Models for Gaseous Slip Flow in Non-Circular Microchannels

2007 ◽  
Author(s):  
Zhipeng Duan ◽  
Y. S. Muzychka
Keyword(s):  
Friction Factor ◽  
Cross Sections ◽  
Slip Flow ◽  
Analytical Models ◽  
Roughness Effects ◽  
Practical Applications ◽  
Micro Channels ◽  
Mems Technology ◽  
Compressibility Effects ◽  
Circular Microchannels

Micro-scale fluid dynamics has received intensive interest due to the emergence of Micro-Electro-Mechanical Systems (MEMS) technology. Non-circular cross sections are common channel shapes that can be produced through a variety of micro-fabrication techniques. Non-circular microchannels have extensive practical applications in MEMS. Slip flow in noncircular microchannels has been examined by the authors and a review of several new models obtained by the authors is presented. These models are general and robust, and can be used by the research community for practical engineering design of microchannel flow systems. The reviewed models address: (i) fully developed slip flow in non-circular microchannels, (ii) hydrodynamically developing slip flow in non-circular microchannels, (iii) compressibility effects, and (iv) roughness effects. A model is proposed to predict the friction factor and Reynolds product fRe for fully developed and developing slip flow in most non-circular micro-channels. Compressibility effects on slip flow in non-circular microchannels have been examined and simple models are proposed to predict the pressure distribution and mass flow rate for slip flow in most non-circular microchannels. Finally, the effect of corrugated surface roughness on fully developed laminar flow in microtubes is examined. Simple analytical models are developed to predict friction factor and pressure drop in corrugated rough microtubes for continuum flow and slip flow.

Friction Factor Correlations of Gas Slip Flow in Concentric Micro Annular Tubes

2009 ◽  
Author(s):  
Chungpyo Hong ◽  
Yutaka Asako ◽  
Koichi Suzuki
Keyword(s):  
Friction Factor ◽  
Cross Sections ◽  
High Speed ◽  
Slip Flow ◽  
Arbitrary Lagrangian Eulerian ◽  
Slip Boundary ◽  
Exit Mach Number ◽  
Fast Flow ◽  
Energy Equations ◽  
Compressibility Effects

A concentric micro annular passage is a basic and important micro-geometry of micro-fluidic-systems from simple heat exchangers to the most complicated nuclear reactors. Therefore, the product of friction factor and Reynolds number (f·Re) for quasi-fully developed high speed and slip flow in a concentric micro annular tubes of Re<1000 and Ma<1.0 was obtained numerically. The numerical methodology was based on the Arbitrary-Lagrangian-Eulerian (ALE) method. The compressible momentum and energy equations with slip boundary conditions were solved for both isothermal flow and no-heat conduction flow conditions. The outer tube radius ranged from 5 to 40 μm with the radius ratios of 0.2, 0.5 and 0.8. The ratio of length to hydraulic diameter was 100. The stagnation pressure was chosen in such a way that the exit Mach number ranged from 0.1 to 1.0. The outlet pressure was fixed at the atmospheric pressure. The value of f·Re for compressible slip flow in concentric micro annular tubes were obtained. The detail of the incompressible slip f·Re is documented and its value defined as a function of r* and Kn is represented. The results show that in the case of fast flow, the values of f·Re for compressible slip flow is higher than those for incompressible slip flow due to compressibility effects. Also, the f·Re correlation for compressible slip flow is obtained from that of compressible no-slip flow and incompressible slip flow as a function of Mach and Knudsen numbers and radius ratio. In addition, a f·Re correlation from the values of f·Re obtained for micro-channel, micro-tube, and micro annular tube referred in author’s previous works that is applicable to micro-geometries whose cross-sections are parallel, rectangular, circular and annular, is proposed.

