Numerical analysis of fluid flow in channels of micron dimensions

Abstract

The recent advances in microtechnology, such as the fabrication of micropumps, valves, etc. has resulted in a great deal of research being concentrated within the field of microfluids. To design efficient micro-fluid devices it is essential to be able to predict flow in cavities of micron dimensions. The macroscopic laws, which are still widely accepted today, were introduced almost two centuries ago thanks to the work of Euler and Cauchy. The classical continuum approach divides the area of flow into small elements, each of these elements contain a vast number of the fluid molecules. These elements are then seen to be point masses exhibiting definite property values, such as density, at each point in space. Over the years there has been a lot of research time devoted to determining if, as predicted by Eringen, flow in cavities of micron dimensions differs greatly from that predicted using classical theories. The literature available on this topic appears to provide conflicting results. For example, Israelachvili reports that the macro-scale model holds for dimensions down to the last molecular layer. However, Harley reports that for a trapezoidal channel with hydraulic diameter of 45 /spl mu/m using n-propanol as the test fluid, the Poiseuille number is larger then expected and concludes that further investigation is required. Also, Pfahler investigated channels ranging in hydraulic diameter from 0.96 to 39.7 /spl mu/m. His results indicate that as the hydraulic diameter gets smaller the results deviate further from the conventional macroscopic models. This study investigates the flow in trapezoidal channels with hydraulic diameters ranging from 50 to 120 /spl mu/m. The experimental differential pressure (/spl Delta/p), mass flow rate (Q) characteristics of the various channels have been determined, which will act as a comparison to the conventional macro-scale theoretical results. In predicting the theoretical /spl Delta/p/Q relationship for the trapezoidal channels an analytical technique is utilised. This is due to the fact that no simple equation or experimental data exists, which is the case for circular ducts, with which to determine the flow characteristics of trapezoidal channels. Shah investigated numerically the flow in various shaped ducts including that ofthe trapezoid, the results for which shall be used as a comparison in this study. As well as comparing the theoretical results to the experimental data the channels were simulated using a commercially available finite element package.