scholarly journals Electro-osmotic flow in a rotating rectangular microchannel

2015 ◽  
Vol 471 (2179) ◽  
pp. 20150200 ◽  
Author(s):  
Chiu-On Ng ◽  
Cheng Qi
Keyword(s):  
Rectangular Channel ◽  
Debye Length ◽  
Ekman Layer ◽  
Secondary Flows ◽  
Mean Flow ◽  
Rectangular Microchannel ◽  
Osmotic Flow ◽  
Zeta Potentials ◽  
Combined Action ◽  
Electro Osmotic Flow

An analytical model is presented for low-Rossby-number electro-osmotic flow in a rectangular channel rotating about an axis perpendicular to its own. The flow is driven under the combined action of Coriolis, pressure, viscous and electric forces. Analytical solutions in the form of eigenfunction expansions are developed for the problem, which is controlled by the rotation parameter (or the inverse Ekman number), the Debye parameter, the aspect ratio of the channel and the distribution of zeta potentials on the channel walls. Under the conditions of fast rotation and a thin electric double layer (EDL), an Ekman–EDL develops on the horizontal walls. This is essentially an Ekman layer subjected to electrokinetic effects. The flow structure of this boundary layer as a function of the Ekman layer thickness normalized by the Debye length is investigated in detail in this study. It is also shown that the channel rotation may have qualitatively different effects on the flow rate, depending on the channel width and the zeta potential distributions. Axial and secondary flows are examined in detail to reveal how the development of a geostrophic core may lead to a rise or fall of the mean flow.

Steady electro-osmotic flow of a micropolar fluid in a microchannel

2008 ◽  
Vol 465 (2102) ◽  
pp. 501-522 ◽  
Author(s):  
Abuzar A Siddiqui ◽  
Akhlesh Lakhtakia
Keyword(s):  
Micropolar Fluid ◽  
Couple Stress ◽  
Numerical Solutions ◽  
Debye Length ◽  
Analytic Solutions ◽  
Rectangular Microchannel ◽  
Micropolar Fluids ◽  
One Dimensional ◽  
Osmotic Flow ◽  
Electro Osmotic Flow

We have formulated and solved the boundary-value problem of steady, symmetric and one-dimensional electro-osmotic flow of a micropolar fluid in a uniform rectangular microchannel, under the action of a uniform applied electric field. The Helmholtz–Smoluchowski equation and velocity for micropolar fluids have also been formulated. Numerical solutions turn out to be virtually identical to the analytic solutions obtained after using the Debye–Hückel approximation, when the microchannel height exceeds the Debye length, provided that the zeta potential is sufficiently small in magnitude. For a fixed Debye length, the mid-channel fluid speed is linearly proportional to the microchannel height when the fluid is micropolar, but not when the fluid is simple Newtonian. The stress and the microrotation are dominant at and in the vicinity of the microchannel walls, regardless of the microchannel height. The mid-channel couple stress decreases, but the couple stress at the walls intensifies, as the microchannel height increases and the flow tends towards turbulence.

scholarly journals The influence of dielectric decrement on electrokinetics

2013 ◽  
Vol 724 ◽  
pp. 69-94 ◽  
Author(s):  
Hui Zhao ◽  
Shengjie Zhai
Keyword(s):  
Asymptotic Analysis ◽  
Double Layer ◽  
Debye Length ◽  
Charged Surface ◽  
Ion Specificity ◽  
Zeta Potentials ◽  
Condensed Layer ◽  
The Impact ◽  
Surface Conduction ◽  
Electro Osmotic Flow

AbstractWe treat the dielectric decrement induced by excess ion polarization as a source of ion specificity and explore its impact on electrokinetics. We employ a modified Poisson–Nernst–Planck (PNP) model accounting for the dielectric decrement. The dielectric decrement is determined by the excess-ion-polarization parameter $\alpha $ and when $\alpha = 0$ the standard PNP model is recovered. Our model shows that ions saturate at large zeta potentials $(\zeta )$. Because of ion saturation, a condensed counterion layer forms adjacent to the charged surface, introducing a new length scale, the thickness of the condensed layer $({l}_{c} )$. For the electro-osmotic mobility, the dielectric decrement weakens the electro-osmotic flow owing to the decrease of the dielectric permittivity. At large $\zeta $, when $\alpha \not = 0$, the electro-osmotic mobility is found to be proportional to $\zeta / 2$, in contrast to $\zeta $ as predicted by the standard PNP model. This is attributed to ion saturation at large $\zeta $. In terms of the electrophoretic mobility ${M}_{e} $, we carry out both an asymptotic analysis in the thin-double-layer limit and solve the full modified PNP model to compute ${M}_{e} $. Our analysis reveals that the impact of the dielectric decrement is intriguing. At small and moderate $\zeta ~({\lt }6kT/ e)$, the dielectric decrement decreases ${M}_{e} $ with increasing $\alpha $. At large $\zeta $, it is known that the surface conduction becomes significant and plays an important role in determining ${M}_{e} $. It is observed that the dielectric decrement effectively reduces the surface conduction. Hence in stark contrast, ${M}_{e} $ increases as $\alpha $ increases. Our predictions of the contrast dependence of the mobility on $\alpha $ at different zeta potentials qualitatively agree with experimental results on the dependence of the mobility among ions and provide a possible explanation for such ion specificity. Finally, the comparisons between the thin-double-layer asymptotic analysis and the full simulations of the modified PNP model suggest that at large $\zeta $ the validity of the thin-double-layer approximation is determined by ${l}_{c} $ rather than the traditional Debye length.

