scholarly journals Steric and Slippage Effects on Mass Transport by Using an Oscillatory Electroosmotic Flow of Power-Law Fluids

Micromachines ◽  
2021 ◽  
Vol 12 (5) ◽  
pp. 539
Author(s):  
Ruben Baños ◽  
José Arcos ◽  
Oscar Bautista ◽  
Federico Méndez
Keyword(s):  
Mass Transport ◽  
Electroosmotic Flow ◽  
Volume Fraction ◽  
Slip Length ◽  
Electrical Potential ◽  
Debye Length ◽  
Ion Concentration ◽  
Steric Effects ◽  
Power Law Fluids ◽  
Poisson Boltzmann

In this paper, the combined effect of the fluid rheology, finite-sized ions, and slippage toward augmenting a non-reacting solute’s mass transport due to an oscillatory electroosmotic flow (OEOF) is determined. Bikerman’s model is used to include the finite-sized ions (steric effects) in the original Poisson-Boltzmann (PB) equation. The volume fraction of ions quantifies the steric effects in the modified Poisson-Boltzmann (MPB) equation to predict the electrical potential and the ion concentration close to the charged microchannel walls. The hydrodynamics is affected by slippage, in which the slip length was used as an index for wall hydrophobicity. A conventional finite difference scheme was used to solve the momentum and species transport equations in the lubrication limit together with the MPB equation. The results suggest that the combined slippage and steric effects promote the best conditions to enhance the mass transport of species in about 90% compared with no steric effect with proper choices of the Debye length, Navier length, steric factor, Womersley number, and the tidal displacement.

Slippage Effect on the Oscillatory Electroosmotic Flow of Power-Law Fluids in a Microchannel

2020 ◽  
Vol 399 ◽  
pp. 92-101
Author(s):  
Ruben Baños ◽  
José Arcos ◽  
Oscar Bautista ◽  
Federico Méndez
Keyword(s):  
Power Law ◽  
Electroosmotic Flow ◽  
Characteristic Length ◽  
Slip Length ◽  
Flow Behavior ◽  
Debye Length ◽  
Channel Width ◽  
Length Scale ◽  
Characteristic Length Scale ◽  
Power Law Fluids

The oscillatory electroosmotic flow (OEOF) under the influence of the Navier slip condition in power law fluids through a microchannel is studied numerically. A time-dependent external electric field (AC) is suddenly imposed at the ends of the microchannel which induces the fluid motion. The continuity and momentum equations in the and direction for the flow field were simplified in the limit of the lubrication approximation theory (LAT), and then solved using a numerical scheme. The solution of the electric potential is based on the Debye-Hückel approximation which suggest that the surface potential is small, say, smaller than 0:025V and for a symmetric () electrolyte. Our results suggest that the velocity profiles across the channel-width are controlled by the following dimensionless parameters: the dimensionless slip length , the Womersley number, , the electrokinetic parameter, , defined as the ratio of the characteristic length scale to the Debye length, the parameter which represents the ratio of the Helmholtz-Smoluchowski velocity to the characteristic length scale and the flow behavior index, . Also, the results reveal that the velocity magnitude gets higher values as increases and become more and more nonuniform across the channel-width as the and are increased, so OEOF can be useful in micro-fluidic devices such as micro-mixers.

Electroosmotic Flow in Hydrophobic Microchannels of General Cross Section

2015 ◽  
Vol 138 (3) ◽  
Author(s):  
Morteza Sadeghi ◽  
Arman Sadeghi ◽  
Mohammad Hassan Saidi
Keyword(s):  
Cross Section ◽  
Flow Rate ◽  
Electroosmotic Flow ◽  
Slip Length ◽  
Debye Length ◽  
Surface Hydrophobicity ◽  
Double Layers ◽  
Slip Conditions ◽  
Wall Boundary Conditions ◽  
Electroosmotic Velocity

