Thermal Creep Flow Research Articles

Observation of dust torus with poloidal rotation in direct current glow discharge plasma

Observation of dust cloud rotation in parallel-plate DC glow discharge plasma is reported here. The experiments are carried out at high pressures (∼130 Pa) with a metallic ring placed on the lower electrode (cathode). The dust cloud rotates poloidally in the vertical plane near the cathode surface. This structure is continuous toroidally. Absence of magnetic field rules out the possibility of E × B induced ion flow as the cause of dust rotation. The dust rotational structures exist even with water cooled cathode. Therefore, temperature gradient driven mechanisms, such as thermophoretic force, thermal creep flow, and free convection cannot be causing the observed dust rotation. Langmuir probe measurement reveals the existence of a sharp density gradient near the location of the rotating dust cloud. The gradient in the density, giving rise to a gradient in the ion drag force, has been identified as the principal cause behind the rotation of dust particles.

A kinetic model of the Boltzmann equation for non-vibrating polyatomic gases

AbstractA kinetic model of the Boltzmann equation for non-vibrating polyatomic gases is proposed, based on the Rykov model for diatomic gases. We adopt two velocity distribution functions (VDFs) to describe the system state; inelastic collisions are the same as in the Rykov model, but elastic collisions are modelled by the Boltzmann collision operator (BCO) for monatomic gases, so that the overall kinetic model equation reduces to the Boltzmann equation for monatomic gases in the limit of no translational–rotational energy exchange. The free parameters in the model are determined by comparing the transport coefficients, obtained by a Chapman–Enskog expansion, to values from experiment and kinetic theory. The kinetic model equations are solved numerically using the fast spectral method for elastic collision operators and the discrete velocity method for inelastic ones. The numerical results for normal shock waves and planar Fourier/Couette flows are in good agreement with both conventional direct simulation Monte Carlo (DSMC) results and experimental data. Poiseuille and thermal creep flows of polyatomic gases between two parallel plates are also investigated. Finally, we find that the spectra of both spontaneous and coherent Rayleigh–Brillouin scattering (RBS) compare well with DSMC results, and the computational speed of our model is approximately 300 times faster. Compared to the Rykov model, our model greatly improves prediction accuracy, and reveals the significant influence of molecular models. For coherent RBS, we find that the Rykov model could overpredict the bulk viscosity by a factor of two.

Numerical study of thermal creep flow between two ratchet surfaces

Several designs of Knudsen pumps, the principle of which is based on a thermally driven flow generated along a microchannel, have been proposed in the literature. The fabrication of efficient prototypes, however, is generally limited by the difficulty to control the temperature distribution along the walls. An alternative possibility, which only requires isothermal hot or cold walls, is investigated. The pumping element consists of two facing isothermal ratchet surfaces with different temperatures. The asymmetric saw-tooth like surfaces lead to a rectified Knudsen flow along the walls. This flow is numerically simulated in the slip flow regime with Navier–Stokes equations and appropriate first-order velocity slip, including thermal creep and wall curvature effects, as well as temperature jump, boundary conditions. The influence of the geometrical parameters is investigated, among which the ratchet angle and the alignment of the ratchet pattern. The influence of the Knudsen number and of the temperature difference is analyzed as well and guidelines are drawn for designing a prototype.

Observation of macroscopic aerosol motion due to thermal creep on chamber walls at low Knudsen number in microgravity

In a rarefied gas the temperature field and the gas motion are closely related, and the temperature field can cause, in a confined flow geometry, a steady flow without the help of external forces. This is due to the creep of the fluid along the walls induced by a wall temperature gradient, as a consequence of the molecular transfer of momentum to the wall. Experiments performed in microgravity conditions in two small cells, with mono- and bi-atomic carrier gases (Ar, N2), and a thermal gradient between upper and bottom horizontal plates, allowed the measurement of the width of the thermal creep and the induced velocity of the gas near the vertical cell wall, due to thermal gradient. In addition, experiments demonstrated the existence of the thermal creep flow in the cells, even with Knudsen number as low as 10−5. The work evidences experimentally, and for the first time, the thermal creep flow in small cells, due to wall temperature gradient, with Knudsen number as low as 10−5. In view of these results, the no-slip boundary conditions of the Navier–Stokes law in the “continuum” regime can be inadequate in non-isothermal flow geometry and in microgravity conditions.

