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.

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.

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.

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.

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.

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.

scholarly journals Involving the Navier–Stokes equations in the derivation of boundary conditions for the lattice Boltzmann method

2011 ◽  
Vol 369 (1944) ◽  
pp. 2184-2192 ◽  
Author(s):  
Joris C. G. Verschaeve
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Grid Spacing ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Boltzmann Method

By means of the continuity equation of the incompressible Navier–Stokes equations, additional physical arguments for the derivation of a formulation of the no-slip boundary condition for the lattice Boltzmann method for straight walls at rest are obtained. This leads to a boundary condition that is second-order accurate with respect to the grid spacing and conserves mass. In addition, the boundary condition is stable for relaxation frequencies close to two.

scholarly journals Comparison and analysis of calculation of Bridge backwater based on Mike21 hydrodynamic model

2021 ◽  
Vol 233 ◽  
pp. 03043
Author(s):  
Jiang Chuan Liu ◽  
Zhu Qiu Hu ◽  
Mao Yuan Zhu
Keyword(s):  
Theoretical Basis ◽  
Impact Analysis ◽  
Navier Stokes ◽  
Efficiency Coefficient ◽  
Navier Stokes Equation ◽  
The Real ◽  
Comparison And Analysis ◽  
Simulation Results ◽  
The Difference ◽  
Local Water

The construction of bridges and other structures across the river will affect the flood discharge capacity and local water potential of the river.Based on navier-Stokes equation of MIKE21FM hydrodynamic module, this paper carries out two-dimensional numerical simulation of part of Shixi River. By optimizing the grid near the piers to reduce the difference brought by the terrain generalized grid of the real river, it simulates and analyzes the length of the curve of yong-high and Yong-water under different flood frequencies,the Nash-Sutcliffe efficiency coefficient and relative error analysis are used to verify the rationality of the results. The simulation results can accurately reflect the real changes of river water level, It provides a theoretical basis for flood impact analysis.

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