Adopting the Navier slip conditions, we analyze the fully developed electroosmotic flow in hydrophobic microducts of general cross section under the Debye–Hückel approximation. The method of analysis includes series solutions which their coefficients are obtained by applying the wall boundary conditions using the least-squares matching method. Although the procedure is general enough to be applied to almost any arbitrary cross section, eight microgeometries including trapezoidal, double-trapezoidal, isosceles triangular, rhombic, elliptical, semi-elliptical, rectangular, and isotropically etched profiles are selected for presentation. We find that the flow rate is a linear increasing function of the slip length with thinner electric double layers (EDLs) providing higher slip effects. We also discover that, unlike the no-slip conditions, there is not a limit for the electroosmotic velocity when EDL extent is reduced. In fact, utilizing an analysis valid for very thin EDLs, it is shown that the maximum electroosmotic velocity in the presence of surface hydrophobicity is by a factor of slip length to Debye length higher than the Helmholtz–Smoluchowski velocity. This approximate procedure also provides an expression for the flow rate which is almost exact when the ratio of the channel hydraulic diameter to the Debye length is equal to or higher than 50.

Effect of Hydrodynamic Slippage on Oscillating Electroosmotic Flows in Infinitely Extended Microcapillary

2015 ◽  
Author(s):  
Guillermo Rojas ◽  
Oscar E. Bautista ◽  
Federico Mendez
Keyword(s):  
Electric Field ◽  
Strouhal Number ◽  
Slip Length ◽  
Fluid Motion ◽  
Electrical Potential ◽  
Debye Length ◽  
Bulk Velocity ◽  
Dimensionless Frequency ◽  
Dimensionless Parameters ◽  
Poisson Boltzmann Equation

In this work we conduct a numerical analysis of the time periodic electroosmotic flow in a cylindrical microcapillary, whose wall is considered hydrophobic. The fluid motion is driven by the sudden imposition of a time-dependent electric field. The electrical potential is obtained by solving the nonlinear Poisson-Boltzmann equation for high zeta potential, under the assumption that the electrokinetic potential is not affected by the oscillatory external field. In addition, we neglect the channel entry and exit effects, in such manner that the flow is fully developed. The governing equations are nondimensionalized, and the solution is obtained as a function of three dimensionless parameters: the ratio of the Navier slip length to the radius of the microcapillary, δ; Rω, which is the dimensionless frequency for the flow or Strouhal number and measures the competition between the diffusion time to the time scale associated to the frequency of the oscillatory electric field; and κ, which represents the ratio of the radius of the microcapillary to the Debye length. The principal results show that using slippage, the bulk velocity increases for increasing values of δ. For the values of the dimensionless parameters used in this analysis, by using hydrophobic walls, the bulk velocity can be increased in about 20% in comparison with the case of no-slip boundary condition. On the other hand, the dimensionless frequency for the flow or Strouhal number plays a fundamental role in determining the motion of the fluid. For Rω ≪ 1, the dissipation is found in resonance with the frequency of the oscillatory electric field. For Rω ≫ 1, the dissipation is not in phase with the frequency and, therefore, the velocity in the center of the microcapillary, in some cases, is almost null, and the maximum value of the velocity is near to the microcapillary wall.

scholarly journals An Exact Solution for Power-Law Fluids in a Slit Microchannel with Different Zeta Potentials under Electroosmotic Forces

Micromachines ◽  
2018 ◽  
Vol 9 (10) ◽  
pp. 504 ◽  
Author(s):  
Du-Soon Choi ◽  
Sungchan Yun ◽  
WooSeok Choi
Keyword(s):  
Power Law ◽  
Applied Pressure ◽  
Debye Length ◽  
Momentum Equation ◽  
Microfluidic System ◽  
Zeta Potentials ◽  
Power Law Fluids ◽  
Poisson Boltzmann ◽  
The Difference ◽  
Poisson Boltzmann Equation

Electroosmotic flow (EOF) is one of the most important techniques in a microfluidic system. Many microfluidic devices are made from a combination of different materials, and thus asymmetric electrochemical boundary conditions should be applied for the reasonable analysis of the EOF. In this study, the EOF of power-law fluids in a slit microchannel with different zeta potentials at the top and bottom walls are studied analytically. The flow is assumed to be steady, fully developed, and unidirectional with no applied pressure. The continuity equation, the Cauchy momentum equation, and the linearized Poisson-Boltzmann equation are solved for the velocity field. The exact solutions of the velocity distribution are obtained in terms of the Appell’s first hypergeometric functions. The velocity distributions are investigated and discussed as a function of the fluid behavior index, Debye length, and the difference in the zeta potential between the top and bottom.