Energy harvesting through gas dynamics in the free molecular flow regime between structured surfaces at different temperatures.

For a gas confined between surfaces held at different temperatures the velocity distribution shows a significant deviation from the Maxwell distribution when the mean free path of the molecules is comparable to or larger than the channel dimensions. If one of the surfaces is suitably structured, this nonequilibrium distribution can be exploited for momentum transfer in a tangential direction between the two surfaces. This opens up the possibility to extract work from the system which operates as a heat engine. Since both surfaces are held at constant temperatures, the mode of momentum transfer is different from the thermal creep flow that has gained more attention so far. This situation is studied in the limit of free-molecular flow for the case that an unstructured surface is allowed to move tangentially with respect to a structured surface. Parameter studies are conducted, and configurations with maximum thermodynamic efficiency are identified. Overall, it is shown that significant efficiencies can be obtained by tangential momentum transfer between structured surfaces.

Solving the Boltzmann equation deterministically by the fast spectral method: application to gas microflows

AbstractBased on the fast spectral approximation to the Boltzmann collision operator, we present an accurate and efficient deterministic numerical method for solving the Boltzmann equation. First, the linearized Boltzmann equation is solved for Poiseuille and thermal creep flows, where the influence of different molecular models on the mass and heat flow rates is assessed, and the Onsager–Casimir relation at the microscopic level for large Knudsen numbers is demonstrated. Recent experimental measurements of mass flow rates along a rectangular tube with large aspect ratio are compared with numerical results for the linearized Boltzmann equation. Then, a number of two-dimensional microflows in the transition and free-molecular flow regimes are simulated using the nonlinear Boltzmann equation. The influence of the molecular model is discussed, as well as the applicability of the linearized Boltzmann equation. For thermally driven flows in the free-molecular regime, it is found that the magnitudes of the flow velocity are inversely proportional to the Knudsen number. The streamline patterns of thermal creep flow inside a closed rectangular channel are analysed in detail: when the Knudsen number is smaller than a critical value, the flow pattern can be predicted based on a linear superposition of the velocity profiles of linearized Poiseuille and thermal creep flows between parallel plates. For large Knudsen numbers, the flow pattern can be determined using the linearized Poiseuille and thermal creep velocity profiles at the critical Knudsen number. The critical Knudsen number is found to be related to the aspect ratio of the rectangular channel.

Numerical design of a Knudsen pump with curved channels operating in the slip flow regime

A numerical procedure has been developed for modeling 2D thermal creep flows with Fluent®. Complete first order velocity slip, including thermal creep and walls curvature effects, as well as temperature jump, boundary conditions, are implemented via C routines. After validation on benchmark flows, the technique is used for designing a Knudsen pump with curved microchannels and it is demonstrated that this micropump can be efficient in the slip flow regime.

Thermal Creep Flow of Helium Gas at Cryogenic Temperatures

We present a molecular dynamics (MD) simulation of nanoscale gas flow due to thermal creep at cryogenic temperatures. Helium is considered because its low liquefying temperature allows a wide range of cryogenic analysis. The thermal creep flow along a nanochannel is generated by applying temperature differences along the channel. Pressure and density variations are measured at various rarefaction conditions, covering the slip flow to the free molecular regimes. Thermo molecular pressure difference (TMPD) values are also calculated. Our results are compared with those in the literature.

