scholarly journals Analysis of an electroosmotic flow in wavy wall microchannels using the lubrication approximation

2020 ◽  
Vol 66 (6 Nov-Dec) ◽  
pp. 761
Author(s):  
J. Arcos ◽  
O. Bautista ◽  
F. Méndez ◽  
M. Peralta
Keyword(s):  
Electroosmotic Flow ◽  
Mathematical Problem ◽  
Volumetric Flow Rate ◽  
Double Layers ◽  
Channel Height ◽  
Wavy Wall ◽  
Poisson Boltzmann ◽  
Hydrodynamic Field ◽  
The Mean ◽  
Analytical Expressions

We present the analysis of an electroosmotic flow (EOF) of a Newtonian fluid in a wavy-wall microchannel. In order to describe the flow and electrical fields, the lubrication and Debye-Hückel approximations are used. The simplified governing equations of continuity, momentum and Poisson-Boltzmann, together with the boundary conditions are presented in dimensionless form. For solving the mathematical problem, numerical and asymptotic techniques were applied. The asymptotic solution is obtained in the limit of very thin electric double layers (EDLs). We show that the lubrication theory is a powerful technique for solving the hydrodynamic field in electroosmotic flows in microchannels where the amplitude of the waviness changes on the order of the  mean semi-channel height. Approximate analytical expressions for the velocity components and pressure distribution are derived, and a closed formula for the volumetric flow rate is obtained.  The results show that the principal parameters that govern this EOF are the geometrical parameter, ε, which characterizes the waviness of the microchannel and the ratio of the mean semi-channel height to the thickness of the EDL, κ.

Viscoelectric Effect on the Electroosmotic Flow in Nanochannels With Heterogeneous Zeta Potentials

2018 ◽  
Author(s):  
Edson M. Jimenez ◽  
Federico Méndez ◽  
Juan P. Escandón
Keyword(s):  
Electroosmotic Flow ◽  
Fluid Velocity ◽  
Volumetric Flow Rate ◽  
Mass Conservation ◽  
Double Layers ◽  
Fluid Viscosity ◽  
Governing Equations ◽  
Flat Plates ◽  
Zeta Potentials ◽  
Poisson Boltzmann

In the present work, we realize a study about the influence of viscoelectric effect on the electroosmotic flow of Newtonian fluids in nanochannels formed by two parallel flat plates. In the problem, the channel walls have heterogeneous zeta potentials which follow a sinusoidal distribution; moreover, viscoelectric effects appear into the electric double layers when high zeta potentials are considered at the channel walls, modifying the fluid viscosity and the fluid velocity. To find the solution of flow field, the modified Poisson-Boltzmann, mass conservation and momentum governing equations, are solved numerically. In the results, combined effects from the zeta potential heterogeneities and viscosity changes yields different kind of flow recirculations controlled by the dephasing angle, amplitude and number of waves of the heterogeneities at the walls. The viscoelectric effect produces a decrease in the magnitude of velocity profiles and volumetric flow rate when the high zeta potentials are magnified. Additionally, the heterogeneous zeta potentials at the walls generate an induced pressure on the flow. This investigation extend the knowledge of electroosmotic flows under field effects for future mixing applications.

Numerical Modeling of Electroosmotically Driven Micro Flows

1999 ◽  
Author(s):  
Prashanta Dutta ◽  
Ali Beskok ◽  
Timothy C. Warburton
Keyword(s):  
Spectral Element ◽  
Double Layers ◽  
Channel Height ◽  
Shear Stresses ◽  
Pressure Gradients ◽  
Pressure Distributions ◽  
Micro Channels ◽  
Micro Flows ◽  
Analytical Relations ◽  
P Type

Abstract Electroosmotically driven flows in micro-channels are analyzed analytically and numerically. Semi-analytical relations for the velocity and pressure distributions in micro channels are obtained for electric double layers that are much smaller than the channel height, by using the Helmholtz Smoluchowski velocity. Analytical relations for wall shear stress and pressure distribution are obtained. Amplification of the normal and shear stresses on the walls are observed and documented. A high-order (h/p type) spectral element method is developed, and verified for numerical simulation of electroosmotic micro fluidic flows. Finally, flow through a step channel geometry is analyzed to document the interaction of the electroosmotic forces with adverse pressure gradients. Significant changes within the separation patterns are observed.

