation protocols used in computer aided design of microfluidic systems. The availability of such design tools increases the probability that the effort to create practical "Lab On a Chip" devices would succeed. The emergence of such devices would have an enormous impact on human health as they would enable biochemical analyses (such as DNA sequencing) that currently take months or years to be completed in minutes.