A Unified Gas-Kinetic Scheme for Continuum and Rarefied Flows III: Microflow Simulations

AbstractDue to the rapid advances in micro-electro-mechanical systems (MEMS), the study of microflows becomes increasingly important. Currently, the molecular-based simulation techniques are the most reliable methods for rarefied flow computation, even though these methods face statistical scattering problem in the low speed limit. With discretized particle velocity space, a unified gas-kinetic scheme (UGKS) for entire Knudsen number flow has been constructed recently for flow computation. Contrary to the particle-based direct simulation Monte Carlo (DSMC) method, the unified scheme is a partial differential equation-based modeling method, where the statistical noise is totally removed. But, the common point between the DSMC and UGKS is that both methods are constructed through direct modeling in the discretized space. Due to the multiscale modeling in the unified method, i.e., the update of both macroscopic flow variables and microscopic gas distribution function, the conventional constraint of time step being less than the particle collision time in many direct Boltzmann solvers is released here. The numerical tests show that the unified scheme is more efficient than the particle-based methods in the low speed rarefied flow computation. The main purpose of the current study is to validate the accuracy of the unified scheme in the capturing of non-equilibrium flow phenomena. In the continuum and free molecular limits, the gas distribution function used in the unified scheme for the flux evaluation at a cell interface goes to the corresponding Navier-Stokes and free molecular solutions. In the transition regime, the DSMC solution will be used for the validation of UGKS results. This study shows that the unified scheme is indeed a reliable and accurate flow solver for low speed non-equilibrium flows. It not only recovers the DSMC results whenever available, but also provides high resolution results in cases where the DSMC can hardly afford the computational cost. In thermal creep flow simulation, surprising solution, such as the gas flowing from hot to cold regions along the wall surface, is observed for the first time by the unified scheme, which is confirmed later through intensive DSMC computation.

Reconfigurable Optothermal Microparticle Trap in Air-Filled Hollow-Core Photonic Crystal Fiber

We report a novel optothermal trapping mechanism that occurs in air-filled hollow-core photonic crystal fiber. In the confined environment of the core, the motion of a laser-guided particle is strongly influenced by the thermal-gradient-driven flow of air along the core surface. Known as "thermal creep flow," this can be induced either statically by local heating, or dynamically by the absorption (at a black mark placed on the fiber surface) of light scattered by the moving particle. The optothermal force on the particle, which can be accurately measured in hollow-core fiber by balancing it against the radiation forces, turns out to exceed the conventional thermophoretic force by 2 orders of magnitude. The system makes it possible to measure pN-scale forces accurately and to explore thermally driven flow in micron-scale structures.

Numerical analysis of thermal creep flow in curved channels for designing a prototype of Knudsen micropump

The possibility to generate a gas flow inside a channel just by imposing a tangential temperature gradient along the walls without the existence of an initial pressure difference is well known. The gas must be under rarefied conditions, meaning that the system must operate between the slip and the free molecular flow regimes, either at low pressure or/and at micro/nano-scale dimensions. This phenomenon is at the basis of the operation principle of Knudsen pumps, which are actually compressors without any moving parts. Nowadays, gas flows in the slip flow regime through microchannels can be modeled using commercial Computational Fluid Dynamics softwares, because in this regime the compressible 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 the axial temperature gradient and the effect of the wall curvature, and the temperature jump boundary condition are applied. The developed simulation tool is used for the preliminary design of Knudsen micropumps consisting of a sequence of curved and straight channels.

Pressure- and Temperature-Driven Flow Through Triangular and Trapezoidal Microchannels

A detailed study of pressure- and temperature-driven flows through long channels of triangular and trapezoidal cross sections is carried out. Due to the imposed pressure and temperature gradients there is a combined gas flow consisting of a thermal creep flow from the cold toward the hot reservoir and a Poiseuille flow from the high- toward the low-pressure reservoir. The formulation is based on the linearized Shakhov model subject to Maxwell boundary conditions, and it is solved numerically using a finite-difference scheme in the physical space and the discrete velocity method in the molecular velocity space. The results are valid in the whole range of the Knudsen number. In addition to the dimensionless flow rates, a methodology is presented to estimate for a certain set of input data the mass flow rates and the pressure distribution along the channel. Finally, special attention is given to the case of zero net mass flow and to the computation of the coefficient of the thermomolecular pressure difference.

