In the present work, the behavior of a millimeter-scale cold-gas thruster operating with the noble gases neon, argon, krypton and xenon is investigated both experimentally and numerically. In the experimental setup, the cold-gas thruster operates under vacuum conditions and the pressure drop in the system is measured at several fixed mass flow rates ranging between 0.178 mg/s and 3.568 mg/s. The estimated Knudsen numbers for all the studied cases are above the continuum flow limit 0.01. At the higher mass flow rates the studied flows are in the slip-flow regime while at the lower mass flow rates, the transition regime is reached. The experimental pressure results are compared with numerical simulations based on the compressible Navier-Stokes equations with a no-slip boundary condition and with simulations based on the Direct Simulation Monte Carlo (DSMC) method. At high values of Kn, the pressure results of the Navier-Stokes based simulations show high deviations from both the DSMC and the experimental results. This is a consequence of the discrepancy between the no-slip boundary condition used for the Navier-Stokes simulations and gas rarefaction effects in the micronozzle becoming dominant at the lower mass flow rates. Based on the comparison between the experimental results and the Navier-Stokes based simulations, a Knudsen-dependent correcting function with four gas-independent accommodation coefficients is developed. The accommodation coefficients allow the accurate estimation of the actual pressure drop along the nozzle based on usually computationally inexpensive Navier-Stokes simulations with no-slip boundary conditions. The flexibility of the proposed approach is advantageous for the study of experimental setups operating at a large range of mass flow rates, where several flow regimes might exist, provided that a rigorous numerical distinction between continuum, slip-flow and transition regime is not essential.

An extended numerical analysis is performed in order to characterize the combined effect of compressibility, rarefaction and conjugate heat transfer (CHT) in counter current and parallel flow micro heat exchanger. Relatively short microchannel geometries are considered, leading to more significant dependence on compressibility and rarefaction effects. A fully compressible numerical solver, coupled with proper slip flow and temperature jump boundary conditions, previously extensively used for CHT computation in microchannel heat sinks, is adopted: thus, viscous dissipation is always taken into account and a wide range of channel exit Mach numbers can be considered, keeping Knudsen number within the limits of slip flow. A comprehensive range of fluid/solid thermal conductivity ratios, pressure ratios, temperature difference and channel aspect ratios are considered, in order to identify the dominant effects, as well as the optimal fluid/solid conductivity ratio, as a function of the heat exchanger design and operating parameters. Results are described in terms of heat exchanger efficiency and local Nusselt number.

A fully conjugate heat transfer analysis of gaseous flow, within slip flow regime, in short microchannels is presented. A Navier Stokes code, coupled with Maxwell slip and Smoluchowski temperature jump models, is adopted. The main focus is on the interaction between compressibility and heat transfer; in particular, due to the link between temperature and velocity field in highly compressible flow, it is important to recast the channel performance parameters in order to take into account the flow cooling due to the conversion between internal and kinetic energy. Results are presented for Nusselt number and a corrected heat sink thermal resistance, as well as resulting wall temperature.

A fully conjugate heat transfer analysis of gaseous flow, within slip flow regime, in short microchannel is presented. A Navier Stokes code, coupled with Maxwell and Smoluchowski slip and temperature jump model, is adopted. Due to the link between temperature and velocity field in highly compressible flows, results are presented for Nusselt number, heat sink thermal resistance and resulting wall temperature as well as Mach number profiles for different conditions, commenting on the relative importance of wall conduction, rarefaction and compressibility. Compressibility plays a major role, and the reduction in heat transfer rate due to axial conduction is quite remarkable.

In this paper, Nusselt number for a flow in a microtube is determined analytically with a constant wall heat flux thermal boundary condition. The flow assumed to be incompressible, laminar, hydrodynamically and thermally fully-developed. The thermo-physical properties of the fluid are assumed to be constant. The effect of rarefaction, viscous dissipation, axial conduction, which are important at the microscale, are included in the analysis. For the implementation of the rarefaction effect, two different second-order slip models are used for the slip-flow and temperature-jump boundary conditions together with the thermal creep at the wall. Closed form solutions for the fully-developed temperature profile and Nusselt number are derived as a function of Knudsen number, Brinkman number and Peclet number.

