Vortex Flow Driven by Electroosmosis in Microchannels

2008 ◽  
Author(s):  
Wu Zhong ◽  
Yunfei Chen
Keyword(s):  
Electroosmotic Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Channel Surface ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Set Up ◽  
Rotational Direction

The governing equations of electroosmotic flow, including the Navier-Stokes (N-S) equations, Laplace equation and Poisson-Boltzmann equation, are set up in a straight microchannel. The meshless method is employed as a discrete scheme for the solution domain. The semi-implicit multistep (SIMS) method is used to solve the Navier-Stokes equations. The simulation results demonstrated that different patterns of the zeta potential over the channel surface could induce different flow profiles for the vortex. The rotational direction of the vortex is determined by the electroosmotic driving force.

Analytical Solution of Mixed Electroosmotic and Pressure-Driven Flow in Rectangular Microchannels

2011 ◽  
Vol 483 ◽  
pp. 679-683 ◽  
Author(s):  
Da Yong Yang
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Microfluidic Chips ◽  
Layer Potential ◽  
Rectangular Microchannels ◽  
Navier Stokes Equations ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Pressure Driven Flow ◽  
Pressure Driven

Analytical solutions for potential distributions, velocity distributions of the mixed electroosmotic and pressure-driven flow in rectangular microchannels are discussed. To simulate the flow, a mathematical model, which includes the Poisson-Boltzmann equation and the modified Navier-Stokes equations, is presented and solved using the finite element method based on the Matlab software. The results show that the velocity distribution of mixed flow is compound of the “plug-like” and paraboloid at the steady state, and the pure electroosmotic flow is “plug-like”, which is similar with the electric double layer potential profile. The results provide the guidelines for the application of mix driven flow in microfluidic chips.

scholarly journals Transient Pressure-Driven Electroosmotic Flow through Elliptic Cross-Sectional Microchannels with Various Eccentricities

Computation ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 27
Author(s):  
Nattakarn Numpanviwat ◽  
Pearanat Chuchard
Keyword(s):  
Laplace Transform ◽  
Electroosmotic Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Mathieu Functions ◽  
Navier Stokes Equations ◽  
Flow Rates ◽  
Elliptic Cross ◽  
Flow Through ◽  
Relative Errors

The semi-analytical solution for transient electroosmotic flow through elliptic cylindrical microchannels is derived from the Navier-Stokes equations using the Laplace transform. The electroosmotic force expressed by the linearized Poisson-Boltzmann equation is considered the external force in the Navier-Stokes equations. The velocity field solution is obtained in the form of the Mathieu and modified Mathieu functions and it is capable of describing the flow behavior in the system when the boundary condition is either constant or varied. The fluid velocity is calculated numerically using the inverse Laplace transform in order to describe the transient behavior. Moreover, the flow rates and the relative errors on the flow rates are presented to investigate the effect of eccentricity of the elliptic cross-section. The investigation shows that, when the area of the channel cross-sections is fixed, the relative errors are less than 1% if the eccentricity is not greater than 0.5. As a result, an elliptic channel with the eccentricity not greater than 0.5 can be assumed to be circular when the solution is written in the form of trigonometric functions in order to avoid the difficulty in computing the Mathieu and modified Mathieu functions.

scholarly journals Thermochemical Nonequilibrium in Rapidly Expanding Flows of High-Temperature Air

1997 ◽  
Vol 52 (4) ◽  
pp. 358-368 ◽  
Author(s):  
Michio Nishida ◽  
Masashi Matsumotob
Keyword(s):  
High Temperature ◽  
Vibrational Energy ◽  
Stokes Equations ◽  
Computational Study ◽  
Mass Conservation ◽  
Navier Stokes ◽  
Tvd Scheme ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Free Jet

Abstract • This paper describes a computational study of the thermal and chemical nonequilibrium occuring in a rapidly expanding flow of high-temperature air transported as a free jet from an orifice into low-density stationary air. Translational, rotational, vibrational and electron temperatures are treated separately, and in particular the vibrational temperatures are individually treated; a multi-vibrational temperature model is adopted. The governing equations are axisymmetric Navier-Stokes equations coupled with species vibrational energy, electron energy and species mass conservation equations. These equations are numerically solved, using the second order upwind TVD scheme of the Harten-Yee type. The calculations were carried out for two different orifice temperatures and also two different orifice diameters to investigate the effects of such parameters on the structure of a nonequilibrium free jet.

