Numerical Simulation of the Interplay of Electrical Double Layers, Electrode Reactions, and Pressure-Driven Flows in Microchannels

2008 ◽  
Author(s):  
Bettina Wa¨lter ◽  
Peter Ehrhard
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Electrical Potential ◽  
Planck Equation ◽  
Forced Flow ◽  
Double Layers ◽  
Rectangular Microchannel ◽  
Small Width ◽  
Electrode Reactions ◽  
Precise Knowledge

We investigate the influence of flow field and electrode reactions onto an electrical double layer (EDL), which is located in the immediate vicinity of the walls of a rectangular microchannel. The precise knowledge of the EDL appears to be important for many technical applications in microchannels of small width, since the electrokinetic effects, as electroosmosis or electrophoresis, in such cases depend on the detailed charge distribution. The mathematical model for the numerical treatment relies on a first–principle description of the EDL and the electrical forces caused by the electrical field between internal electrodes. Hence, the so–called Debye–Hu¨ckel approximation is avoided. The governing system of equations consists of a Poisson equation for the electrical potential, the Navier–Stokes equations for the flow field, species transport equations, based on the Nernst–Planck equation, and a model for the electrode reactions, based on the Butler–Volmer equation. The simulations are time–dependent and two–dimensional (plane) in nature and employ a finite–volume method. It is discussed, e.g., how the thickness of the EDL expands at the stagnation point of a forced flow, as the velocity (or Reynolds number) is increased. Furthermore, the effect of electrode reactions on the ionic strength and, hence, on the EDL and the electroosmotic flow, are discussed.

Numerical Simulation of Fluid Flows and Mixing in Microchannels Induced by Internal Electrodes

2009 ◽  
Author(s):  
Bettina Wa¨lter ◽  
Peter Ehrhard
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Electrical Potential ◽  
Planck Equation ◽  
Navier Stokes ◽  
Electrical Field ◽  
Rectangular Microchannel ◽  
Electrical Field Strength ◽  
Electrode Reactions ◽  
A Charge

We investigate the influence of internal electrodes onto the flow field, governed by electroosmosis and electrophoresis in a modular rectangular microchannel. As internal electrodes can be positioned at lower distances, they can be operated at lower voltages and still ensure strong electrical field strength. Even at lower voltages, electrode reactions influence the species concentration fields, and the crucial question arises, whether at the electrodes all species can be kept in dissolution or whether some species are released in gaseous form. The position and charge of multiple internal electrodes is a further focus of our investigations: wall-tangential electrical field components are responsible for pumping, wall-normal electrical field components are responsible for mixing. Hence, an optimized position and charge of all electrodes will lead to an optimized electrical field, designed to fulfill the desired tasks of the modular microchannel. The mathematical model for the numerical treatment relies on a first-principle description of the EDL and the electrical forces caused by the electrical field between the internal electrodes. Hence, the so-called Debye-Hu¨ckel approximation is avoided. The governing system of equations consists of a Poisson equation for the electrical potential, the continuity and Navier-Stokes equations for the flow field, species transport equations, based on the Nernst-Planck equation, and a charge transport equation. Further, a model for the electrode reactions, based on the Butler-Volmer equation, is in place. The simulations are time-dependent and two-dimensional in nature and employ a FVM.

Analytical approximations to the flow field induced by electroosmosis during isotachophoretic transport through a channel

2011 ◽  
Vol 682 ◽  
pp. 101-119 ◽  
Author(s):  
TOBIAS BAIER ◽  
FRIEDHELM SCHÖNFELD ◽  
STEFFEN HARDT
Keyword(s):  
Flow Field ◽  
Transition Zone ◽  
Stokes Equations ◽  
Planck Equation ◽  
Ionic Species ◽  
Analytical Approximation ◽  
Double Layers ◽  
Analytical Expression ◽  
Transition Zones ◽  
Analytical Approximations