Computing Separated Flows in MEMS Devices

2002 ◽  
Author(s):  
Oktay Baysal ◽  
Alim Rustem Aslan
Keyword(s):  
Temperature Jump ◽  
Slip Flow ◽  
Fluid Flows ◽  
Synthetic Jets ◽  
Separated Flows ◽  
Navier Stokes ◽  
Mems Devices ◽  
Micro Channels ◽  
Analytical Formulae ◽  
Compressibility Effects

Fluid flows in micro devices span the entire Knudsen (Kn) number regime. Depending on the Kn range, a full continuum or a full free-molecular analysis may be applicable. In the present study, flows in the Kn range of 10−3 to 10−1 are considered and they are modeled using a conventional Navier-Stokes solver. Its boundary conditions, however, have been modified to account for the slip velocity and the temperature jump conditions encountered in these micro-sized geometries. The computations have been performed for straight micro channels, a micro backward facing step, and a micro filter. The present results are then compared with analytical formulae and other computations available in the literature. The results indicate that the rarefaction and compressibility effects present in these micro devices have been accurately predicted. In the case of slip flow, the separation is found to occur at a higher Reynolds number compared to the corresponding no-slip flow case. As the next step of the study, micro synthetic jets will be computed and the optimal cavity actuator geometries will be sought for desired flow deflections.

Hydrodynamic Behaviour and Influence of Channel Wall Roughness and Hydrophobicity in Microchannels

2004 ◽  
Author(s):  
G. P. Celata ◽  
M. Cumo ◽  
S. McPhail ◽  
G. Zummo
Keyword(s):  
Friction Factor ◽  
Channel Wall ◽  
Slip Flow ◽  
Hydrophobic Surface ◽  
Wall Roughness ◽  
Flow Conditions ◽  
Adiabatic Flow ◽  
Hydrodynamic Behaviour ◽  
Inner Diameter ◽  
Circular Microchannels

The sometimes contradictory results available for fluid flow in micropipes show that much is yet to be verified in micro fluid dynamics. In this study the influence of channel wall roughness and of channel wall roughness and of channel wall hydrophobicity on adiabatic flow in circular microchannels is investigated, varying in diameter from 70 μm to 326 μm. The hydrodynamic behaviour of water in smooth tubes down to 30 μm inner diameter (ID) is also ascertained. Within the current experimental accuracy it is found that the classical Hagen-Poiseuille law for friction factor vs. Reynolds number is respected for all diameters measured and Re > 300. With degassed water, no effect of slip flow conditions due to hydrophobic channel walls even at 70 μm ID was noted, which might suggest that the slip flow phenomenon is associated with local desorption of dissolved gases on the hydrophobic surface, as reported elsewhere in the literature. For roughened glass channels, an increase in friction factor above 64/Re was observed only at the smallest diameter measured, 126 μm. For all experiments, no anticipated transition to turbulent flow was observed (2000 < Retr < 3000).

Slip Flow in the Hydrodynamic Entrance Region of Circular and Noncircular Microchannels

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
Zhipeng Duan ◽  
Y. S. Muzychka
Keyword(s):  
Friction Factor ◽  
Slip Flow ◽  
Velocity Slip ◽  
Mean Free Path ◽  
Momentum Equation ◽  
Linearization Method ◽  
Asymptotic Results ◽  
Cross Sectional ◽  
Practical Applications ◽  
Continuum Flow

Microscale fluid dynamics has received intensive interest due to the emergence of micro-electro-mechanical systems (MEMS) technology. When the mean free path of the gas is comparable to the channel’s characteristic dimension, the continuum assumption is no longer valid and a velocity slip may occur at the duct walls. Noncircular cross sections are common channel shapes that can be produced by microfabrication. The noncircular microchannels have extensive practical applications in MEMS. The paper deals with issues of hydrodynamic flow development. Slip flow in the entrance of circular and parallel plate microchannels is first considered by solving a linearized momentum equation. It is found that slip flow is less sensitive to analytical linearized approximations than continuum flow and the linearization method is an accurate approximation for slip flow. Also, it is found that the entrance friction factor Reynolds product is of finite value and dependent on the Kn and tangential momentum accommodation coefficient but independent of the cross-sectional geometry. Slip flow and continuum flow in the hydrodynamic entrance of noncircular microchannels has been examined and a model is proposed to predict the friction factor and Reynolds product f Re for developing slip flow and continuum flow in most noncircular microchannels. It is shown that the complete problem may be easily analyzed by combining the asymptotic results for short and long ducts. Through the selection of a characteristic length scale, the square root of cross-sectional area, the effect of duct shape has been minimized. The proposed model has an approximate accuracy of 10% for most common duct shapes.

