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Microfluidics is used in a wide array of applications including photonics, catalysis, optoelectronics, particle synthesis, bio-diagnosis and tissue engineering. Poly(dimethyl) siloxane (PDMS) is one of the most widely used materials for the fabrication of such devices. In many applications, applied flow gives rise to pressure variations along the length of the channel and a commensurate spatially varying channel height. We have previously performed a scaling analysis of the relaxation time ofdoi:10.1088/1367-2630/11/11/115001 fatcat:75strtpz2zf3feuorxqlzmyoam