A time-dependent method for the measurement of mass flow rate of gases in microchannels

Accurate measurement methods are required in the analysis of thermodynamic non-equilibrium effects associated with rarefied gas flows. For example, for the specific case of accommodation coefficients measurements, the quantity of interest is often the mass flow rate along the channel. For this purpose, the following paper presents a new time-dependent version of the well-known constant volume method for the accurate measurement of mass flow rates of gases in microchannels. The technique proposed here is an improvement in respect to the classic technique since it can be used for transient experiments. Moreover, it can be applied to configurations with arbitrary upstream and downstream reservoirs dimensions. Particularly, the proposed method relies on the assumption that the flow conductance varies linearly during the experiments and thus the pressure variations in the reservoirs can be fitted by a well-defined exponential function. Then, the instantaneous mass flow rate through the channel can be determined directly from the pressure fitting coefficients. A great advantage of the time-dependent constant volume method is that the measurements can be obtained from a single experiment for a wide range of rarefaction conditions, since the mean pressure between the reservoirs is allowed to change with time. Moreover, this technique represents a convenient manner to provide raw data of pressure variation with time in the reservoirs and transient mass flow rate in the channel by simply providing the fitting coefficients of the theoretically derived functions. A clear geometric criterion is also presented to determine when such mass flow rate measurements can be considered as quasi-steady, corresponding closely to results obtained under steady conditions, when ideally the channel connects two infinite reservoirs at different pressures. Results for flows of nitrogen through a stainless steel microtube (L=92.22±0.01 mm and D=435.5±3.5 µm) were obtained from 118 independent experiments, provided in this work, using two different experimental setups and three different configurations of the system volumes. As expected, no deviation was observed between all experimental campaigns in terms of the reduced mass flow rate. In addition, all results indicate that nitrogen can be considered completely accommodated at the surface of the microtube used, with α=0.986±0.019 when the diffuse-specular gas-surface interaction model is adopted and αt=0.991±0.020 (αn=1) when the Cercignani-Lampis model is adopted.