Heat-Assisted Magnetic Recording Air Bearing Simulations That Account for Lateral Air Temperature Variation

Heat assisted magnetic recording (HAMR) is a promising hard disk drive technology to reach 4 Tb/in2 storage densities. However, HAMR introduces significant thermal considerations that must be accounted for in air bearing simulations; the laser spot on the recording bit and heat dissipated into the slider by the laser delivery system result in boundary wall temperatures that are several hundred degrees Celsius above ambient. Since the air bearing film between the slider and disk is non-isothermal, the local air properties should be used in the lubrication equation that governs the pressure generation. A molecular gas lubrication equation for the air bearing that accounts for large temperature variation along the film was previously proposed by Fukui and Kaneko, but it has yet to be applied to a HAMR hard disk drive. This paper explains the generalized lubrication equation and also implements it into a realistic 2D simulation using a production slider with approximate HAMR conditions. The minimum flying height increases substantially, while the pitch and roll are inappreciably affected. Thermal creep flow is negligible compared with Poiseuille and Couette flows, and it can be omitted from consideration. The sensitivity of the read/write transducer would be affected by the large increase in minimum flying height; therefore, the thermal flying height control design process must consider these variations due to thermal variations in the air bearing.

Momentum and mass fluxes in a gas confined between periodically structured surfaces at different temperatures

It is well known that in a gas-filled duct or channel along which a temperature gradient is applied, a thermal creep flow is created. Here we show that a mass and momentum flux can also be induced in a gas confined between two parallel structured surfaces at different temperatures, i.e., orthogonal to the temperature gradient. We use both analytical and numerical methods to compute the resulting fluxes. The momentum flux assumes its maximum value in the free-molecular flow regime, the (normalized) mass flux in the transition flow regime. The discovered phenomena could find applications in methods for energy-conversion and thermal pumping of gases.

Multiple temperature model for the information preservation method and its application to nonequilibrium gas flows

The information preservation (IP) method has been successfully applied to various nonequilibrium gas flows. Comparing with the direct simulation Monte Carlo (DSMC) method, the IP method dramatically reduces the statistical scatter by preserving collective information of simulation molecules. In this paper, a multiple temperature model is proposed to extend the IP method to strongly translational nonequilibrium gas flows. The governing equations for the IP quantities have been derived from the Boltzmann equation based on an assumption that each simulation molecule represents a Gaussian distribution function with a second-order temperature tensor. According to the governing equations, the implementation of IP method is divided into three steps: molecular movement, molecular collision, and update step. With a reasonable multiple temperature collision model and the flux splitting method in the update step, the transport of IP quantities can be accurately modeled. We apply the IP method with the multiple temperature model to shear-driven Couette flow, external force-driven Poiseuille flow and thermal creep flow, respectively. In the former two cases, the separation of different temperature components is clearly observed in the transition regime, and the velocity, temperature and pressure distributions are also well captured. The thermal creep flow, resulting from the presence of temperature gradients along boundary walls, is properly simulated. All of the IP results compare well with the corresponding DSMC results, whereas the IP method uses much smaller sampling sizes than the DSMC method. This paper shows that the IP method with the multiple temperature model is an accurate and efficient tool to simulate strongly translational nonequilibrium gas flows.

Calculation of Knudsen layers and jump conditions using the linearised G13 and R13 moment methods

For gas flows in micro-channels the molecular mean free path is often comparable to the channel dimensions and the flow must be modelled using one of the methods of non-continuum gas dynamics. For slip-flow or lower transition regime calculations the Grad 13-moment (G13) method or its extension the Regularised 13-moment (R13) method has been proposed. The R13 method is assumed to be an improvement over the G13 because it can capture, at least to some extent, Knudsen layers close to solid surfaces. This paper investigates the capabilities of the two methods by using them to address the classical problems of viscous slip, temperature jump and thermal creep. For the linearised equations it is possible to obtain analytical solutions and these provide physical insight as well as numerical values. The analysis shows that the Knudsen layer associated with temperature and normal stress decouples from the layer associated with velocity and heat flux. Comparison with more accurate solutions of the kinetic equation shows that the LR13 method underpredicts the velocity slip and temperature jump coefficients by about 10% and only provides a slight improvement over the much simpler LG13 method. Furthermore, the Knudsen layer velocity and temperature profiles bear only a superficial resemblance to more accurate solutions. For reasons that are unclear, the calculation of the thermal creep flow is very much more successful. It is concluded that considerable improvements need to be made before the LR13 method becomes a reliable technique for solving non-continuum flow problems.

