Slip-Flow Pressure Drop in Microchannels of General Cross Section

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
M. Bahrami ◽  
A. Tamayol ◽  
P. Taheri
Keyword(s):  
Boundary Condition ◽  
Pressure Drop ◽  
Cross Section ◽  
Slip Flow ◽  
Homogeneous Boundary Condition ◽  
Slip Boundary Condition ◽  
Arbitrary Cross Section ◽  
Geometrical Parameters ◽  
Cross Sectional ◽  
Slip Boundary

In the present study, a compact analytical model is developed to determine the pressure drop of fully-developed, incompressible, and constant properties slip-flow through arbitrary cross section microchannels. An averaged first-order Maxwell slip boundary condition is considered. Introducing a relative velocity, the difference between the bulk flow and the boundary velocities, the axial momentum reduces to Poisson’s equation with homogeneous boundary condition. Square root of area is selected as the characteristic length scale. The model of Bahrami et al. (2006, “Pressure Drop of Laminar, Fully Developed Flow in Microchannels of Arbitrary Cross Section,” ASME J. Fluids Eng., 128, pp. 1036–1044), which was developed for no-slip boundary condition, is extended to cover the slip-flow regime in this study. The proposed model for pressure drop is a function of geometrical parameters of the channel: cross sectional area, perimeter, polar moment of inertia, and the Knudsen number. The model is successfully validated against existing numerical and experimental data collected from different sources in literature for several shapes, including circular, rectangular, trapezoidal, and double-trapezoidal cross sections and a variety of gases such as nitrogen, argon, and helium.

Slip-Flow Pressure Drop in Microchannels of General Cross-Section

2008 ◽  
Author(s):  
A. Tamayol ◽  
M. Bahrami ◽  
P. Taheri
Keyword(s):  
Boundary Condition ◽  
Pressure Drop ◽  
Cross Section ◽  
Slip Flow ◽  
Homogeneous Boundary Condition ◽  
Slip Boundary Condition ◽  
Arbitrary Cross Section ◽  
Geometrical Parameters ◽  
Cross Sectional ◽  
Slip Boundary

In the present study, a compact analytical model is developed to determine the pressure drop of fully-developed, incompressible, and constant properties slip-flow through arbitrary cross-section microchannels. An averaged first-order Maxwell slip boundary condition is considered. Introducing a relative velocity, the difference between the bulk flow and the boundary velocities, the axial momentum reduces to the Poisson’s equation with homogeneous boundary condition. Square root of area is selected as the characteristic length scale. Bahrami et al.’s model, which was developed no-slip boundary condition, is extended to cover the slip-flow regime in this study. The proposed model is a function of geometrical parameters of the channel: cross-sectional area, perimeter, polar moment of inertia and the Knudsen number. The model is successfully validated against existing numerical and experimental data from different sources in the literature for several shapes, including: circular, rectangular, trapezoidal, and double-trapezoidal cross-sections and a variety of gases such as: nitrogen, argon, and helium.

MEMS-Scale Turbomachinery Based Vacuum Roughing Pump

2014 ◽  
Vol 136 (10) ◽  
Author(s):  
Anthony J. Gannon ◽  
Garth V. Hobson ◽  
Michael J. Shea ◽  
Christopher S. Clay ◽  
Knox T. Millsaps
Keyword(s):  
Boundary Condition ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Boundary Conditions ◽  
Knudsen Number ◽  
Slip Flow ◽  
Slip Boundary Condition ◽  
3D Simulations ◽  
Slip Boundary ◽  
Wall Shear

This study forms part of a program to develop a micro-electro-mechanical systems (MEMS) scale turbomachinery based vacuum pump and investigates the roughing portion of such a system. Such a machine would have many radial stages with the exhaust stages operating near atmospheric conditions while the inlet stages operate at near vacuum conditions. In low vacuum such as those to the inlet of a roughing pump, the flow can still be treated as a continuum; however, the no-slip boundary condition is not accurate. The Knudsen number becomes a dominant nondimensional parameter in these machines due to their small size and low pressures. As the Knudsen number increases, slip-flow becomes present at the walls. The study begins with a basic overview on implementing the slip wall boundary condition in a commercial code by specifying the wall shear stress based on the mean-free-path of the gas molecules. This is validated against an available micro-Poiseuille classical solution at Knudsen numbers between 0.001 and 0.1 with reasonable agreement found. The method of specifying the wall shear stress is then applied to a generic MEMS scale roughing pump stage that consists of two stators and a rotor operating at a nominal absolute pressure of 500 Pa. The zero flow case was simulated in all cases as the pump down time for these machines is small due to the small volume being evacuated. Initial transient two-dimensional (2D) simulations are used to evaluate three boundary conditions, classical no-slip, specified-shear, and slip-flow. It is found that the stage pressure rise increased as the flow began to slip at the walls. In addition, it was found that at lower pressures the pure slip boundary condition resulted in very similar predictions to the specified-shear simulations. As the specified-shear simulations are computationally expensive it is reasonable to use slip-flow boundary conditions. This approach was used to perform three-dimensional (3D) simulations of the stage. Again the stage pressure increased when slip-flow was present compared with the classical no-slip boundaries. A characteristic of MEMS scale turbomachinery are the large relative tip gaps requiring 3D simulations. A tip gap sensitivity study was performed and it was found that when no-slip boundaries were present the pressure ratio increased significantly with decreasing tip gap. When slip-flow boundaries were present, this relationship was far weaker.

