Slip Flow Regime Research Articles

Nanoscale Fluid-Structure Interaction Model for Multilayer Graphene Based-Resonators: Slip and Transition Flow Regimes

Nanoscale Fluid-Structure Interaction Model for Multilayer Graphene Based-Resonators: Slip and Transition Flow Regimes

An analytical solution for aerosol penetration in the slip flow regime

The classical theory for the diffusional loss of aerosol particles in a fully developed laminar flow through a circular tube derived by Gormley and Kennedy (1949) did not consider the slip-flow condition. However, the non-slip condition for the gas velocity boundary condition may not be appropriate for the gas flow in microgeometries such as microchannels and microtubes. This paper extends the work of Gormley and Kennedy (GK) to include the effect of slip-flow, which often occurs in the gas flow at low pressure or with a small characteristic length scale. In the present solution, the separation of variables was applied to solve the convection-diffusion equation, then confluent hypergeometric function was used to solve for the number concentration as a function of radial distance analytically. Eigenvalues were evaluated for Knudsen numbers ranging from 0.001 to 0.1. Finally, a simple power series correlation was developed to describe aerosol penetration in the slip flow regime as a function of the dimensionless deposition factor and Knudsen number (Kn). In the slip flow regime, the penetration decreases with increasing Kn. The correlation is reduced to GK’s solution when Kn = 0. The present solution of aerosol penetration calculated at Kn = 0 shows good agreement with GK’s solution and validates the applicable range of the approximate solution by Alonso et al. (2016).

Curved boundary conditions of the lattice Boltzmann method for simulating microgaseous flows in the slip flow regime

The lattice Boltzmann method (LBM) has shown its promising capability in simulating microscale gas flows in the slip regime. However, the suitable boundary condition is still one of the critical issues for the LBM to model microgaseous flows involving curved geometries. In this paper, a local boundary condition of the LBM is proposed to treat curved solid walls of microgaseous flows in slip flow regime. The developed boundary treatment combines the Maxwellian diffuse reflection scheme (Ansumali and Karlin, 2002) and a single-node boundary scheme (Zhao et al., 2019) which contains a free parameter as well as the distance ratio. The curved boundary condition is analyzed within the multiple-relaxation-time (MRT) model for a unidirectional microflow. It is shown that the derived slip velocity depends on the free parameter as well as the distance ratio and relaxation times. By virtue of the free parameter, the combination parameter and the uniform relaxation time are theoretically determined to realize the accurate slip boundary condition. In addition, it is found that besides the halfway diffuse-bounce-back (DBB) scheme, previous curved boundary schemes only containing the distance ratio cannot ensure uniform relaxation times to realize the slip boundary condition. Some numerical examples with planar and curved boundaries are carried out to validate the present curved boundary scheme. The good and robust consistency of numerical predictions with analytical solutions demonstrates our theoretical analysis.

Computational fluid dynamics modeling of spatial atomic layer deposition on microgroove substrates

Spatial atomic layer deposition (ALD) is a promising high-throughput technique capable of producing ultrathin films on large substrates. Compared to flat wafers, deposition on substrates with microstructures has a wider range of applications such as photovoltaic cells, electronics, flexible displays, etc. However, spatial ALD on microstructure substrates is a complex and strong-coupled process of fluid flow, heat and mass transfer, as well as chemical reactions. The fluid dynamics and the precursor distribution in spatial ALD are of great importance to obtain conformal growth with high throughput. In this study, a two-dimensional model coupling computational fluid dynamics with chemical kinetics is established to quantitatively explore the effect of microgroove structures on the fluid dynamics, precursor distribution and film conformality in an atmospheric spatial ALD system. Slip boundary condition is adopted to model the slip flow regime in the micro-gap between the injector and the substrate surface, and dynamic layering method is implemented to simulate an entire ALD cycle with the in-line movement of the substrate. Results show that while the flow field is very smooth with a flat substrate, vortices always exist in the micro-gap with microgroove substrates. Due to the angle differences between the flow direction and the vertical microstructure surface, the inflow and outflow of precursors and purging gas are prevented at the microgroove corners. A relatively lower moving speed of the substrate is beneficial for the saturated film growth and better film conformality. Increasing the carrier gas flow rate can effectively reduce the non-uniformity and non-conformality of the film, but the precursor utilization also decreases. Compared with the nonoptimal conditions, within a moderate range of carrier gas flow rate and substrate speed, the precursor utilization and film conformality have been improved. Focusing on the effect of the micro-scale features of the substrate, this study is a valuable step in extending spatial ALD for ultrathin films on miniature devices.

