Irina Graur

Mass flow rate measurements in a microchannel, from hydrodynamic to near free molecular regimes

Helium mass flow rates in a microchannel were measured, for a wide Knudsen-number range, in isothermal steady conditions. The flow Knudsen numbers, considered here, cover the range from continuum slip regime to the near free molecular regime. We used a single-channel system involved in an experimental platform more powerful than those previously used. The experimental errors and uncertainties were accurately investigated and estimated. In the continuum slip regime, it was found that the first-order approach is pertinent for Knudsen number between 0.03 and 0.3. Moreover, the slip coefficient was deduced by comparing the experiments with the theoretical first-order slip continuum approach. For Knudsen number between 0.03 and 0.7, a polynomial second-power form is proposed for the mass flow rate expression. Otherwise, the experimental results on the mass flow rate were compared with theoretical values calculated from kinetic approaches over the 0.03-50 Knudsen number range, and an overall agreement appears through the comparison. It was also found, when the Knudsen number increased, that the wall influence on measurement occurred first through the accommodation process in the transition regime followed by the wall influence through the aspect ratio in the free molecular regime.

Mass flow rate measurements in microtubes: From hydrodynamic to near free molecular regime

An experimental investigation of the reflection/accommodation process at the wall in a single silica microtube and isothermal stationary flow conditions was carried out. Several gases and different diameters were studied through various regimes. Especially for helium, the Knudsen number range was investigated as far as the free molecular regime. This kind of investigation requires a powerful experimental platform to measure mass flow rates, which we have carried out. An analytic expression of the mass flow rate, based on the Navier–Stokes equations with second order boundary condition, was used to yield the tangential momentum accommodation coefficient (TMAC) in the 0.003–0.3 Knudsen number range. Otherwise, the experimental results of the mass flow rate were compared with theoretical values calculated from kinetic approaches using variable TMAC as parameter over the 0.3–30 Knudsen number range, and an overall agreement appears through the comparison. Finally, whatever the theoretical approach the TMAC ob...

Measurements of tangential momentum accommodation coefficient for various gases in plane microchannel

Mass flow rate measurements in a single silicon microchannel were carried out for various gases in isothermal steady flows. The results obtained from hydrodynamic to near free molecular regime by using a powerful experimental platform allowed us to deduce interesting information, notably about the reflection/accommodation process at the wall. In the 0–0.3 Knudsen range, a continuum analytic approach was derived from the NS equations, associated with first or second order slip boundary conditions. Identifying the experimental mass flow rate curves to the theoretical ones the tangential momentum accommodation coefficient (TMAC) of various gases was extracted. Over the full Knudsen range [0–30] the experimental results were compared with theoretical values calculated from the kinetic approaches: using variable accommodation coefficient values as fitting parameter, the theoretical curves were fitted to the experimental ones. Whatever the Knudsen range and whatever the theoretical approach, the TMAC values are...

Thermal transpiration flow: A circular cross-section microtube submitted to a temperature gradient

Thermal transpiration is the macroscopic movement of rarefied gas molecules induced by a temperature gradient. The gas moves from the lower to the higher temperature zone. An original method is proposed here to measure the mean macroscopic movement of gas in the case of a long circular cross-section glass microtube onto which a gradient of temperature is applied. The mass flow rate and the thermomolecular pressure difference have been measured by monitoring the absolute pressure evolution in time at both ends of the capillary using high-speed response pressure gauges. Two gases, nitrogen and helium, are studied and three different temperature differences of 50, 60, and 70 °C are applied to the tube. The analyzed gas rarefaction conditions vary from transitional to slip regime.

Time-dependent experimental analysis of a thermal transpiration rarefied gas flow

Thermal transpiration is the macroscopic movement induced in a rarefied gas by a temperature gradient. The gas moves from the lower to the higher temperature zone. An original method is proposed here to measure the stationary mass flow rate of gas created by thermal transpiration in a micro-tube heated at its outlet. In addition, by means of a time-dependent study, parameters such as the pressure variation, the pressure variation speed, and the characteristic time of the system are analyzed. The experimental system is composed of a glass tube of circular cross section and two reservoirs positioned one at the inlet and one at the outlet of the capillary. The reservoirs are connected to two fast response time capacitance diaphragm gauges. By monitoring the pressure variation with time inside both reservoirs, it is possible to measure the macroscopic movement of the gas along the tube. Three gases, nitrogen, argon, and helium, are studied and three temperature differences ΔT = 37, 53.5, and 71 K are applied ...