Estimation of Nusselt Number in Microchannels of Arbitrary Cross-Section With Constant Axial Heat Flux

2008 ◽  
Author(s):  
Ehsan Sadeghi ◽  
Majid Bahrami ◽  
Ned Djilali
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Cross Section ◽  
Cross Sections ◽  
Numerical Solutions ◽  
Arbitrary Cross Section ◽  
Geometrical Parameters ◽  
Thermal Systems ◽  
Cross Sectional ◽  
Axial Heat

In many practical instances such as basic design, parametric study, and optimization analysis of thermal systems, it is often very convenient to have closed form relations to obtain the trends and a reasonable estimate of the Nusselt number. However, finding exact solutions for many practical singly-connected cross-sections, such as trapezoidal microchannels, is complex. In the present study, the square root of cross-sectional area is proposed as the characteristic length scale for Nusselt number. Using analytical solutions of rectangular, elliptical, and triangular ducts, a compact model for estimation of Nusselt number of fully-developed, laminar flow in microchannels of arbitrary cross-sections with “H1” boundary condition (constant axial wall heat flux with constant peripheral wall temperature) is developed. The proposed model is only a function of geometrical parameters of the cross-section, i.e., area, perimeter, and polar moment of inertia. The present model is verified against analytical and numerical solutions for a wide variety of cross-sections with a maximum difference on the order of 9%.

Numerical Investigation of Slip Flow and Heat Transfer in Rotating Rectangular Microchannels

2012 ◽  
Author(s):  
Pratanu Roy ◽  
N. K. Anand ◽  
Debjyoti Banerjee
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Convective Heat Transfer ◽  
Secondary Flow ◽  
Convective Heat ◽  
Slip Flow ◽  
Slip Boundary Condition ◽  
Fluid Temperature ◽  
Slip Boundary ◽  
Flow And Heat Transfer

Investigation of fluid flow and heat transfer in rotating microchannels is important for centrifugal microfluidics, which has emerged as an advanced technique in biomedical applications and chemical separations. The pseudo forces namely the centrifugal force and the Coriolis force arising as a consequence of the rotating reference frame change the flow pattern significantly from the parabolic profile in a non-rotating channel. The convective heat transfer process is also influenced by the secondary flow introduced by the rotational effect. Moreover, if the microchannel wall is hydrophobic, slip flow can occur inside the channel when the conventional no slip boundary condition is no longer valid. In this work, we have numerically investigated the flow and heat transfer inside a straight rotating rectangular microchannel in the slip flow regime. A pressure based finite volume technique in a staggered grid was applied to solve the steady incompressible Navier-Stokes and energy equations. It has been observed that, depending on the rotational velocity, different slip velocities are induced at the channel walls. The average fluid temperature increases with the increase of rotation as convective heat transfer mechanism is increased due to the secondary flow. However, the slip boundary condition has a negligible effect on the temperature profiles.

Slip-Flow in Microchannels of Non-Circular Cross Sections

2011 ◽  
Vol 133 (9) ◽  
Author(s):  
A. Tamayol ◽  
K. Hooman
Keyword(s):  
Cross Sections ◽  
Slip Flow ◽  
Slip Boundary Condition ◽  
Arbitrary Cross Section ◽  
Closed Form Solutions ◽  
Slip Boundary ◽  
Cylindrical Coordinate ◽  
Different Types ◽  
Developed Pressure ◽  
Limiting Case

Closed form solutions are presented for fully developed pressure driven slip-flow in straight microchannels of uniform noncircular cross-sections. To achieve this goal, starting from the general solution of the Poisson’s equation in the cylindrical coordinate, a least-squares-matching of boundary values is employed for applying the slip boundary condition at the wall. Then the application of boundary conditions for three different types of cross sections is examined. While the model is general enough to be extended to almost any arbitrary cross section, microchannels of polygonal (with circular as a limiting case), rectangular, and rhombic cross sections are analyzed in this study. The results are then successfully compared to the existing data in the literature.