S165014 境界面の温度分布を考慮した浮動へッドの分子気体潤滑解析([S16501]ヘッド・ディスク・インターフェイス)

This paper analyzes i) the static characteristics of thermally induced levitation (T1L) forces caused by thermal creep flow, which occur only in regions where the Knudsen number is not negligible and a temperature gradient exists, and ii) the static lubrication characteristics of a plane inclined slider over a running boundary wall. Using the molecular gas-film lubrication (MGL) equation with consideration of thermal creep flow, we investigated the basic characteristics both theoretically and numerically, especially when the boundary wall has an inverse V-shaped temperature distribution.

Working gas temperature and pressure changes for microscale thermal creep-driven flow caused by discontinuous wall temperatures

Microscale temperature gradient-driven (thermal creep/transpiration) gas flows have attracted significant interest during the past decade. For free molecular and transitional conditions, applying temperature gradients to a flow channel's walls induces the thermal creep effect. This results in a working gas flowing through the channel from cold to hot, which is generally accompanied by a rising pressure from cold to hot in the channel. Working gas temperature and pressure distributions can vary significantly, depending on a flow channel's configuration and wall temperature distribution. Understanding working gas temperature excursions, both increases and decreases, is essential to ensure the effective use of thermal creep flows in microscale applications. In this study, the characterizations of working gas temperature variations, due to both temperature discontinuities and more gradual changes, on a variety of flow channel walls, were systematically investigated using the direct simulation Monte Carlo (DSMC) method. A micro/meso-scale pump, the Knudsen compressor, was chosen to illustrate the importance of controlling working gas temperature in thermal creep-driven flows. Gas pressure and temperature variations, through several Knudsen compressor stage configurations, were studied to determine the most advantageous flow phenomena for the efficient operation of Knudsen compressors.

Gas flow driven by thermal creep in dusty plasma

Thermal creep flow (TCF) is a flow of gas driven by a temperature gradient along a solid boundary. Here, TCF is demonstrated experimentally in a dusty plasma. Stripes on a glass box are heated by laser beam absorption, leading to both TCF and a thermophoretic force. The design of the experiment allows isolating the effect of TCF. A stirring motion of the dust particle suspension is observed. By eliminating all other explanations for this motion, we conclude that TCF at the boundary couples by drag to the bulk gas, causing the bulk gas to flow, thereby stirring the suspension of dust particles. This result provides an experimental verification, for the field of fluid mechanics, that TCF in the slip-flow regime causes steady-state gas flow in a confined volume.

Creep and depinning of vortices in a nontwinned YBa2Cu3O6.87 single crystal

We present the results of a transport study of vortex dynamics in YBa2Cu3O6.87 crystals in magnetic field H∥c. At low magnetic fields, H<4kOe, the measurements were performed in the range of vortex velocities v=10−4–2m∕s, which covers the thermal creep and flux flow modes. The pinning force Fp depends nonmonotonically on magnetic field in both modes, though the low-field minimum in the Fp(H) curve shifts to higher fields with increasing velocity v, which is interpreted as partial ordering of the vortex lattice. The increase of the pinning force Fp with increasing field, which is observed in the flux flow mode in fields H⩾3kOe, is interpreted by the presence of finite transverse barriers. The barriers result in preserving the entangled vortex solid phase for the above-barrier vortex motion along the action of the Lorentz force. We also show that field variation of the depinning current has a single maximum, while the field variation of the pinning force in the deep creep mode has two maxima. The appearance of two maxima is associated with nonmonotonic field variation of the activation energy Upl, which corresponds to plastic vortex creep mediated by the motion of dislocations.