Gas flow through microtubes with different internal surface coatings

An experimental setup based on the constant volume technique is developed to measure the mass flow rate through microtubes under isothermal stationary flow conditions. Four different working gases (helium, nitrogen, argon, and carbon dioxide), and two surface materials (stainless steel and Sulfinert) are considered. The Knudsen number calculated for the experimental conditions varies from ∼10−4 (hydrodynamic regime) to ∼ 5 (transitional regime). In the reduced range (10−4−0.1) corresponding to the hydrodynamic and slip regimes, an approach based on the analytical solution of the Stokes equation subjected to a first order velocity slip boundary condition is used. The velocity slip coefficient and the tangential momentum accommodation coefficient are extracted from the experimental data of the mass flow rate using their analytical expressions. The results are summarized in the tables representing the accommodation coefficients for the corresponding gas-surface material combinations. The influence of the mol...

Experimental investigation of the temperature field in the gas-liquid two-layer system

Results of an experimental investigation of the temperature field across the liquid-gas two-layer system are presented. The liquid layer is locally heated from the bottom substrate, and the intensive liquid evaporation is observed. A technique for measuring the temperature profile across the liquid and gas layers (including their interface) is developed. To do these measurements, the microthermocouple is moved across the layers with the help of precision micropositioner with a step of 1 μm. The temperature jump at the liquid-gas interface is measured, and its value increases with the temperature increase. Detailed information on the temperature field near the interface is obtained by using the precise thermocouple displacement with a small step.

Leak rate of water into vacuum through microtubes

A numerical model of water leak into vacuum through microcracks and crevices is proposed. A crevice is modeled by a long tube with a radius size of the order of 1 μm. It is assumed that the water is in its liquid phase in the inlet, while it is in its gaseous phase in the outlet. In such a situation, the evaporation of water happens inside the tube when the water pressure reaches the pressure of saturated vapor. The molecular mean free path of vapor varies in a wide range along the tube so that the flow changes from the hydrodynamic to the free-molecular regime. Under such conditions, the water leak is calculated by combining the methods of rarefied gas dynamics and continuum mechanics. The leak rate is calculated for some values of the tube radius and several temperature gradients. The pressure distribution along the tube is also reported.

Effects of two transversal finite dimensions in long microchannel: Analytical approach in slip regime

An analytical approach has been developed to take account of the influence of the lateral walls on a stationary isothermal gas flow through a rectangular microchannel. The study concerns pressure-gradient-driven flows in channels where the length is large compared to the critical smallest dimension, namely, the channel height. The calculation of the bulk velocity is based on the Stokes equation treatment and uses the property of the Laplace operator. This novel method remains very easy to use when the second order term with respect to the Knudsen number is taken into account in the wall boundary conditions. The method is notably of high practical interest when applied to rectangular-cross-section microchannels that connect upstream and downstream high capacity reservoirs. The mass flow rates measured along such systems are fitted to first or second order polynomial forms following the mean Knudsen number of the flow. The present calculation also leads to a completely explicit second order expression for t...

Experimental study of the gas flows through channels with circular cross sections

The experimental setup based on the constant volume technique is developed to measure the mass flow rate through the microtubes under the isothermal flow conditions. Four different gases: Helium, Nitrogen, Argon and Carbon dioxide, and two surface materials (Stainless stainless Steel steel and Sulfinert) are considered. In this study the Knudsen number varies from ~ 10−4 to 0.3. In this range the approach based on the analytical solution of the Stokes equation subjected to the first and second order velocity slip boundary conditions is used. The tangential momentum accommodation coefficient (TMAC) is extracted from the experimental data on the mass flow rate using its analytical expression. The results are summarized in the tables representing the accommodation coefficients for the couples corresponding gas-surface material combinations. The influence of the molecular mass on the tangential momentum accommodation is discussed.