An analytical approximation is derived for the flow field in the vicinity of a transition zone between electrolytes of different mobility in isotachophoretic transport through a channel. Due to the difference in electroosmotic mobility and electric field on both sides of the transition zone, the flow field consists of a superposition of electroosmotic and pressure-driven flow. The corresponding convective ion transport inherently reduces the resolution of isotachophoretic separation processes. The derived analytical result is adequate for both wide and narrow transition zones and valid in the limit of thin electric double layers, relevant for most situations where isotachophoresis is employed. In this way, it complements and generalizes the results obtained for wide transition zones in the lubrication approximation. The analysis is extended to multiple sample zones with ions of different electrophoretic mobility, a scenario characteristic for applications in the field of analytical chemistry. The results are validated by comparison to finite-element calculations accounting for the transport of different ionic species governed by the coupled Nernst–Planck and Stokes equations, both for situations with only a single transition zone as well as for several transition zones. Excellent agreement is obtained between the analytical and the numerical results for realistic parameter values encountered in ITP experiments. This suggests using the analytical expression for the flow field in the framework of numerical studies of species transport in ITP experiments, since the time-consuming computation of the velocity field is essentially eliminated. The latter is successfully demonstrated using an iterative procedure, numerically solving the Nernst–Planck equation for a given flow field, and using the resulting concentration fields as an input for the derived analytical expression.

Numerical Simulation on the Electrophoretic Motion of Multiple Particles in Microchannels

2004 ◽  
Author(s):  
Chunzhen Ye ◽  
Dongqing Li
Keyword(s):  
Numerical Simulation ◽  
Flow Field ◽  
Electric Field ◽  
Particle Motion ◽  
Outer Region ◽  
Numerical Results ◽  
The Other ◽  
Double Layers ◽  
Rectangular Microchannel ◽  
Moving Particle

This paper considers the electrophoretic motion of multiple spheres in an aqueous electrolyte solution in a straight rectangular microchannel, where the size of the channel is close to that of the particles. This is a complicated 3-D transient process where the electric field, the flow field and the particle motion are coupled together. The objective is to numerically investigate how one particle influences the electric field and the flow field surrounding the other particle and the particle moving velocity. It is also aimed to investigate and demonstrate that the effects of particle size and electrokinetic properties on particle moving velocity. Under the assumption of thin electrical double layers, the electroosmotic flow velocity is used to describe the flow in the inner region. The model governing the electric field and the flow field in the outer region and the particle motion is developed. A direct numerical simulation method using the finite element method is adopted to solve the model. The numerical results show that the presence of one particle influences the electric field and the flow field adjacent to the other particle and the particle motion, and that this influences weaken when the separation distance becomes bigger. The particle motion is dependent on its size, with the smaller particle moving a little faster. In addition, the zeta potential of particle has an effective influence on the particle motion. For a faster particle moving from behind a slower one, numerical results show that the faster moving particle will climb and then pass the slower moving particle then two particles’ centers are not located on a line parallel to the electric field.

scholarly journals On the thermodynamic boundary conditions of a solidifying mushy layer with outflow

2014 ◽  
Vol 762 ◽  
Author(s):  
David W. Rees Jones ◽  
M. Grae Worster
Keyword(s):  
Transition Region ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Darcy Number ◽  
Forced Flow ◽  
Mushy Layer ◽  
Liquid Region ◽  
Precise Knowledge ◽  
Steady Solutions ◽  
Velocity Changes

AbstractThe free-boundary problem between a liquid region and a mushy layer (a reactive porous medium) must respect both thermodynamic and fluid dynamical considerations. We develop a steady two-dimensional forced-flow configuration to investigate the thermodynamic condition of marginal equilibrium that applies to a solidifying mushy layer with outflow and requires that streamlines are tangent to isotherms at the interface. We show that a ‘two-domain’ approach in which the mushy layer and liquid region are distinct domains is consistent with marginal equilibrium by extending the Stokes equations in a narrow transition region within the mushy layer. We show that the tangential fluid velocity changes rapidly in the transition region to satisfy marginal equilibrium. In convecting mushy layers with liquid channels, a buoyancy gradient can drive this tangential flow. We use asymptotic analysis in the limit of small Darcy number to derive a regime diagram for the existence of steady solutions. Thus we show that marginal equilibrium is a robust boundary condition and can be used without precise knowledge of the fluid flow near the interface.

