An Efficient CAD-Integrated Multi-Dimensional Model for Microfluidic Simulations

Abstract

Microfluidic devices exhibit high-aspect ratio in that their channel-widths are much smaller than their overall lengths. High-aspect geometry leads to an unduly large finite element mesh, making the (otherwise popular) finite-element method (FEM) a poor choice for modeling microfluidic devices. An alternate computational strategy is to exploit well-known analytical solutions for fluid flow over the narrow-channels of a device, and then either: (a) assume the same analytical solutions for the (wider) cross-flow regions, or (b) exploit these solutions to set-up artificial boundary conditions over the cross-flow regions. Such simplified models are computationally far superior to FEM, but do not support the generality or flexibility of FEM. In this paper, we propose a third strategy for exploiting the analytical solutions: (c) directly incorporate them into standard FE-based analysis via model reduction techniques. The advantages of the proposed strategy are: (1) designers can use standard CAD/CAE environments to model, analyze and post-process microfluidic simulation, (2) well-established dual-weighted residuals can be used to estimate modeling errors, and (3), if desired, one can eliminate the dependency on possibly inaccurate analytical solutions over selected regions. The simplicity and generality of the proposed method is inherited from the model reduction process, so are its theoretical properties, while simultaneously its computational efficiency is inherited from the use of analytical solutions.