Numerical Investigation of Blade Flutter at or Near Stall in Axial Flow Turbomachines

2001 ◽  
Author(s):  
Wolfgang Höhn
Keyword(s):  
Viscous Flow ◽  
Stokes Equations ◽  
Separated Flow ◽  
Parallel Computer ◽  
Navier Stokes ◽  
Computational Domain ◽  
Compressor Cascade ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Blade Flutter

During the design of the compressor and turbine stages of today’s aeroengines, aerodynamically induced vibrations become increasingly important since higher blade load and better efficiency are desired. In this paper the development of a method based on the unsteady, compressible Navier-Stokes equations in two dimensions is described in order to study the physics of flutter for unsteady viscous flow around cascaded vibrating blades at stall. The governing equations are solved by a finite difference technique in boundary fitted coordinates. The numerical scheme uses the Advection Upstream Splitting Method to discretize the convective terms and central differences discretizing the viscous terms of the fully non-linear Navier-Stokes equations on a moving H-type mesh. The unsteady governing equations are explicitly and implicitly marched in time in a time-accurate way using a four stage Runge-Kutta scheme on a parallel computer or an implicit scheme of the Beam-Warming type on a single processor. Turbulence is modelled using the Baldwin-Lomax turbulence model. The blade flutter phenomenon is simulated by imposing a harmonic motion on the blade, which consists of harmonic body translation in two directions and a rotation, allowing an interblade phase angle between neighboring blades. Non-reflecting boundary conditions are used for the unsteady analysis at inlet and outlet of the computational domain. The computations are performed on multiple blade passages in order to account for nonlinear effects. A subsonic massively stalled unsteady flow case in a compressor cascade is studied. The results, compared with experiments and the predictions of other researchers, show reasonable agreement for inviscid and viscous flow cases for the investigated flow situations with respect to the Steady and unsteady pressure distribution on the blade in separated flow areas as well as the aeroelastic damping. The results show the applicability of the scheme for stalled flow around cascaded blades. As expected the viscous and inviscid computations show different results in regions where viscous effects are important, i.e. in separated flow areas. In particular, different predictions for inviscid and viscous flow for the aerodynamic damping for the investigated flow cases are found.

On the flow near the trailing edge of a flat plate

1968 ◽  
Vol 306 (1486) ◽  
pp. 275-290 ◽  
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Governing Equations ◽  
Trailing Edge ◽  
Navier Stokes Equations ◽  
Multiplicative Constant ◽  
Boundary Layer Approximation ◽  
Uniform Shear

It is shown that the boundary layer approximation to the flow of a viscous fluid past a flat plate of length l , generally valid near the plate when the Reynolds number Re is large, fails within a distance O( lRe -3/4 ) of the trailing edge. The appropriate governing equations in this neighbourhood are the full Navier- Stokes equations. On the basis of Imai (1966) these equations are linearized with respect to a uniform shear and are then completely solved by means of a Wiener-Hopf integral equation. The solution so obtained joins smoothly on to that of the boundary layer for a flat plate upstream of the trailing edge and for a wake downstream of the trailing edge. The contribution to the drag coefficient is found to be O ( Re -3/4 ) and the multiplicative constant is explicitly worked out for the linearized equations.

scholarly journals Investigating the Effect of the Closure in Partially-Averaged Navier–Stokes Equations

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Filipe S. Pereira ◽  
Luís Eça ◽  
Guilherme Vaz
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Coherent Structures ◽  
Stokes Equations ◽  
The Other ◽  
Navier Stokes ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Auxiliary Functions ◽  
Modeling Accuracy

The importance of the turbulence closure to the modeling accuracy of the partially-averaged Navier–Stokes equations (PANS) is investigated in prediction of the flow around a circular cylinder at Reynolds number of 3900. A series of PANS calculations at various degrees of physical resolution is conducted using three Reynolds-averaged Navier–Stokes equations (RANS)-based closures: the standard, shear-stress transport (SST), and turbulent/nonturbulent (TNT) k–ω models. The latter is proposed in this work. The results illustrate the dependence of PANS on the closure. At coarse physical resolutions, a narrower range of scales is resolved so that the influence of the closure on the simulations accuracy increases significantly. Among all closures, PANS–TNT achieves the lowest comparison errors. The reduced sensitivity of this closure to freestream turbulence quantities and the absence of auxiliary functions from its governing equations are certainly contributing to this result. It is demonstrated that the use of partial turbulence quantities in such auxiliary functions calibrated for total turbulent (RANS) quantities affects their behavior. On the other hand, the successive increase of physical resolution reduces the relevance of the closure, causing the convergence of the three models toward the same solution. This outcome is achieved once the physical resolution and closure guarantee the precise replication of the spatial development of the key coherent structures of the flow.

scholarly journals Numerical Simulation of Micromixing of Particles and Fluids with Galloping Cylinder

