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Abstract Existing analytical flow models for predicting flow rates at microscale seal displacements are limited to two separate domains. The first assumes a small channel length to height aspect ratio at relatively large seal displacements. The second assumes a large channel length to height aspect ratio at relatively small seal displacements. A piecewise analytical model for compressible flow is developed here to enable predicting flow rates in valves with fluid pathways of any aspect ratio. The new model is validated by numerical studies and experiment. The results are applicable to flat valve seals having a cylindrical seal boss feature with fluid passage length to height aspect ratios ranging from 3.3 to 800. The new model is particularly useful for the design of microvalves and macroscale valves with small actuator displacements. 

Compressible flow through arrays of circular micro-orifices was experimentally and numerically studied to better understand how the characteristic dimensions of micro-orifices used in macroscale fluidic systems using a plurality of micro-orifices impacts discharge coefficient. The studies were carried out with micro-orifice diameters ranging from 125 μm to 1000 μm, with the number of micro-orifices in an array ranging from 2 to 64, and at gauge inlet pressures ranging from 25 to 600 kPa venting to atmospheric pressure. Results showed `that micro-orifice diameter to thickness aspect ratio and wall profile were significant factors in determining discharge coefficient. The number of micro-orifices in a system was found to have negligible impact on discharge coefficient so long as the micro-orifices were separated by two diameters or more. When this spacing was maintained, two dimensional axisymmetric micro-orifice numerical studies produced discharge coefficients that agreed well with experimental data gathered on three dimensional micro-orifice arrays. The micro-orifice arrays produced discharge coefficients as high as 0.997 using photochemically etched micro-orifices, 0.981 using silicon etched micro-orifices, and 0.831 with drilled micro-orifices.