Separation of a binary gas mixture outflowing into vacuum through a micronozzle

The present paper studies the separation phenomenon for argon–helium mixture outflowing through a convergent–divergent micronozzle into a vacuum. We numerically investigate the effect of the geometrical parameters of the micronozzle and gas rarefaction (Knudsen number is varied in range ≈0.01−100). Simulations were performed using the event-driven molecular dynamics method. Performed analysis revealed several interesting and important features of the separation process. First, it was shown that separation in the present problem results mainly from a lateral component, which appears when significant curvature of gas streamlines is present. Second, it was demonstrated how the fine-tuning of micronozzle geometry can enhance separation efficiency. At the same time, the simplest microslit arrangement (a microchannel without converging and diverging parts) was shown to provide results comparable to micronozzles and may be preferable due to its manufacturing simplicity. Then, it was shown that the position of the product gas selector is crucial for effective separation and its proper placement brings more influence than the geometry of the micronozzle itself. Finally, it was shown that maximal purity of product gas can be obtained in a peripheral area in transitional and slip flow regimes inside the micronozzle. Therefore, for effective separation, there is no need to achieve high rarefaction levels inside the micronozzle.

Periodic permeable free convective 3-dimensional flow of a second grade fluid with slip effect

This study addresses the development of a mathematical model and theoretical analysis of a free convective three-directional flow of an incompressible second-grade fluid through a highly porous medium bounded by a vertical infinite plate in slip flow regime subjected to a constant suction. The free stream velocity is rumored to be constant while permeability of the medium is presumed to be periodic. It is well known that the assumption of either time dependent or constant permeability of a porous medium leads to two-dimensional flows, of course, the flow comes to be three-dimensional due to variation in permeability of the porous medium. Approximate solutions of velocity and temperature fields, heat flux and skin friction are established by applying the regular perturbation technique. Results are discussed and visualized graphically in the light of physical parameters emerging in the mathematical model of the physical phenomenon with carefully selected and viable data. The significance of current study reveals that presence of slip parameter reduces the thickness of boundary layer causing the enhancement in the main flow velocity component. With increasing permeability parameter fluid velocity is decelerated whereas it is accelerated with increasing Grashof number. With increasing non-Newtonian parameter, a similar response is noted as for the permeability parameter. It is also noted that permeability parameter, Prandtl number, Grashof number and elastic parameter provide mechanism to control the skin friction. In addition, Reynolds number also plays a vital role to control the skin friction. Furthermore, Reynolds number significantly boosts the coefficient of heat transfer, and Prandtl number causes to reduce the thermal boundary layer thickness.

On the forced convective flow inside thermal collectors enhanced by porous media: from macro to micro-channels

PurposeAiming at finding the velocity distribution profile and other flow characteristic parameters such as the Poiseuille (Po) number, this study aims to focus on the three-dimensional forced convective flow inside rectangular ducts filled with porous media commonly used in air-based solar thermal collectors to enhance the thermal performance. The most general model for the fluid flow (i.e. the non-linear Darcy–Brinkman–Forchheimer partial differential equation subjected to slip and no-slip boundary conditions) is considered.Design/methodology/approachThe general governing equations are solved analytically based on the perturbation technique and the results are validated against numerical simulation study based on a finite-difference solution over a non-uniform but structured grid.FindingsThe analytical velocity distribution profile based on exponential functions for the above-mentioned general case is obtained, and accordingly, expressions for the Po are introduced. It is found that the velocity distribution tends to be uniform by increasing the aspect ratio of the duct. Moreover, a criterion for considering/neglecting the nonlinear drag term in the momentum equation (i.e. the Forchheimer term) is proposed. According to the sensitivity analysis, results show that the nonlinear drag term effects on the Nusselt number are important only in porous media with high Darcy numbers.Originality/valueA general analytic solution for three-dimensional forced convection flows through rectangular ducts filled with porous media for the general model of Darcy–Brinkman–Forchheimer and the general boundary condition including both no-slip and slip-flow regimes is obtained. An analytic expression to calculate Po number is obtained which can be practical for engineering estimations and a basis for validation of numerical simulations. A criterion for considering/neglecting the nonlinear drag term in the momentum equation is also introduced.

