Integral transform analysis of microchannel fluid flow: Irregular geometry estimation using velocimetry data

A hybrid numerical-analytical solution to fluid flow in irregularly-shaped microchannels has been developed. The solution is based on the Generalized Integral Transform Technique (GITT) applied to a trapezoid-like duct to account for fabrication imperfections, as commonly found in commercially manufactured microchannels. With this approach, the eigenseries expansion is done using a 2D eigenfunction basis, constructed from a combination of simple 1D eigenfunctions defined within the original irregular domain. In order to improve convergence, a new filtering scheme based on an analytical solution to the problem in a rectangular channel, which is distorted to match the irregular domain, is employed. The solution is tested on a real microchannel geometry, obtained from a SEM image, and compared with micro-PIV measurements for the flow field in the same channel. In addition, the actual velocimetry data is input to an inverse problem implementation for recovering geometric parameters related to the irregular geometry using the GITT results as the forward solution. The numerical results obtained with the GITT presented a very satisfactory convergence, and the inverse solution was able to recover the channel geometric parameters with very reasonable accuracy.