Gas flow in micro-channels

1995 ◽  
Vol 284 ◽  
pp. 257-274 ◽  
Author(s):  
John C. Harley ◽  
Yufeng Huang ◽  
Haim H. Bau ◽  
Jay N. Zemel
Keyword(s):  
Reynolds Number ◽  
Mach Number ◽  
Friction Factor ◽  
Theoretical Investigation ◽  
Gas Flow ◽  
Slip Flow ◽  
First Order ◽  
Micro Channels ◽  
Theoretical Predictions ◽  
Good Agreement

An experimental and theoretical investigation of low Reynolds number, high subsonic Mach number, compressible gas flow in channels is presented. Nitrogen, helium, and argon gases were used. The channels were microfabricated on silicon wafers and were typically 100 μm wide, 104 μm long, and ranged in depth from 0.5 to 20 μm. The Knudsen number ranged from 10-3 to 0.4. The measured friction factor was in good agreement with theoretical predictions assuming isothermal, locally fully developed, first-order, slip flow.

A Comparison of Homogenization and Averaging Techniques for the Treatment of Roughness in Slip-Flow-Modified Reynolds Equation

2001 ◽  
Vol 124 (2) ◽  
pp. 327-335 ◽  
Author(s):  
M. Jai ◽  
B. Bou-Saı¨d
Keyword(s):  
Slip Flow ◽  
Rotating Disk ◽  
Homogenization Theory ◽  
Storage Device ◽  
Magnetic Storage ◽  
Roughness Effects ◽  
Small Surface ◽  
Air Gaps ◽  
Practical Applications ◽  
Recent Developments

This article is concerned with the simulation of a magnetic storage device consisting of a flying head above a rigid rotating disk. The need to improve the transfer rate has led, at present, to very small surface-to-surface distances (air gaps). In this situation it is compulsory to take into account roughness effects. A popular method consists in averaging film-thickness from Mitsuya et al. (1989), with good reported results compared with experimental data. To overcome some limitations that become apparent at very small air gaps, notably when the roughness is two-dimensional, Jai in 1995 introduced a new technique based on a rigorous homogenization theory. Recent developments from Buscaglia and Jai (2000) have greatly reduced the computational complexity of the homogenization-based method, rendering it suitable for practical applications. We propose in this paper an original approach based on strength and rigorous mathematical model to avoid numerical problems which are usually encountered in classical approaches. The validation of the homogenization-based method is in some sense, a generalization of the film-averaging technique suitable for configurations in which some parameters of the latter (such as the Boltzmann correction factor) are not unambiguously defined.

Experimental Study on Roughness Effect for Laminar Micro-Channel Gas Flow

2001 ◽  
Author(s):  
Jih-Hsing Tu ◽  
Fangang Tseng ◽  
Ching-Chang Chieng
Keyword(s):  
Experimental Study ◽  
Surface Roughness ◽  
Friction Factor ◽  
Gas Flow ◽  
Micro Channel ◽  
Micro Machining ◽  
Roughness Effect ◽  
Relative Roughness ◽  
Smooth Channel ◽  
Micro Channels

Abstract Present study investigates the roughness effect on laminar gas flow for microchannels ranging from 40 to 600 μm with various roughness heights (40–82 nm) by systematical experiments. The micro-channels are manufactured by micro-machining technology and KOH anisotropic etching is employed to achieve various roughness patterns. Experimental results shows that higher product levels of Reynolds number (Reh) and friction factor (f) are obtained for microchannels of larger size and smaller relative roughness and friction factor f approaches to laminar flow theory value f0 for very smooth channel but the ratio of (f/f0) decreases as the surface roughness increases.