Analysis of Thermal Creep Effects on Fluid Flow and Heat Transfer in a Microchannel Gas Heating

Abstract Thermal creep effects on fluid flow and heat transfer in a microchannel gas flow at low velocities are studied numerically. The continuity and Navier–Stokes equations in vorticity–stream function form, coupled with the energy equation, are solved, considering the thermal creep effect due to the longitudinal temperature gradient along the channel wall in addition to the combined effects of viscous dissipation, pressure work, axial conduction, shear work, and nonequilibrium conditions at the gas–wall interface. The governing equations are also solved without thermal creep, and comparisons between the two solutions are presented to evaluate the thermal creep effect on the flow field in the slip flow regime at relatively low Reynolds numbers. The results presented show that the thermal creep effect on both velocity and temperature fields become more significant as the Reynolds number decreases. Thermal creep effect on the velocity field also extends a longer distance downstream the channel as the Reynolds number decreases, hence increasing the hydrodynamics entrance length. Thermal creep can cause high positive velocity gradients at the upper channel wall for gas heating and hence reverse the flow rotation in the fluid layers adjacent to the wall. Thermal creep also results in a higher gas temperature in the developing region and higher heat exchange between the fluid and the channel wall in the entrance region. Thermal creep effect on heat exchange between the gas and the channel wall becomes more significant as the Knudsen number decreases.

Computational analysis of gas permeability of slip flow through microannulus replete by based‐circular Sierpinski porous medium

AbstractThere are wide applications for flow in a microporous medium. In this study, a computational analysis of airflow through a porous microannulus constructed by circular‐based Sierpinski has been performed in a slip flow regime, where several parameters played an important role in the flow characteristics. These parameters are the Knudsen number, the average friction factor, radius ratio, and porosity. The impacts of these parameters on permeability and the gas flow characteristics are examined and analyzed thoroughly. The ranges of the investigated parameters are as follows (0.001 ≤ Kn ≤ 0.1 and the porosity range is 0.75 ≤ ε ≤ 0.95). The results showed that porosity has a significant impact on the velocity distribution and Darcy number. The Knudsen number has also a direct effect on the velocity distribution, while it has a positive logarithmic proportionality with a dimensionless permeability but the radius ratio does have a neglected effect on the Darcy number. Moreover, the effect of the average friction factor has an inverse proportional relationship to the Darcy number.

Pumping Power Performance and Frictional Resistance of Textured Microchannels in Gaseous Slip Flows

The investigation of pressure drop characteristics along the microchannels with surface texturing is crucial to arrive at a desired structural size and performance of a microchannel. This study presents the comparison of flow friction and pumping power for two different Reynolds numbers (Re = 1.01 and 50.31) for rarefied gas flows in textured microchannels. The three-dimensional microchannel is computationally modeled with ratios of the height of texture to the height of the microchannel taken as 20, 40, and 60 and texture shapes as rectangular, circular, and triangular. All simulations are conducted in the slip flow regime for the Knudsen number ranging from 1.10 A� 10-3 to 2.07 A� 10-2 and tangential momentum accommodation coefficient (TMAC) ranging from 0.1 to 0.9. The time- and cost-effective Taguchi statistical analysis of the L18 orthogonal array is carried out to find the efficiency of the textured microchannels in terms of Poiseuille number and pumping power per unit mass flow rate. It is found that the height of texture is the most important control factor for efficiency, while the shape is the least important factor for both Reynolds numbers. The second most significant factor for Re = 50.31 is the Knudsen number and that for Re = 1.01 is the TMAC. The present numerical work can be applied for designing micropiping systems and diffusers with lower pumping power, lower frictional resistance, and higher efficiency. ©

Low-Speed DSMC Simulations of Hotwire Anemometers at High-Altitude Conditions

Numerical simulations of hotwire anemometers in low-speed, high-altitude conditions have been carried out using the direct simulation Monte Carlo (DSMC) method. Hotwire instruments are commonly used for in-situ turbulence measurements because of their ability to obtain high spatial and temporal resolution data. Fast time responses are achieved by the wires having small diameters (1–5 μm). Hotwire instruments are currently being used to make in-situ measurements of high-altitude turbulence (20–40 km). At these altitudes, hotwires experience Knudsen number values that lie in the transition-regime between slip-flow and free-molecular flow. This article expands the current knowledge of hotwire anemometers by investigating their behavior in the transition-regime. Challenges involved with simulating hotwires at high Knudsen number and low Reynolds number conditions are discussed. The ability of the DSMC method to simulate hotwires from the free-molecular to slip-flow regimes is demonstrated. Dependence of heat transfer on surface accommodation coefficient is explored and discussed. Simulation results of Nusselt number dependence on Reynolds number show good agreement with experimental data. Magnitude discrepancies are attributed to differences between simulation and experimental conditions, while discrepancies in trend are attributed to finite simulation domain size.