Similar Region in Electroosmotic Flow Rate for Newtonian and Non-Newtonian Fluids Using Dissipative Particle Dynamics (DPD)

2014 ◽  
Author(s):  
Ramin Zakeri ◽  
Eon Soo Lee
Keyword(s):  
Electroosmotic Flow ◽  
Flow Behavior ◽  
Dissipative Particle Dynamics ◽  
Debye Length ◽  
Particle Dynamics ◽  
Newtonian Fluids ◽  
Channel Height ◽  
Flow Rates ◽  
Power Law Fluids ◽  
Force Calculation

In this paper, analysis of electroosmotic flow in Newtonian and non Newtonian fluids in nanochannel with dissipative particle dynamics (DPD) method is presented and our results are validated with analytical solutions. Our aim is that which region or regions, based on the volumetric flow rates, in non-Newtonian fluids are similar with comparison to Newtonian ones in regards to various effective EOF parameters. For numerical simulation, the linearized Poisson Boltzmann for external force calculation is used and DPD method is applied for power law fluids to predict non-Newtonian fluids behavior in electroosmotic in various conditions such as different zeta potential, external electric fields, kh parameter (mainly Debye length and channel height), and flow behavior index. Based on the our results, for certain values of effective parameters, there are regions for volumetric flow rates which both Newtonian and non Newtonian electroosmotic flows have similar behavior while out of these regions, there are obviously significant differences and it is not possible to take Newtonian assumption for these regions. Based on our results validated with analytical solution, simplified assumption of taking non Newtonian fluid as Newtonians ones, in different EOF conditions in most cases, have a clearly inaccuracy and presented method can predict which EOF rates in both cases are correctly similar.

Electroosmotic Flow Through a Circular Tube With Slip-Stick Striped Wall

2012 ◽  
Vol 134 (11) ◽  
Author(s):  
Henry C. W. Chu ◽  
Chiu-On Ng
Keyword(s):  
Electroosmotic Flow ◽  
Circular Tube ◽  
Plane Surface ◽  
Slip Length ◽  
Point Collocation ◽  
Hydrodynamic Slip ◽  
Poisson Boltzmann ◽  
Flow Enhancement ◽  
Circular Surface ◽  
Poisson Boltzmann Equation

This is an analytical study on electrohydrodynamic flows through a circular tube, of which the wall is micropatterned with a periodic array of longitudinal or transverse slip-stick stripes. One unit of the wall pattern comprises two stripes, one slipping and the other nonslipping, and each with a distinct ζ potential. Using the methods of eigenfunction expansion and point collocation, the electric potential and velocity fields are determined by solving the linearized Poisson–Boltzmann equation and the Stokes equation subject to the mixed electrohydrodynamic boundary conditions. The effective equations for the fluid and current fluxes are deduced as functions of the slipping area fraction of the wall, the intrinsic hydrodynamic slip length, the Debye parameter, and the ζ potentials. The theoretical limits for some particular wall patterns, which are available in the literature only for plane channels, are extended in this paper to the case of a circular channel. We confirm that some remarks made earlier for electroosmotic flow over a plane surface are also applicable to the present problem involving patterns on a circular surface. We pay particular attention to the effects of the pattern pitch on the flow in both the longitudinal and transverse configurations. When the wall is uniformly charged, the adverse effect on the electroosmotic flow enhancement due to a small fraction of area being covered by no-slip slots can be amplified if the pitch decreases. Reducing the pitch will also lead to a greater deviation from the Helmholtz–Smoluchowski limit when the slipping regions are uncharged. With oppositely charged slipping regions, local recirculation or a net reversed flow is possible, even when the wall is on the average electropositive or neutral. The flow morphology is found to be subject to the combined influence of the geometry of the tube and the electrohydrodynamic properties of the wall.