An analytic study of vibrational energy harvesting using piezoelectric tiles in stairways subjected to human traffic

2018 ◽  
Vol 30 (5) ◽  
pp. 968-985
Author(s):  
CONNOR EDLUND ◽  
SUBRAMANIAN RAMAKRISHNAN
Keyword(s):  
Energy Harvesting ◽  
Vibrational Energy ◽  
Electrical Power ◽  
Random Excitation ◽  
Analytical Models ◽  
Practical Applications ◽  
Type Iii ◽  
Pedestrian Traffic ◽  
Type V ◽  
Vibrational Energy Harvesting

This work investigates analytically, the use of piezoelectric tiles placed on stairways for vibrational energy harvesting – harnessing electrical power from natural vibrational phenomena – from pedestrian footfalls. While energy harvesting from pedestrian traffic along flat pathways has been studied in the linear regime and realised in practical applications, the greater amounts of energy naturally expended in traversing stairways suggest better prospects for harvesting. Considering the characteristics of two types of commercially available piezoelectric tiles – Navy Type III and Navy Type V – analytical models for the coupled electromechanical system are formulated. The harvesting potential of the tiles is then studied under conditions of both deterministic and carefully developed random excitation profiles for three distinct cases: linear, monostable nonlinear and an array of monostable nonlinear tiles on adjacent steps with linear coupling between them. The results indicate enhanced power output when the tiles are: (1) placed on stairways, (2) uncoupled and (3) subjected to excitation profiles with stochastic frequency. In addition, the Navy Type V tiles are seen to outperform the Navy Type III tiles. Finally, the strongly nonlinear regime outperforms the linear one suggesting that the realisation of commercially available piezoelectric tiles with appropriately tailored nonlinear characteristics will likely have a significant impact on energy harvesting from pedestrian traffic.

scholarly journals ESTIMATION OF THE SLIP LENGTH IN THE FLOW OF LIQUID IN MICRO-CHANNELS

2018 ◽  
Vol 40 (2) ◽  
pp. 12-19
Author(s):  
Y.Y. Kovetska
Keyword(s):  
Slip Length ◽  
Slip Flow ◽  
Gas Bubbles ◽  
Hydrophobic Surface ◽  
Dissipative Heating ◽  
Research Review ◽  
Surface Shear Stress ◽  
Surface Shear ◽  
Lower Viscosity ◽  
Micro Channels

Research review of phenomenon for slip flow in micro and nanocannels is presented in the paper. The analysis of theoretical and experimental data characterizing the slip length is carried out. In slip flow in microchannels the slip length is affected by the contact angle of the liquid with the surface, shear stress, pressure, dissipative heating, the amount and nature of the dissolved gas in the liquid, electrical characteristics, surface roughness. Studies of flow in microchannels with hydrophobic walls, which are based on molecular dynamics, showed that the slip length has order of 20 nm. This is much less than the values observed in the experiment. The introduction of an effective (apparent) slip length suggests the existence of a thin layer of gas bubbles near the hydrophobic surface or liquid layer with low value of viscosity and density. Since the idealized model for the total coverage of a hydrophobic surface by gas bubbles gives, as a rule, overestimated values of the slip length in comparison with experimental ones, some researchers consider the inhomogeneous coating of the wall by gas bubbles. In this case, the effect of a layer with a lower viscosity on the slip length turns out to be weaker.

An Investigation on Micro Slip Flows in Micro Channels

2010 ◽  
Author(s):  
Gh. Reza Salehi ◽  
Masoud JalaliBidgoli ◽  
Saeed ZeinaliDanaloo ◽  
Kazem HasanZadeh
Keyword(s):  
Flow Rate ◽  
Pressure Ratio ◽  
Slip Flow ◽  
Accommodation Coefficient ◽  
Flow Rate Ratio ◽  
Numerical Representation ◽  
Micro Channel ◽  
Parallel Plates ◽  
Dimensionless Numbers ◽  
Micro Channels

In this paper, distributions of velocity and flow rate of micro channels are studied. Moreover, the parameters which influence them were also discussed, as well as their effects and relevant curves. In the Analytical study, the governing equation in specific micro flows is obtained. This equation is specifically investigated for slip flow in two micro parallel plates (micro channel).At the next step numerical representation shows the influence of the related parameters in micro channel flow such as Knudsen number, thermal -accommodation coefficient, mass flow rate ratio and pressure ratio (outlet to inlet), Tangential Momentum Accommodation Coefficient with relative curves, and flow rate distribution in slippery state to no slip state has been compared as the another part of this solution. Finally, the results of investigating parameters and dimensionless numbers in micro channels are reviewed.

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