Numerical analysis of forced convection heat transfer in a rectangular micro-channel totally filled with Ag/ water nano fluid in slip flow regime using the lattice Boltzmann method

Numerical simulation reported on heat transfer and fluid flow in a two-dimensional rectangular micro channel totally filled with Ag/water. The first –order slip/jump boundary conditions were uniformly imposed to the up and bottom walls. The governing conservation equations are translated in dimensionless form using the thermal Single Relaxation Time (T-SRT) modified Lattice Boltzmann Method (LBM) with double distribution functions (DDFs). The viscous dissipations effects are adopted into the energy equation. Effects of nanoparticle volume fraction φ, slip coefficient, B, on the flow of Nano fluid and heat transfer were studied. The results were interpreter in terms of slip velocity; temperature jump and Nusselt number. Based on the results found, it can be concluded that decreasing the values of slip coefficient enhances the convective heat transfer coefficient and consequently the Nusselt number (Nu) but increases the slip velocity at the wall and temperature jump values.

MHD free convection flow past a vertical porous plate in a slip flow regime with radiation chemical reaction and temperature gradient dependent heat source in presence of Dufour effect

MHD free convection flow past a vertical porous plate in a slip flow regime with radiation chemical reaction and temperature gradient dependent heat source in presence of Dufour effect

Numerical Simulation of Frost Formation in Interrupted Micro Channel Heat Sinks Considering Microfluidic Effects in Slip Regime

Frost formation is a renowned phenomenon in HVAC, aeronautical and refrigeration industries. In this paper, numerical modeling and parametric study of the frost formation in the interrupted Micro Channels Heat sinks (MCHS) is investigated considering microfluidic effects in slip flow regime. For numerical modeling, basic equations of humid air and frost including continuum, momentum, energy and phase change mechanism are numerically solved and results are compared with reported data. Knudsen number (Kn) is changed so that slip flow regime requirement is accomplished. This requirement is also considered for setting boundary conditions. The effect of different parameters like cold surface temperature, time and Kn are studied on the frost formation and details of the flow field. Results revealed that with an increase in time and a decrease in Kn and cold surface temperature, weight and thickness of the frost increase. Moreover, with thicker frost maximum flow velocity rises in the microchannel. The details of frost formation and flow field, revealed by the numerical results can remarkably assist designing interrupted microchannel.

Flows between parallel plates: Analytical solutions of regularized 13-moment equations for inverse-power-law models

We study the structure of stationary channel flows predicted by the regularized 13-moment equations. Compared with the work of Taheri et al. [“Couette and Poiseuille microflows: Analytical solutions for regularized 13-moment equations,” Phys. Fluids 21, 017102 (2009)], we focus on gases whose molecules satisfy the general inverse power law. The analytical solutions are obtained for the semi-linear equations, and the structures of Couette, Fourier, and Poiseuille flows are solved by coupling the general solutions with newly derived boundary conditions. The results show excellent agreement with the reference solution in the slip-flow regime. Our results also show that the R13 equations derived from inverse-power-law models can have better accuracy than the R13 equations of Maxwell molecules with altered viscosity.

Poiseuille number behavior in an adiabatically choked microchannel in the slip regime

The influence of subsonic adiabatic choking on frictional resistance inside three-dimensional (3D) microchannels has not been studied for rarefied gas flows. In the present work, the variation of the Poiseuille number with respect to the Mach number has been documented for a 3D microchannel of aspect ratio (width/height) 0.49. Measurements of mass flow rate, static pressure, and temperature have been conducted with nitrogen in highly compressible and slightly rarefied (slip flow) regime: outlet Mach number (0.43–0.99), outlet Knudsen number (4.04 × 10−3–7.04 × 10−3), and pressure ratio (8.17–8.72). The present 3D measurements are compared with available analytical solutions for isothermal and adiabatic flows. A maximum deviation of only 4.8% from the adiabatic slip flow solution points toward the adiabatic nature of the exit choked state, which is being experimentally demonstrated for the first time in the highly compressible slip flow regime. Furthermore, the influence of losses of microchannel end manifolds on the overall pressure drop is calculated to be negligible. We further propose the ranges of the area ratio, Reynolds number, and Knudsen number for which these losses continue to be unimportant for gaseous slip flow. This study gives insights into the influence of subsonic choking on the frictional resistance at various mass flow rates and is relevant for future space expeditions and in certain biological applications.