Nowadays, modeling gas flows in the slip flow regime through microchannels can be achieved using commercial Computational Fluid Dynamics codes. In this regime the Navier-Stokes equations with appropriate boundary conditions are still valid. A simulation procedure has been developed for the modeling of thermal creep flow using ANSYS Fluent®. The implementation of the boundary conditions is achieved by developing User Defined Functions (UDFs) by means of C++ routines. The complete first order velocity slip boundary condition, including the thermal creep effects due to an axial temperature gradient and the effect of the wall curvature, and the temperature jump boundary condition are applied. Motivation of the present work is the development of a simulation tool which will help in the pre-calculations and the preliminary design of a Knudsen micropump consisting of successively connected curved and straight channels and in a second step in the numerical optimization of the pump, in terms of geometrical parameters and operating conditions of the system.

Flow in microchannels is an important area of research in engineering because its importance in areas such as micro-machinery. In addition, hydrophobic materials have become increasingly attractive for use in fabrication of microfluidic devices. However, even when in macroscopic flows the non-slip boundary condition on solid wall has been well accepted, a number of recent studies have found evidences of slip velocities for liquid flow on hydrophobic surface. In this study, numerical simulations of two-phase flow of micro-droplet in a continuous base fluid in a 2D microchannel were performed using a commercial software package. Both slip and non-slip flows were considered. Continuous phase slip over wall channels was considered modeling all range of possible Knudsen numbers. Three drops of different sizes were modeled. Results were expressed in term of pressure drop and Reynolds numbers. Droplet interface deformation and velocity fields inside both droplets and continuous phase were determined. Results show that for Knudsen numbers between 0.01 and 0.1, Reynolds number increases in a proportion in the order of 20%. In addition pressure drop notably increase when large drops are considered.

The Molecular Tagging Velocimetry (MTV) technique has been widely used for analyzing velocity fields in liquid mini- and microflows. Concerning gaseous flows, only few works describe the implementation of MTV at millimetric scale, and these studies are limited to the analysis of external flows, such as jet flows. The goal of the present work is to develop this technique for the analysis of internal gas flows in minichannels. It is a first step toward the visualization of velocity profiles in rarefied conditions, and direct measurement of velocity slip at the walls. A specific experimental setup has been designed. Its features are detailed. Velocity profiles are obtained in a pressure driven steady flow of argon through a long rectangular minichannel of 1.2 × 5 mm 2 cross-section and 15 cm length using acetone molecules as tracer. Experiments are carried out at atmospheric pressure, in a laminar continuum flow regime. The accuracy of the method is discussed by comparison between experimental and theoretical velocity profiles. The potential of the MTV technique for analyzing mini or micro gaseous internal flows is commented on. Perspectives of the work for discussing the validity of boundary conditions in the slip flow regime are presented.

In this work we use a three dimensional Molecular Dynamics simulation method to study the effect of different geometries and Knudsen number regimes on the gas flow in micro-nanochannels. Argon molecules have been used for the simulations. Thermal wall and diffusive-specular wall types were used for the boundaries of the channels. The velocity profiles in the channel were obtained and analyzed with three different channel geometries that are commonly used in the industry: circular, rectangular (square), and slit channel. We found that when using the same driving force, the maximum velocity of the flow increases when the geometry changes in the order from circular geometry to rectangular geometry to slit geometry, where the latter becomes 1.2∼1.5 times as large compared with either the rectangular or circular channel. While the absolute values of the velocity profiles show a distinct difference according to the different geometries, geometry effect on the shape of the velocity profile also shows interesting features. Rectangular tube shows much flatter profile compared with the other two channels. Also the effect of the size of the channels and different Knudsen numbers on the velocity profiles is investigated. Two different sizes were used here: 100nm and 10nm corresponding to typical sizes of a nano channel and carbon nanotubes. We found that the Knudsen number has an effect on the slip and maximum flow velocity for the slit geometry even for higher Knudsen number. For the Kn higher than approximately 3, it was found that the Knudsen number has a small influence on the slip flow velocity for the circular channel and rectangular channel than for lower Knudsen number.

