Effects of fabrication imperfections on fully developed flow in rectangular micro-channels

Over the past few decades, the microfluidics field has been established itself as an emerging technology, serving as a tool for many areas both in science and in industry. As a result, research involving the analysis of micro-flows has been growing dramatically and is acting in the advancement of new technologies and microfluidic devices. As small diameters are considered, on most occasion laminar flow occurs, which allows simpler numerical solution of the problem to be carried-out. In fact, for fully developed velocity profiles the advective terms become unimportant and the problem becomes linear, which allows analytical solutions to be carried out if regular geometries are considered. While for macro-channel flows, the fabrication of channels with regular geometries such as circular or rectangular is fairly simple, when micro-fabrication is considered the resulting channels geometry in many occasions cannot be treated as regular, even if the nominal profile is so. On such example is seen channels with rectangular nominal geometries. For this type of channels, on many occasions the resulting cross-section geometry is somewhat trapezoidal with slightly rounded corners. While for large scale channels these imperfections can be neglected, in micro channels they may be of notable influence on the flow field. In this context, the purpose of the paper is to analyze the influence that the aforementioned fabrication imperfections has on the fully developed flow field in nominally rectangular microchannels. The solution methodology is based on the Generalized Integral Transform Technique applied to irregular geometries.