Dispersion coefficient in an electro-osmotic flow of a viscoelastic fluid through a microchannel with a slowly varying wall zeta potential

2018 ◽  
Vol 839 ◽  
pp. 348-386 ◽  
Author(s):  
J. C. Arcos ◽  
F. Méndez ◽  
E. G. Bautista ◽  
O. Bautista
Keyword(s):  
Dispersion Coefficient ◽  
Fluid Model ◽  
Perturbation Technique ◽  
Debye Length ◽  
Rheological Behaviour ◽  
Governing Equations ◽  
Regular Perturbation ◽  
Axial Distribution ◽  
Osmotic Flow ◽  
Electro Osmotic Flow

The dispersion coefficient of a passive solute in a steady-state pure electro-osmotic flow (EOF) of a viscoelastic liquid, whose rheological behaviour follows the simplified Phan-Thien–Tanner (sPTT) model, along a parallel flat plate microchannel, is studied. The walls of the microchannel are assumed to have modulated and low $\unicode[STIX]{x1D701}$ potentials, which vary slowly in the axial direction in a sinusoidal manner. The flow field required to obtain the dispersion coefficient was solved using the lubrication approximation theory (LAT). The solution of the electric potential is based on the Debye–Hückel approximation for a symmetric $(z:z)$ electrolyte. The viscoelasticity of the fluid is observed to notably amplify the axial distribution of the effective dispersion coefficients due to the variation in the $\unicode[STIX]{x1D701}$ potentials of the walls. The problem was formulated for two cases: when the Debye layer thickness (EDL) was on the order of unity (thick EDL) and in the limit where the thickness of the EDL was very small compared with the height of the microchannel (thin EDL limit). Due to the coupling between the nonlinear governing equations and the sPTT fluid model, they were replaced by their approximate linearized forms and solved in the limit of $\unicode[STIX]{x1D700}\ll 1$ using the regular perturbation technique. Here $\unicode[STIX]{x1D700}$ is the amplitude of the sinusoidal function of the $\unicode[STIX]{x1D701}$ potentials. Additionally, the numerical solution of the simplified governing equations was also obtained for $\unicode[STIX]{x1D700}=O(1)$ and compared with the approximate solution, showing excellent agreement for $0\leqslant \unicode[STIX]{x1D700}\leqslant 0.3$. Note that the dispersion coefficient primarily depends on the Deborah number, on the ratio of the half-height of the microchannel to the Debye length, and on the assumed variation in the $\unicode[STIX]{x1D701}$ potentials of the walls.

Maxwell stress-induced flow control of a free surface electro-osmotic flow in a rectangular microchannel

2013 ◽  
Vol 16 (4) ◽  
pp. 721-728 ◽  
Author(s):  
Manik Mayur ◽  
Sakir Amiroudine ◽  
Didier Lasseux ◽  
Suman Chakraborty
Keyword(s):  
Free Surface ◽  
Flow Control ◽  
Maxwell Stress ◽  
Rectangular Microchannel ◽  
Osmotic Flow ◽  
Induced Flow ◽  
Electro Osmotic Flow

Electro-Osmotic Flow in Reservoir-Connected Flat Microchannels With Non-Uniform Zeta Potential

2006 ◽  
Vol 128 (6) ◽  
pp. 1133-1143 ◽  
Author(s):  
S. A. Mirbozorgi ◽  
H. Niazmand ◽  
M. Renksizbulut
Keyword(s):  
Zeta Potential ◽  
Electric Potential ◽  
Stokes Equations ◽  
Planck Equation ◽  
Ionic Concentration ◽  
Complex Flow ◽  
Layer Potential ◽  
Osmotic Flow ◽  
Zeta Potentials ◽  
Electro Osmotic Flow

The effects of non-uniform zeta potentials on electro-osmotic flows in flat microchannels have been investigated with particular attention to reservoir effects. The governing equations, which consist of a Laplace equation for the distribution of external electric potential, a Poisson equation for the distribution of electric double layer potential, the Nernst-Planck equation for the distribution of charge density, and modified Navier-Stokes equations for the flow field are solved numerically for an incompressible steady flow of a Newtonian fluid using the finite-volume method. For the validation of the numerical scheme, the key features of an ideal electro-osmotic flow with uniform zeta potential have been compared with analytical solutions for the ionic concentration, electric potential, pressure, and velocity fields. When reservoirs are included in the analysis, an adverse pressure gradient is induced in the channel due to entrance and exit effects even when the reservoirs are at the same pressure. Non-uniform zeta potentials lead to complex flow fields, which are examined in detail.

