In this study, the effect of two important parameters have been evaluated for pressure driven liquid flows in microchannel in laminar regime by analytical modeling, followed by experimental measurement. These parameters are wettability conditions of microchannel surfaces and aspect ratio of rectangular microchannels. For small values of aspect ratio, the channel was considered to have a rectangular cross-section, instead of being two parallel plates. Novel expressions for these kinds of channels were derived using eigenfunction expansion method. The obtained two-dimensional solutions based on dual finite series were then extended to the case of a constant slip velocity at the bottom wall. In addition, for large values of aspect ratio, a general equation was obtained which is capable of accounting for different values of slip lengths for both upper and lower channel walls. Firstly, it was found out that for low aspect ratio microchannels, the results obtained by analytical rectangular 2-D model agree well with the experimental measurements as compared to one dimensional solution. For high aspect ratio microchannels, both models predict the same trend. This finding indicates that using the conventional 1-D solution may not be accurate for the channels where the width is of the same order as the height. Secondly, experimental results showed that up to 2.5% and 16% drag reduction can be achieved for 1000 and 250 micron channel height, respectively. It can be concluded that increasing the surface wettability can reduce the pressure drop in laminar regime and the effect is more pronounced by decreasing the channel height.
Flow through a helical pipe with rectangular cross-section