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 580 ◽  
Author(s):  
Zahra Abdelmalek ◽  
Mohammad Yaghoub Abdollahzadeh Jamalabadi
Keyword(s):  
Continuity Equation ◽  
Stokes Equations ◽  
The Self ◽  
Moving Mesh ◽  
Navier Stokes ◽  
Parameter Study ◽  
Mems Devices ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Moving Cylinder

Micromixers are significant segments inside miniaturized scale biomedical frameworks. Numerical investigation of the effects of galloping cylinder characteristics inside a microchannel Newtonian, incompressible fluid in nonstationary condition is performed. Governing equations of the system include the continuity equation, and Navier–Stokes equations are solved within a moving mesh domain. The symmetry of laminar entering the channel is broken by the self-sustained motion of the cylinder. A parameter study on the amplitude and frequency of passive moving cylinder on the mixing of tiny particles in the fluid is performed. The results show a significant increase to the index of mixing uses of the galloping body in biomedical frameworks in the course of micro-electromechanical systems (MEMS) devices.

Melting From a Horizontal Rotating Disk

1989 ◽  
Vol 56 (1) ◽  
pp. 47-50 ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Heat Transfer ◽  
Numerical Integration ◽  
Stokes Equations ◽  
Rotating Disk ◽  
Similarity Solutions ◽  
Navier Stokes ◽  
Relative Importance ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Transfer Rates

Melting of a disk is facilitated by rotation. The problem is governed by a nondimensional parameter α which represents the relative importance of injection (melt) rate and rotation times viscosity. The nonlinear governing equations are solved by perturbations for small α and numerical integration for arbitrary α. Torque and heat transfer rates are found. The solution is one of the rare exact similarity solutions of the Navier-Stokes equations.

scholarly journals Design and Numerical Study of Micropump Based on Induced Electroosmotic Flow

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Kai Zhang ◽  
Lengjun Jiang ◽  
Zhihan Gao ◽  
Changxiu Zhai ◽  
Weiwei Yan ◽  
...  
Keyword(s):  
Electroosmotic Flow ◽  
Stokes Equations ◽  
Numerical Study ◽  
Cross Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Driving Mode ◽  
Electric Driving ◽  
Induced Charge ◽  
The Cross

Induced charge electroosmotic flow is a new electric driving mode. Based on the Navier–Stokes equations and the Poisson–Nernst–Planck (PNP) ion transport equations, the finite volume method is adopted to calculate the equations and boundary conditions of the induced charge electroosmotic flow. In this paper, the formula of the induced zeta potential of the polarized solid surface is proposed, and a UDF program suitable for the simulation of the induced charge electroosmotic is prepared according to this theory. At the same time, on the basis of this theory, a cross micropump driven by induced charge electroosmotic flow is designed, and the voltage, electric potential, charge density, and streamline of the induced electroosmotic micropump are obtained. Studies have shown that when the cross-shaped micropump is energized, in the center of the induction electrode near the formation of a dense electric double layer, there exist four symmetrical vortices at the four corners, and they push the solution towards both outlets; it can be found that the average velocity of the solution in the cross-flow microfluidic pump is nonlinear with the applied electric field, which maybe helpful for the practical application of induced electroosmotic flow in the field of micropump.

scholarly journals Direct Numerical Simulation of Liquid Flow in a Horizontal Microchannel

2005 ◽  
Author(s):  
Cenk Evren Ku¨krer ◽  
I˙lker Tarı
Keyword(s):  
Liquid Flow ◽  
Energy Equation ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Micro Channel ◽  
Governing Equations ◽  
Qualitative Comparison ◽  
Navier Stokes Equations ◽  
Axial Conduction ◽  
Micro Channels

Numerical Simulations of liquid flow in a micro-channel between two horizontal plates are performed. The channel is infinite in streamwise and spanwise directions and its height is taken as 3.1×10−4 m which falls within the dimension ranges of micro-channels. The Navier-Stokes equations with the addition of Brinkman number (Br) to the energy equation are used as the governing equations and a spectral methods based approach is applied to obtain the required accuracy to handle liquid flow in the micro-channel. It is known for micro-channels that Br combines the effects of conduction and viscous dissipation in liquids and is also a way of comparing the importance of later relative to former. A laminar flow of a liquid in a micro-channel shows different characteristics compared to a similar flow in a macro-channel. To observe the differences, three different cases are run over each of a range of Reynolds numbers: one with no axial conduction assumption that correspond to a case similar to macro-channel flow, another case with axial conduction included in the energy equation to simulate one of the main differences and lastly a case with inclusion of Br number in the governing equations. The results are compared with each other to see the effects of axial conduction and Br inclusion. A qualitative comparison is made with the previous results in literature.

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