GASEOUS SLIP FLOW FORCED CONVECTION IN A MICROPIPE AND PARALLEL-PLATE MICROCHANNEL WITH A PIECEWISE UNIFORM WALL HEAT FLUX AND AXIAL HEAT CONDUCTION

A forced convective heat transfer problem inside a micropipe as well as inside a microchannel with parallel walls in the laminar gaseous slip flow regime, a with finite heating region and a prescribed wall heat flux, including the axial heat conduction effect, is analytically investigated. The temperature field and Nusselt number are derived under the assumption that the flow is hydrodynamically fully developed in the finite-length heating region. The solution is found by applying the functional analysis method, by decomposing the energy equation into a pair of first-order partial differential equations. The first-order slip boundary conditions are imposed at the gas–wall interface. The analytical solution is compared with available calculations. The results show that the thermal characteristics in the heating region are significantly affected by the axial heat conduction, rarefaction effects, and finite length of the heating region.

Molecular dynamics simulations on the scattering of heavy gases on the composite surfaces

Cercignani-Lampis-Lord (CLL) is a boundary condition used in the DSMC method, due to the use of tangential and normal momentum accommodation coefficients (TMAC and NMAC) extractable by Molecular Dynamics (MD) simulations or experimental platforms, the accuracy of this boundary condition is by up to 15% relative to diffuse model (Mehta et al., 2014) [1]. These coefficients in slip, transitional, and free molecular flow regimes takes a value other than the unit. Since the temperature and velocity of the molecules after their scattering from the surface in the CLL model, drag coefficient, slip velocity, shear stress, and jumping temperature is completely dependent on the values of these coefficients, it is very important to determine these coefficients for different gases and surfaces. In this paper, first the DGEBA-TETA/carbon composite was simulated with MD method using an efficient algorithm and then using this method shown that in the interaction of heavy gases such as uranium, tellurium and sulfur hexafluoride with a composite surface, TMAC and NMAC were strongly dependent on Knudsen number and temperature of gases, velocity and temperature of composite, and the dependency of the TMAC was less than the NMAC for different conditions of gas characteristics. In these cases, tellurium hexafluoride had the greatest impact.

Variational derivation of thermal slip coefficients on the basis of the Boltzmann equation for hard-sphere molecules and Cercignani–Lampis boundary conditions: Comparison with experimental results

In the present paper, a variational method is applied to solve the Boltzmann equation based on the true linearized collision operator for hard-sphere molecules and the Cercignani–Lampis boundary conditions. This technique allows us to obtain an explicit relation between the first- and second-order thermal slip coefficients and the tangential momentum and normal energy accommodation coefficients, defined in the frame of the Cercignani–Lampis scattering kernel. Comparing the theoretical results with the experimental data from the work of Yamaguchi et al. [“Mass flow rate measurement of thermal creep flow from transitional to slip flow regime,” J. Fluid Mech. 795, 690 (2016)], a pair of accommodation coefficients has been extracted for each noble gas considered in the experiments. Then, these values have been used to compute, by means of our variational technique, the temperature-driven mass flow rates, and the outputs have been compared with the measurements for helium, neon, and argon. Good agreement has been obtained between the theoretical and the experimental data, within the range of validity of the proposed second-order slip model. For all the gases analyzed, the tangential accommodation coefficient is found to be much larger than the normal energy coefficient. The general trend, according to which, by increasing the molecular weight of the different gases, the values of both accommodation coefficients also increase, is confirmed in this study.

A Stochastic Two-Scale Model for Rarefied Gas Flow in Highly Heterogeneous Porous Media

This paper presents the development of a model enabling the analysis of rarefied gas flow through highly heterogeneous porous media. To capture the characteristics associated with the global- and the local-scale topology of the permeable phase in a typical porous medium, the heterogeneous multi-scale method, which is a flexible framework for constructing two-scale models, was employed. The rapid spatial variations associated with the local-scale topology are accounted for stochastically, by treating the permeability of different local-scale domains as a random variable. The results obtained with the present model show that an increase in the spatial variability in the heterogeneous topology of the porous medium significantly reduces the relevance of rarefaction effects. This clearly shows the necessity of considering a realistic description of the pore topology and questions the applicability of the results obtained for topologies exhibiting regular pore patterns. Although the present model is developed to study low Knudsen number flows, i.e. the slip-flow regime, the same development procedure could be readily adapted for other regimes as well.