A Mean-Field Lattice Boltzmann Model for Electrokinetic Slip Flow

2007 ◽  
Author(s):  
Xu Fu ◽  
Baoming Li ◽  
Junfeng Zhang ◽  
Fuzhi Tian ◽  
Daniel Y. Kwok
Keyword(s):  
Fluid Flow ◽  
Slip Flow ◽  
Mean Field ◽  
Slip Boundary Condition ◽  
Lattice Boltzmann Model ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Slip Boundary ◽  
Surface Energetics ◽  
Boltzmann Model

Traditional computational fluid dynamics does not normally consider surface energetic effect on fluid flow in microchannels. Even if it does, the effect is usually translated into an arbitrary selected slip boundary condition in solving the Navier-Stokes equation. Moreover, this treatment has neglected another important phenomenon: electrokinetics. In this paper, we consider both effects of electrokinetics and surface energetics on fluid flow in microfluidics which are normally considered independently.

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.

COMPARISON OF GAS SLIP MODELS WITH SOLUTIONS OF LINEARIZED BOLTZMANN EQUATION AND DIRECT SIMULATION OF MONTE CARLO METHOD

2007 ◽  
Vol 18 (02) ◽  
pp. 203-216 ◽  
Author(s):  
G. H. TANG ◽  
Y. L. HE ◽  
W. Q. TAO
Keyword(s):  
Friction Factor ◽  
Flow Rate ◽  
Slip Flow ◽  
Flow Analysis ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Slip Boundary ◽  
Slip Regime ◽  
Linearized Boltzmann Equation

Analytical solutions of the Navier–Stokes equation based on a locally fully-developed flow assumption with various gas slip models are presented and comparisons for velocity profile, flow rate, friction factor, and pressure distribution are performed. The effect of the second-order coefficient in the slip boundary condition becomes significant as the Knudsen number increases. Most slip models are limited to slip regime or marginally transition regime and break down around Kn = 0.1 while Sreekanth's model, followed by Mitsuya's model, gives a good agreement with the linearized Boltzmann solutions from slip regime up to Kn = 2 for flow rate and friction factor predictions. These two models should be of great use for slip flow analysis in micro-electro-mechanical systems (MEMS) and, in particular, in situations where the flow rate and flow resistance are of interest.

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.

Liquid Leak Predictions in Micro and Nano-Porous Gaskets

2010 ◽  
Author(s):  
Lotfi Grine ◽  
Abdel-Hakim Bouzid
Keyword(s):  
Stokes Equations ◽  
Slip Flow ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Gas Leak ◽  
Flow Through ◽  
Parameter Approach ◽  
Experimental And Theoretical Studies

In recent years, few experimental and theoretical studies have been conducted to predict gas leak rate through gaskets. However a very limited work is done on liquid leak rates through gaskets. A new method based on a slip flow model to predict liquid flow through nano-porous gaskets is presented. A recent study [1] had shown that the leakage prediction based on the porosity parameter approach was successful in predicting gaseous leaks and an extrapolation of the latter to liquid leaks is the purpose of this study. In the present article, an analytical-computational methodology based on the number and pore size to predict liquid nanoflow in the slip flow regime through gaskets is presented. The formulation is based on the Navier-Stokes equations associated to slip boundary condition at the wall. The mass leak rates through a gasket considered as a porous media under variable experimentally conditions of (fluid media, pressure, and gasket stress) were conducted on a test bench. Gaseous and liquid leaks are measured and comparisons are made with the analytical predictions.

Analytic Solution for Microscale Poiseuille Flow Based on Super-Burnett Equations

2013 ◽  
Vol 705 ◽  
pp. 609-615
Author(s):  
Cheng Qian Song ◽  
Xie Yuan Yin ◽  
Feng Hua Qin
Keyword(s):  
Poiseuille Flow ◽  
Constitutive Relations ◽  
Slip Boundary Condition ◽  
Continuous Model ◽  
Analytic Solutions ◽  
High Order ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Slip Boundary ◽  
The Difference

The previous studies show that the transverse distribution of pressure and temperature in microscale Poiseuille flow cannot be predicted by Navier-Stokes equation with the slip boundary condition. In this paper, we analyzed the planar microchannel force-driven Poiseuille flow by high order continuum model. The super-Burnett constitutive relations were used and the nonlinear ordinary differential Equations of higher-orders were obtained by the hypothesis of parallel flow. With a perturbations theory, we linearized the equations and obtained the analytic solutions. The results show that the solutions can capture the temperature dip which is the same as the DSMC result. However, we also find that the temperature profile near the wall does always not match with the DSMC result. Especially, the difference in the qualitative exists when the Knudsen number is large enough. The non-equilibrium effect near the wall such as Knudsen layer can not be described entirely by continuous model even with high order constitutive relations and this confines the extension of the continuous model such as super-Burnett one.

Liquid Leak Predictions in Micro- and Nanoporous Gaskets

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
Lotfi Grine ◽  
Abdel-Hakim Bouzid
Keyword(s):  
Gas Flow ◽  
Stokes Equations ◽  
Slip Flow ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Experimental Conditions ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Gas Leak ◽  
Flow Through

In recent years, quite few experimental and theoretical studies have been conducted to predict gas leak rate through gaskets. However, a very limited work is done on liquid leak rates through gaskets. The slip flow model is used to predict liquid flow through porous gaskets based on measurements of gas flow at different pressures. In fact, an extrapolation of the porosity parameter approach (Grine, L., and Bouzid, A., 2009, “Correlation of Gaseous Mass Leak Rates Through Micro and Nano-Porous Gaskets,” ASME Paper No. PVP2009-77205) used to correlate leak rates between different gases is used to predict liquid leak rates. In the present article, an analytical-computational methodology based on the number and pore size to predict liquid micro- and nanoflows in the slip flow regime through gaskets is presented. The formulation is based on the Navier–Stokes equations associated with slip boundary condition at the wall. The mass leak rates through a gasket considered as a porous media under various experimental conditions of fluid media, pressure, and gasket stress were conducted on a special gasket test rig. Gaseous and liquid leaks are measured and comparisons with the analytical predictions are made.

Numerical Simulation of an Electroosmotic Micromixer

2003 ◽  
Author(s):  
Han Chen ◽  
Yanting Zhang ◽  
Igor Mezic ◽  
Carl Meinhart ◽  
Linda Petzold
Keyword(s):  
Electric Field ◽  
Electroosmotic Flow ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Reynolds Number Flow ◽  
Slip Boundary ◽  
Mems Technology ◽  
Number Flow ◽  
Incompressible Navier Stokes Equation

We present a micromixer fabricated using MEMS technology which takes advantage of electroosmosis to mix fluids. A time dependent electric field is applied and the resulting electroosmosis perturbs the low Reynolds number flow. It is shown that the electric field can be deemed quasi-steady and the electroosmotic slip boundary condition can be applied when the incompressible Navier Stokes equation is solved. Both the electric field and the electroosmotic flow are simulated numerically. Study of the particle traces shows folding and stretching of material lines, and a positive Lyapunov exponent is found which indicates chaotic-like mixing.

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