A Preliminary Study of Turbulence Characteristics of Flow Along a Corner

1961 ◽  
Vol 83 (4) ◽  
pp. 657-661 ◽  
Author(s):  
F. B. Gessner ◽  
J. B. Jones
Keyword(s):  
Turbulence Intensity ◽  
Free Stream ◽  
Flow Direction ◽  
Rectangular Channel ◽  
Secondary Flows ◽  
Mean Flow ◽  
Free Stream Turbulence ◽  
Plane Normal ◽  
The Mean ◽  
Preliminary Study

In the turbulent flow of a fluid along a corner, secondary flows occur which have a marked influence on the velocity distributions in planes normal to the mean flow direction. All published explanations of the cause of these secondary flows deal with the turbulent structure of the flow. In this paper, measurements of isotach patterns and directional turbulence intensities in the corner of a rectangular channel with zero pressure gradient and a range of free-stream turbulence intensity of 0.8 to 2.3 per cent are reported. (An isotach is a constant velocity line in a plane normal to the mean flow direction.) Within the range of variables investigated, the following conclusions are drawn: (a) Isotach patterns are essentially independent of free-stream turbulence intensity; (b) at any point the ratio of turbulence components in orthogonal directions in a plane normal to the mean flow direction is a maximum for directions tangent and normal to the isotach at that point; (c) the ratio w′/v′, where w′ and v′ are turbulence components, respectively, tangent and normal to the isotach at any point, is always greater than unity; and (d) in the vicinity of the bisector of the corner angle the ratio w′/v′ increases with increasing isotach curvature.

A New Approach for Modeling Electro-Osmotic Flow Micro-Cooling Systems

2013 ◽  
Vol 705 ◽  
pp. 393-399
Author(s):  
Alireza Taklifi ◽  
Abbas Aliabadi
Keyword(s):  
Kinetic Parameter ◽  
Bessel Function ◽  
Debye Length ◽  
Second Law Of Thermodynamics ◽  
Simple Method ◽  
Cooling Systems ◽  
Flux Boundary Condition ◽  
Osmotic Flow ◽  
Micro Channels ◽  
Electro Osmotic Flow

The problem of entropy generation due to heat transfer in an electro-osmotic flow with circular type area section micro-channels for small values of electro-kinetic parameterκα(whereκis the Debye length andais the radius of the micro-channel) is investigated analytically. The momentum and energy conservation equations in cylindrical coordinates for an electro-osmotic flow are derived in non-dimensional form. The momentum equation is solved and velocity distribution in terms of modified Bessel function of the first kind is obtained. An approximation is used for the Bessel function of first kind. Considering the approximate velocity profile, the energy equation including viscous dissipation effects is solved to obtain the temperature distribution in terms of parametric values of the electro-kinetic parameter and the Brinkman number. A uniform surface heat flux boundary condition is considered. The importance of this investigation is development of an engineering simple method of design for electro-osmotic circular micro-electronic cooling systems and possible optimizations of these kinds of flows with respect to the second-law of thermodynamics through the micro-coolers.

scholarly journals Towards bio-inspired artificial muscle: a mechanism based on electro-osmotic flow simulated using dissipative particle dynamics

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Ramin Zakeri
Keyword(s):  
Zeta Potential ◽  
Electric Field ◽  
Dissipative Particle Dynamics ◽  
Artificial Muscle ◽  
Particle Dynamics ◽  
Polymer Membrane ◽  
Channel Width ◽  
Micro Channel ◽  
Osmotic Flow ◽  
Electro Osmotic Flow

AbstractOne of the unresolved issues in physiology is how exactly myosin moves in a filament as the smallest responsible organ for contracting of a natural muscle. In this research, inspired by nature, a model is presented consisting of DPD (dissipative particle dynamics) particles driven by electro-osmotic flow (EOF) in micro channel that a thin movable impermeable polymer membrane has been attached across channel width, thus momentum of fluid can directly transfer to myosin stem. At the first, by validation of electro-osmotic flow in micro channel in different conditions with accuracy of less than 10 percentage error compared to analytical results, the DPD results have been developed to displacement of an impermeable polymer membrane in EOF. It has been shown that by the presence of electric field of 250 V/m and Zeta potential − 25 mV and the dimensionless ratio of the channel width to the thickness of the electric double layer or kH = 8, about 15% displacement in 8 s time will be obtained compared to channel width. The influential parameters on the displacement of the polymer membrane from DPD particles in EOF such as changes in electric field, ion concentration, zeta potential effect, polymer material and the amount of membrane elasticity have been investigated which in each cases, the radius of gyration and auto correlation velocity of different polymer membrane cases have been compared together. This simulation method in addition of probably helping understand natural myosin displacement mechanism, can be extended to design the contraction of an artificial muscle tissue close to nature.

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