CFD Assisted Design of a Wearable Artificial Pump Lung Device

2008 ◽  
Author(s):  
M. Ertan Taskin ◽  
Tao Zhang ◽  
Changfu Wu ◽  
Bartley P. Griffith ◽  
Zhongjun J. Wu
Keyword(s):  
Blood Flow ◽  
Shear Stress ◽  
Flow Field ◽  
Oxygen Transfer ◽  
Stokes Equations ◽  
Hollow Fiber Membrane ◽  
Impeller Blade ◽  
Blood Damage ◽  
Chronic Lung Diseases ◽  
Precise Knowledge

A wearable artificial pump lung (APL) device is being developed to provide ambulatory respiratory support for patients with acute or chronic lung diseases. The design objective of the APL is to create an assembly free, ultracompact, all-in-one system with an optimized blood flow path and minimized device-induced blood damage. This device will combine a magnetically levitated pump/rotor with a uniquely configured hollow fiber membrane (HFM). Computational fluid dynamics (CFD) based multidisciplinary modeling of the device functional performance and biocompatibility was utilized to acquire the precise knowledge of flow field, gas transfer and blood damage characteristics through the whole device. With this knowledge available, the device can be evaluated and optimized to obtain best performance, i.e., maximizing the gas exchange efficiency and minimizing blood damage. The HFM bundle was modeled as porous media with a constant porosity. Flow field was obtained by solving the Navier-Stokes equations, and oxygen transfer process was modeled as a scalar transport. The hemolysis was evaluated based on the shear stress and exposure time distributions which were obtained by post-processing the flow solution. According to the preliminary CFD results, among several designs, the satisfactory one was found regarding flow dynamics, overall biocompatibility and oxygen transfer performances. The average shear stress value was less than 10 Pa, and the outlet oxygen saturation was higher than 95% at standard operating condition. The impeller blade and diffuser angles were compatible to each other resulting in a smooth blood flow in the corresponding region.

On the Flow Fields of Inertial Impactors

1974 ◽  
Vol 96 (4) ◽  
pp. 394-400 ◽  
Author(s):  
V. A. Marple ◽  
B. Y. H. Liu ◽  
K. T. Whitby
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Relaxation Method ◽  
Water Model ◽  
Navier Stokes ◽  
Visualization Technique ◽  
Navier Stokes Equations ◽  
Theoretical Results ◽  
Plate Distance ◽  
Good Agreement

The flow field in an inertial impactor was studied experimentally with a water model by means of a flow visualization technique. The influence of such parameters as Reynolds number and jet-to-plate distance on the flow field was determined. The Navier-Stokes equations describing the laminar flow field in the impactor were solved numerically by means of a finite difference relaxation method. The theoretical results were found to be in good agreement with the empirical observations made with the water model.

Numerical Simulation of Flowfield around High Speed Trains Passing by each other at the same Speed

2011 ◽  
Vol 97-98 ◽  
pp. 698-701
Author(s):  
Ming Lu Zhang ◽  
Yi Ren Yang ◽  
Li Lu ◽  
Chen Guang Fan
Keyword(s):  
Numerical Simulation ◽  
Wind Tunnel ◽  
Flow Field ◽  
Point Source ◽  
High Speed ◽  
Stokes Equations ◽  
Field Structure ◽  
Vehicle Speed ◽  
Mesh Method ◽  
High Speed Trains

Large eddy simulation (LES) was made to solve the flow around two simplified CRH2 high speed trains passing by each other at the same speed base on the finite volume method and dynamic layering mesh method and three dimensional incompressible Navier-Stokes equations. Wind tunnel experimental method of resting train with relative flowing air and dynamic mesh method of moving train were compared. The results of numerical simulation show that the flow field structure around train is completely different between wind tunnel experiment and factual running. Two opposite moving couple of point source and point sink constitute the whole flow field structure during the high speed trains passing by each other. All of streamlines originate from point source (nose) and finish with the closer point sink (tail). The flow field structure around train is similar with different vehicle speed.

Effects of Inlet Distortion on the Flow Field in a Transonic Compressor Rotor

1996 ◽  
Author(s):  
Chunill Hah ◽  
Douglas C. Rabe ◽  
Thomas J. Sullivan ◽  
Aspi R. Wadia
Keyword(s):  
Boundary Layer ◽  
Flow Field ◽  
Viscous Flow ◽  
Total Pressure ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Aerodynamic Loss ◽  
Transonic Compressor ◽  
Inlet Distortion ◽  
Compressor Rotor