Pressure Drop of Fully-Developed, Laminar Flow in Microchannels of Arbitrary Cross-Section

2006 ◽  
Vol 128 (5) ◽  
pp. 1036-1044 ◽  
Author(s):  
M. Bahrami ◽  
M. M. Yovanovich ◽  
J. R. Culham
Keyword(s):  
Experimental Data ◽  
Pressure Drop ◽  
Cross Section ◽  
Numerical Solutions ◽  
Approximate Model ◽  
Arbitrary Cross Section ◽  
Geometrical Parameters ◽  
Polar Moment ◽  
Proposed Model ◽  
Good Agreement

The pressure drop of fully developed, laminar, incompressible flow in smooth mini- and microchannels of arbitrary cross-section is investigated. A compact approximate model is proposed that predicts the pressure drop for a wide variety of shapes. The model is only a function of geometrical parameters of the cross-section, i.e., area, perimeter, and polar moment of inertia. The proposed model is compared with analytical and numerical solutions for several shapes. Also, the comparison of the model with experimental data, collected by several researchers, shows good agreement.

ELECTROKINETIC SLIP FLOW OF MICROFLUIDICS IN TERMS OF STREAMING POTENTIAL BY A LATTICE BOLTZMANN METHOD: A BOTTOM-UP APPROACH

2007 ◽  
Vol 18 (04) ◽  
pp. 693-700 ◽  
Author(s):  
XIN FU ◽  
BAOMING LI ◽  
JUNFENG ZHANG ◽  
FUZHI TIAN ◽  
DANIEL Y. KWOK
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Slip Flow ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Slip Boundary ◽  
Surface Energetics ◽  
Boltzmann Method

In traditional computational fluid dynamics, the effect of surface energetics on fluid flow is often ignored or translated into an arbitrary selected slip boundary condition in solving the Navier-Stokes equation. Using a bottom-up approach, we show in this paper that variation of surface energetics through intermolecular theory can be employed in a lattice Boltzmann method to investigate both slip and non-slip phenomena in microfluidics in conjunction with the description of electrokinetic phenomena for electrokinetic slip flow. Rather than using the conventional Navier-Stokes equation with a slip boundary condition, the description of electrokinetic slip flow in microfluidics is manifested by the more physical solid-liquid energy parameters, electrical double layer and contact angle in the mean-field description of the lattice Boltzmann method.

scholarly journals AFM Slip Length Measurements for Water at Selected Phyllosilicate Surfaces

2021 ◽  
Vol 5 (4) ◽  
pp. 44
Author(s):  
Chen Zhang ◽  
Xuming Wang ◽  
Jiaqi Jin ◽  
Lixia Li ◽  
Jan D. Miller
Keyword(s):  
Boundary Condition ◽  
Silica Surface ◽  
Slip Length ◽  
Slip Flow ◽  
Slip Boundary Condition ◽  
Exclusion Zone ◽  
Slip Boundary ◽  
Hydrophobic Silica ◽  
Synthetic Materials ◽  
Length Measurements

Most reported slip length measurements have been made at the surfaces of synthetic materials and modified synthetic materials. In contrast, few slip length measurements at the surface of unmodified natural mineral surfaces have been reported. In this regard, flow at the silica face surfaces of the phyllosilicate minerals, talc and mica, was considered. A slip boundary condition was expected at the nonpolar hydrophobic silica surface of talc leading to enhanced flow, and a no-slip boundary condition was expected at the hydrophilic silica surface of mica. Atomic force microscopy (AFM) slip length measurements were made at the talc and mica surfaces. The slip length results for the hydrophobic silica surface of talc were contrasted to the results for the hydrophilic silica surface of mica (no-slip flow). The results are discussed based on molecular dynamics simulations (MDS), as reported in the literature, and AFM images of surface nanobubbles. For nonpolar hydrophobic surfaces (such as talc), it is doubtful that the MDS interfacial water structure and the water exclusion zone (3.2 Å) account for the AFM slip flow with slip lengths as great as 95 nm. Rather, a better explanation for the AFM slip flow condition is based on reduced interfacial viscosity due to the presence of dissolved gas and the accommodation of pancake nanobubbles at the talc surface having a height dimension of magnitude similar to the slip length.

Incompressible slip flow past a semi-infinite flat plate

1965 ◽  
Vol 22 (3) ◽  
pp. 463-469 ◽  
Author(s):  
J. D. Murray
Keyword(s):  
Boundary Condition ◽  
Shear Stress ◽  
Viscous Fluid ◽  
Flat Plate ◽  
Slip Velocity ◽  
Slip Flow ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Slip Boundary

An asymptotic solution to the Navier-Stokes equation is obtained for the incompressible flow of a viscous fluid past a semi-infinite flat plate when a slip boundary condition is applied at the plate. The results for the shear stress (and hence the slip velocity) on the plate differ basically from those obtained by previous authors who considered the same problem using some form of the Oseen equations.

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