Micro- and nano-scale fluid systems can behave very differently from their macro-scale counterparts. Remarkably, there is no sufficiently accurate, computationally efficient, and — most importantly — generally agreed fluid dynamic model that encapsulates all of this important behaviour. The only thing that researchers can agree on is that the conventional Navier-Stokes fluid equations are unable to capture the unique complexity of these often locally non-thermodynamic-equilibrium flows. Here, we outline recent work on developing and exploring new models for these flows, highlighting, in particular, slip flow as a quintessential non-equilibrium (or sub-continuum) phenomenon. We describe the successes and failures of various hydrodynamic and molecular models in capturing the non-equilibrium flow physics in current test applications in micro and nano engineering, including the aerodynamic drag of a sphere in a rarefied gas, and the flow of water along carbon nanotubes.

Microscale flow simulation is considered in this paper for a microchannel flow geometry. Higher order Lattice Boltzmann Model was used as the numerical method for flow simulation, in which an effective mean free path was used in relaxation time appeared in LBM. To accurately describe rarefied gas dynamics beyond the Navier-Stokes level, high-order LB models have been used. One reason the standard lattice BGK model fails to capture the nonlinear constitutive behavior is that it only retains velocity terms up to second order in the Hermite expansion of the equilibrium distribution function. This is not sufficient to accurately describe stresses in isothermal flows. To capture nonequilibrium effects, we should retain up to fourth-order terms in the Hermite expansion. The effective mean free path makes it possible to investigate flow characteristics in slip flow regime, for which Knudsen number varies from 0.1 to 10 while does not change the computational efficiency of standard LBM. Results are obtained for pressure-driven and a shear flow configurations in microchannels. The nonlinear flow characteristics of the Knudsen layer were captured in shear flow regime.

Microfilters are commonly used to block undesirable particles in the fluid flows and to control the flow patterns in MEMS. The main purpose of this study is to understand the effect of gas type on density, pressure, Mach number, and velocity distributions of fluid flows through a microfilter. The Knudsen number is the slip flow regime passing through the microfilter. We use direct simulation Monte Carlo (DSMC) method to simulate the flow of nitrogen, helium, oxygen, air and methane passing through a specific microfilter. The geometry of microfilter is unique in all cases. Our results confirm that every gas performs a different performance passing through a specific microfilter, and that the efficiency of a microfilter varies in different gas type environments. For example, among different gases, nitrogen and air have the lowest the pressure drops and that helium has the maximum pressure loss passing through a microfilter.

Gaseous flow in circular and noncircular microchannels has been examined and a simple analytical model with second-order slip boundary conditions for normalized Poiseuille number is proposed. The model is applicable to arbitrary length scale. It extends previous studies to the transition regime by employing the second-order slip boundary conditions. The effects of the second-order slip boundary conditions are analyzed. As in slip and transition regimes, no solutions or graphical and tabulated data exist for most geometries, the developed simple model can be used to predict friction factor, mass flow rate, tangential momentum accommodation coefficient, pressure distribution of gaseous flow in noncircular microchannels by the research community for the practical engineering design of microchannels such as rectangular, trapezoidal, double-trapezoidal, triangular, rhombic, hexagonal, octagonal, elliptical, semielliptical, parabolic, circular sector, circular segment, annular sector, rectangular duct with unilateral elliptical or circular end, annular, and even comparatively complex doubly-connected microducts. The developed second-order models are preferable since the difficulty and “investment” is negligible compared with the cost of alternative methods such as molecular simulations or solutions of Boltzmann equation. Navier-Stokes equations with second-order slip models can be used to predict quantities of engineering interest such as Poiseuille number, tangential momentum accommodation coefficient, mass flow rate, pressure distribution, and pressure drop beyond its typically acknowledged limit of application. The appropriate or effective second-order slip coefficients include the contribution of the Knudsen layers in order to capture the complete solution of the Boltzmann equation for the Poiseuille number, mass flow rate, and pressure distribution. It could be reasonable that various researchers proposed different second-order slip coefficients because the values are naturally different in different Knudsen number regimes. The transition regime is a varying mixture of different transport mechanisms and the mixed degree relies on the magnitude of the Knudsen number. It is analytically shown that the Knudsen’s minimum can be predicted with the second-order model and the Knudsen value of the occurrence of Knudsen’s minimum depends on inlet and outlet pressure ratio. The compressibility and rarefaction effects on mass flow rate and the curvature of the pressure distribution by employing first-order and second-order slip flow models are analyzed and compared. The condition of linear pressure distribution is given. This paper demonstrates that with some relatively simple ideas from knowledge, observation, and intuition, one can predict some fairly complex flows.