The effects of circumferential distortions in inlet total pressure on the flow field in a low-aspect-ratio, high-speed, high-pressure-ratio, transonic compressor rotor are investigated in this paper. The flow field was studied experimentally and numerically with and without inlet total pressure distortion. Total pressure distortion was created by screens mounted upstream from the rotor inlet. Circumferential distortions of 8 periods per revolution were investigated at two different rotor speeds. The unsteady blade surface pressures were measured with miniature pressure transducers mounted in the blade. The flow fields with and without inlet total pressure distortion were analyzed numerically by solving steady and unsteady forms of the Reynolds-averaged Navier-Stokes equations. Steady three-dimensional viscous flow calculations were performed for the flow without inlet distortion while unsteady three-dimensional viscous flow calculations were used for the flow with inlet distortion. For the time-accurate calculation, circumferential and radial variations of the inlet total pressure were used as a time-dependent inflow boundary condition. A second-order implicit scheme was used for the time integration. The experimental measurements and the numerical analysis are highly complementary for this study because of the extreme complexity of the flow field. The current investigation shows that inlet flow distortions travel through the rotor blade passage and are convected into the following stator. At a high rotor speed where the flow is transonic, the passage shock was found to oscillate by as much as 20% of the blade chord, and very strong interactions between the unsteady passage shock and the blade boundary layer were observed. This interaction increases the effective blockage of the passage, resulting in an increased aerodynamic loss and a reduced stall margin. The strong interaction between the passage shock and the blade boundary layer increases the peak aerodynamic loss by about one percent.

Fluid flow over and through a regular bundle of rigid fibres

2016 ◽  
Vol 792 ◽  
pp. 5-35 ◽  
Author(s):  
Giuseppe A. Zampogna ◽  
Alessandro Bottaro
Keyword(s):  
Porous Medium ◽  
Fluid Flow ◽  
Flow Field ◽  
Stokes Equations ◽  
Transversely Isotropic ◽  
Navier Stokes ◽  
Leading Order ◽  
Macroscopic Scale ◽  
Navier Stokes Equations ◽  
Homogenized Model

The interaction between a fluid flow and a transversely isotropic porous medium is described. A homogenized model is used to treat the flow field in the porous region, and different interface conditions, needed to match solutions at the boundary between the pure fluid and the porous regions, are evaluated. Two problems in different flow regimes (laminar and turbulent) are considered to validate the system, which includes inertia in the leading-order equations for the permeability tensor through a Oseen approximation. The components of the permeability, which characterize microscopically the porous medium and determine the flow field at the macroscopic scale, are reasonably well estimated by the theory, both in the laminar and the turbulent case. This is demonstrated by comparing the model’s results to both experimental measurements and direct numerical simulations of the Navier–Stokes equations which resolve the flow also through the pores of the medium.

Numerical investigation of supercritical Taylor-vortex flow for a wide gap

1984 ◽  
Vol 138 ◽  
pp. 21-52 ◽  
Author(s):  
H. Fasel ◽  
O. Booz
Keyword(s):  
Flow Field ◽  
Vortex Flow ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Taylor Number ◽  
Taylor Vortex ◽  
Plane Boundary ◽  
Aspect Ratios ◽  
Taylor Vortex Flow ◽  
Wide Gap

For a wide gap (R1/R2= 0.5) and large aspect ratiosL/d, axisymmetric Taylor-vortex flow has been observed in experiments up to very high supercritical Taylor (or Reynolds) numbers. This axisymmetric Taylor-vortex flow was investigated numerically by solving the Navier–Stokes equations using a very accurate (fourth-order in space) implicit finite-difference method. The high-order accuracy of the numerical method, in combination with large numbers of grid points used in the calculations, yielded accurate and reliable results for large supercritical Taylor numbers of up to 100Tac(or 10Rec). Prior to this study numerical solutions were reported up to only 16Tac. The emphasis of the present paper is placed upon displaying and elaborating the details of the flow field for large supercritical Taylor numbers. The flow field undergoes drastic changes as the Taylor number is increased from just supercritical to 100Tac. Spectral analysis (with respect toz) of the flow variables indicates that the number of harmonics contributing substantially to the total solution increases sharply when the Taylor number is raised. The number of relevant harmonics is already unexpectedly high at moderate supercriticalTa. For larger Taylor numbers, the evolution of a jetlike or shocklike flow structure can be observed. In the axial plane, boundary layers develop along the inner and outer cylinder walls while the flow in the core region of the Taylor cells behaves in an increasingly inviscid manner.

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