Unsteady Rotating Electroosmotic Flow Through a Slit Microchannel

2016 ◽  
Vol 32 (5) ◽  
pp. 603-611 ◽  
Author(s):  
D.-Q. Si ◽  
Y.-J. Jian ◽  
L. Chang ◽  
Q.-S. Liu
Keyword(s):  
Flow Rate ◽  
Electroosmotic Flow ◽  
Volume Flow Rate ◽  
Electrical Potential ◽  
Velocity Fields ◽  
Volume Flow ◽  
Half Height ◽  
Poisson Boltzmann ◽  
Flow Through ◽  
Poisson Boltzmann Equation

AbstractUsing the method of Laplace transform, an analytical solution of unsteady rotating electroosmotic flow (EOF) through a parallel plate microchannel is presented. The analysis is based upon the linearized Poisson-Boltzmann equation describing electrical potential distribution and the Navies Stokes equation representing flow field in the rotating coordinate system. The discrepancy of present problem from classical EOF is that the velocity fields are two-dimensional. The rotating EOF velocity profile and flow rate greatly depend on time t, rotating parameter ω and the electrokinetic width K (ratio of half height of microchannel to thickness of electric double layer). The influence of the above dimensionless parameters on transient EOF velocity, volume flow rate and EO spiral is investigated.

scholarly journals Electrothermal Transport in Biological Systems: An Analytical Approach for Electrokinetically Modulated Peristaltic Flow

2017 ◽  
Vol 9 (4) ◽  
Author(s):  
Dharmendra Tripathi ◽  
Ashish Sharma ◽  
O. Anwar Bég ◽  
Abhishek Tiwari
Keyword(s):  
Joule Heating ◽  
Body Force ◽  
Electrical Potential ◽  
Debye Length ◽  
Planck Equation ◽  
Volumetric Flow Rate ◽  
Flow And Heat Transfer ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
The Impact

A mathematical model is presented to study the combined viscous electro-osmotic (EO) flow and heat transfer in a finite length microchannel with peristaltic wavy walls in the presence of Joule heating. The unsteady two-dimensional conservation equations for mass, momentum, and energy conservation with viscous dissipation, heat absorption, and electrokinetic body force, are formulated in a Cartesian co-ordinate system. Both single and train wave propagations are considered. The electrical field terms are rendered into electrical potential terms via the Poisson–Boltzmann equation, Debye length approximation, and ionic Nernst Planck equation. A parametric study is conducted to evaluate the impact of isothermal Joule heating and electro-osmotic velocity on axial velocity, temperature distribution, pressure difference, volumetric flow rate, skin friction, Nusselt number, and streamline distributions.

Electroosmotic Flow of Power-Law Fluids in a Slit Microchannel

2009 ◽  
Author(s):  
Cunlu Zhao ◽  
Chun Yang
Keyword(s):  
Shear Stress ◽  
Double Layer ◽  
Power Law ◽  
Dynamic Viscosity ◽  
Electroosmotic Flow ◽  
Flow Behavior ◽  
Flow Behavior Index ◽  
Power Law Fluids ◽  
Hyperbolic Cosine ◽  
Behavior Index

Electroosmotic flow of power-law fluids in a slit channel is analyzed. The governing equations including the linearized Poisson–Boltzmann equation, the Cauchy momentum equation and the continuity equation are solved to seek analytical expressions for the shear stress, dynamic viscosity and velocity distributions. Specifically, exact solutions of the velocity distributions are explicitly found for several special values of the flow behavior index. Furthermore, with the implementation of an approximate scheme for the hyperbolic cosine function, approximate solutions of the velocity distributions are obtained. In addition, a mathematical expression for the average electroosmotic velocity is derived for large values of the dimensionless electrokinetic parameter, κH, in a fashion similar to the Smoluchowski equation. Hence, a generalized Smoluchowski velocity is introduced by taking into account contributions due to the finite thickness of the electric double layer and the flow behavior index of power-law fluids. Finally, calculations are performed to examine the effects of κH, flow behavior index, double layer thickness, and applied electric field on the shear stress, dynamic viscosity, velocity distribution, and average velocity/flow rate of the electroosmotic flow of power-law fluids.

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