Developing natural convection gaseous flows in an open-ended parallel plate vertical microchannel with isothermal wall conditions are numerically investigated to analyze the rarefaction effects on heat transfer and flow characteristics in slip flow regime. The Navier-Stokes and energy equations are solve by a control volume technique subject to higher-order temperature jump and velocity slip conditions including thermal creep effects. The flow and thermal fields in the entrance and fully developed regions along with the axial variations of velocity slip, temperature jump, and heat transfer rates are examined in detail. It is found that rarefaction effects significantly influence the flow and thermal fields such that mass flow and heat transfer rates are increased considerably as compared to the continuum regime. Furthermore, thermal creep contribution to the velocity slip is found to be dominant close to the channel inlet and vanishes in the fully developed region, while velocity slip approaches a finite value there. Both Mass flow rate and thermal entrance length increase with increasing Knudsen number in slip flow regime.

Fluid flow and heat transfer in the entrance region of rectangular microchannels of various aspect ratios, 0.2 ≤ α* ≤ 1, are numerically investigated in the slip flow regime, 10 −3 ≤ Kn ≤ 10 −1 , with particular attention to the thermal creep effects. Uniform inlet velocity and temperature profiles are prescribed in a microchannel with constant wall temperature. The gas inlet temperature is prescribed higher than the wall temperature in order to study the thermal creep effects in a fluid cooling process. To avoid unrealistically large axial temperature gradients due to the prescribed uniform inlet temperature and upstream conduction associated with low Reynolds number flows encountered in microchannels, an adiabatic section is added to the inlet of the channel, which resembles an adiabatic reservoir. A control volume technique is employed to solve the Navier-Stokes and energy equations which are accompanied with appropriate velocity-slip and temperature-jump boundary conditions at walls. Despite the constant wall temperature, axial and peripheral temperature gradients form in the gas layer adjacent to the wall due to temperature-jump. The simultaneous effects of velocity-slip, temperature-jump and thermal creep on the flow and thermal patterns along with the key flow parameters are examined in detail for a wide range of cross sectional aspect ratios, and Knudsen and Reynolds numbers (0.1 ≤ Re ≤ 5). Present results indicate that thermal creep effects influence the flow field and the temperature distribution significantly in the early section of the channel.

The Cassie-Baxter state is a phenomenon in which a liquid rests on top of a textured surface with a gas layer trapped underneath the liquid layer. This gas layer introduces an effective shear free boundary that induces slip at the liquid-gas interface, allowing for friction reduction in liquid channel flows. Multiple studies have shown that different surface configurations result in different friction reduction characteristics, and most work is aimed at controlling the roughness factor and its shape in order to achieve an increased slip flow. This paper investigates the effects that different texturing geometries have on the stability of the Cassie state under pressurized microchannel flow conditions. To test the stability effects associated with the pressurized microchannel flow conditions, microfluidic channels with microstructures on the side walls were designed and fabricated. The microstructures were designed to induce the Cassie state with a liquid-air interface forming between the texturing trenches. The air trapped within the microstructure is treated as an ideal gas, with the compressibility induced pressure rise acting as a restrictive force against the Wenzel wetting transition. The model was validated against experimental flow data obtained using microchannel samples with microtextured boundaries. The microchannels were fabricated in PDMS (poly-dimethylsiloxane) using soft lithography and were baked on a hot plate to ensure the hydrophobicity of the microtexture. Pressure versus flow rate data was obtained using a constant gravitational pressure head setup and a flow meter. The liquid-gas interface layer in the microchannel was visualized using bright field microscopy that allowed measurement of the liquid penetration depth into the microtexturing throughout the microhannel. The experimental results indicate that air trapped in the pockets created by micro-cavity structures prevented the liquid layer from completely filling the void. As expected, the pressure drop in the micro-cavity textured channel showed a considerable decrease compared to that in the flat surfaced channel. These results also suggest that micro-cavities can maintain the Cassie state of a liquid meniscus, resting on top of the surface, in larger pressure ranges than open spaced micro-pillars arrays.

