Compressibility effects in microchannel flows between two-parallel plates at low reynolds and mach numbers: Numerical analysis

Abstract

Under certain circumstances, flow in microchannels can exhibit compressibility effects even at Reynolds numbers (Re) around (below 2,300) and low Mach numbers (below 0.3). This is particularly true for gases, especially when the flow undergoes significant pressure changes or acceleration within the microchannel. This study investigates the compressibility effects encountered in two-parallel plates microchannels at these low Reynolds and Mach numbers, due to the high-pressure drop associated with the small scale of the microchannels. This uncommon flow is characterized by an exceptionally small channel diameter-to-length aspect ratio (∼10^–3), resulting in a friction coefficient that deviates from the typical value for laminar flow between parallel plates (f = 96/Re). Both steady and transient effects on the flow field are examined under low Re subsonic flow, assuming continuum behavior. The ideal gas equation is used to model gas density, while the isothermal Tait-Murnaghan equation models liquid density. For gases, compressibility effects are observed primarily when the inlet pressure ratio exceeds 0.1. The results show that these effects are less pronounced for liquids, even at elevated inlet pressure ratios. Additionally, a flow delay across the channel exhibits a first-order transient response. For liquid flow, this effect depends on the channel resistance, the total fluid volume within the channel, and the liquid's bulk properties, rather than the inlet pressure ratio.