This paper concern is to study the gas properties effect in flow and heat transfer behaviors through microchannels using the direct simulation Monte Carlo method. The flow is rarefied and supersonic. The channels are investigated at two different inlet boundary conditions. The collision process is modeled using the NTC (no-time-counter) scheme. The VHS model is chosen to simulate collision between particle pairs. The study is provided for many different gases including nitrogen, helium, and oxygen. The Knudsen number is chosen in a manner to provide slip flow through the channel. The results show that the heat transfer from the wall is lower for heavier gases. A comparative study among the monatomic, diatomic, polyatomic gases shows that the heat transfer rate is lower for the polyatomic gases. The result shows that, the heat transfer from the wall is lower for the heavier gases than that for the lighter gas. For a fixed Mach number, the heat transfer from the wall decreases as the molecular diameter increases.

Accurate modeling of gas microvection is crucial for a lot of MEMS applications (micro-heat exchangers, pressure gauges, fluidic microactuators for active control of aerodynamic flows, mass flow and temperature micro-sensors, micropumps and microsystems for mixing or separation for local gas analysis, mass spectrometers, vacuum and dosing valves…). Gas flows in microsystems are often in the slip flow regime, characterized by a moderate rarefaction with a Knudsen number of the order of 10 −2 –10 −1 . In this regime, velocity slip and temperature jump at the walls play a major role in heat transfer. This paper presents a state of the art review on convective heat transfer in microchannels, focusing on rarefaction effects in the slip flow regime. Analytical and numerical models are compared for various microchannel geometries and heat transfer conditions (constant heat flux or constant wall temperature). The validity of simplifying assumptions is detailed and the role played by the kind of velocity slip and temperature jump boundary conditions is shown. The influence of specific effects, such as viscous dissipation, axial conduction and variable fluid properties is also discussed.

Many industrial processes make extensive use of membranes to separate fluxes while allowing some of the constituent species to diffuse into each other. In recent years, high production and maintenance costs induced by fouling, poisoning and clogging of the membrane pores due to impurities have create conditions to study alternative way of making liquid and/or gaseous streams interact and diffuse without the presence of a physical barrier. One of the possibilities is offered by the essentially laminar character of the flow in microfluidic devices that allows two or more different fluid streams to merge without mixing in a large range of experimental and industrial conditions. In this work, we will study, numerically, the case of two streams of different composition merging in a micro-channel. The upper and lower sides of the micro-channel are heated differentially and the inlet velocity of the streams is set independently in the range 0–1m/s. Simulations are carried out in 2D and 3D while fluids are chosen by considering their industrial importance and application. The main results are that the stability of the streams is very sensitive to the inlet conditions and that it is possible to modulate the mixing layer thickness by acting on thermal gradients, geometrical constraints and slip flow conditions.

Slip flow in noncircular microchannels has been examined and a simple model for normalized Poiseuille number is proposed to predict the friction factor and Reynolds number product fRe for slip flow. The developed model for normalized Poiseuille number has an accuracy of 4.2 percent for all common duct shapes. As for slip flow, no solutions or graphical and tabulated data exist for most geometries, the developed simple model can be used to predict friction factor, mass flow rate, and pressure distribution of slip flow in noncircular microchannels for the practical engineering design of microchannels such as rectangular, trapezoidal, double-trapezoidal, triangular, rhombic, hexagonal, octagonal, elliptical, semielliptical, parabolic, circular sector, circular segment, annular sector, rectangular duct with unilateral elliptical or circular end, annular, and even comparatively complex doubly-connected microducts.