STUDY OF THERMODYNAMIC PROPERTIES OF ZINC-BLENDE-TYPE SEMICONDUCTORS: TEMPERATURE AND PRESSURE DEPENDENCES

2011 ◽  
Vol 25 (12n13) ◽  
pp. 1041-1051 ◽  
Author(s):  
HO KHAC HIEU ◽  
VU VAN HUNG
Keyword(s):  
Nearest Neighbor ◽  
Thermodynamic Quantities ◽  
Atomic Displacements ◽  
Zinc Blende ◽  
The Mean ◽  
Temperature And Pressure ◽  
Analytical Expressions ◽  
Theoretical Results ◽  
Nearest Neighbor Distances ◽  
Statistical Moment Method

Using the statistical moment method (SMM), the temperature and pressure dependences of thermodynamic quantities of zinc-blende-type semiconductors have been investigated. The analytical expressions of the nearest-neighbor distances, the change of volumes and the mean-square atomic displacements (MSDs) have been derived. Numerical calculations have been performed for a series of zinc-blende-type semiconductors: GaAs , GaP , GaSb , InAs , InP and InSb . The agreement between our calculations and both earlier other theoretical results and experimental data is a support for our new theory in investigating the temperature and pressure dependences of thermodynamic quantities of semiconductors.

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.

scholarly journals Structure and thermodynamics in the linear modified Poisson-Boltzmann theories in restricted primitive model electrolytes

2021 ◽  
Vol 24 (2) ◽  
pp. 23801
Author(s):  
L. B. Bhuiyan
Keyword(s):  
Activity Coefficient ◽  
Distribution Functions ◽  
Spherical Approximation ◽  
Mean Spherical Approximation ◽  
Primitive Model ◽  
Restricted Primitive Model ◽  
Mean Activity Coefficient ◽  
Poisson Boltzmann ◽  
Electrical Part ◽  
The Mean

Structure and thermodynamics in restricted primitive model electrolytes are examined using three recently developed versions of a linear form of the modified Poisson-Boltzmann equation. Analytical expressions for the osmotic coefficient and the electrical part of the mean activity coefficient are obtained and the results for the osmotic and the mean activity coefficients are compared with that from the more established mean spherical approximation, symmetric Poisson-Boltzmann, modified Poisson-Boltzmann theories, and available Monte Carlo simulation results. The linear theories predict the thermodynamics to a remarkable degree of accuracy relative to the simulations and are consistent with the mean spherical approximation and modified Poisson-Boltzmann results. The predicted structure in the form of the radial distribution functions and the mean electrostatic potential also compare well with the corresponding results from the formal theories. The excess internal energy and the electrical part of the mean activity coefficient are shown to be identical analytically for the mean spherical approximation and the linear modified Poisson-Boltzmann theories.

Fully-Developed Laminar Flow in Sinusoidal Grooves

2001 ◽  
Vol 123 (3) ◽  
pp. 656-661 ◽  
Author(s):  
Scott K. Thomas ◽  
Richard C. Lykins ◽  
Kirk L. Yerkes
Keyword(s):  
Contact Angle ◽  
Shear Stress ◽  
Volumetric Flow Rate ◽  
Numerical Data ◽  
Mean Velocity ◽  
Constant Property ◽  
Fully Developed Flow ◽  
Vapor Interface ◽  
The Mean ◽  
Poiseuille Number

The flow of a constant property fluid through a sinusoidal groove has been analyzed. A numerical solution of the conservation of mass and momentum equations for fully developed flow is presented. The mean velocity, volumetric flow rate, and Poiseuille number are presented as functions of the groove geometry, meniscus contact angle, and shear stress at the liquid-vapor interface. In addition, a semi-analytical solution for the normalized mean velocity in terms of the normalized shear stress at the meniscus is shown to agree with the numerical data quite well.

Ionic Layering and Overcharging in Electrical Double Layers in a Poisson-Boltzmann Model

2020 ◽  
Vol 125 (18) ◽  
Author(s):  
Ankur Gupta ◽  
Ananth Govind Rajan ◽  
Emily A. Carter ◽  
Howard A. Stone
Keyword(s):  
Double Layers ◽  
Electrical Double Layers ◽  
Poisson Boltzmann ◽  
Boltzmann Model ◽  
Ionic Layering

scholarly journals Effects of Structure Boundary Conditions and Snow-Pack Properties on Snow-Creep Pressures

1989 ◽  
Vol 13 ◽  
pp. 175-179
Author(s):  
D.M. McClung ◽  
J.O. Larsen
Keyword(s):  
Theoretical Analysis ◽  
Field Data ◽  
Nonlinear Deformation ◽  
Design Consideration ◽  
Snow Pack ◽  
Deformation Law ◽  
Linear Creep ◽  
The Mean ◽  
Structure Boundary ◽  
Analytical Expressions

Structures placed in deep snow covers are subject to forces caused by interruption of the down-slope snow-pack deformation components. The resulting creep pressures are often the primary design consideration. In this paper, accurate field data (pressures) and theoretical analysis of the problem using a linear creep law to define snow deformation are presented. Results include analytical expressions for the pressures, and it is demonstrated that the resulting linear theory underestimates the mean pressures by about 20%. Higher accuracy will require that a nonlinear deformation law be formulated.

scholarly journals Analytical Solution for Heat Transfer in Electroosmotic Flow of a Carreau Fluid in a Wavy Microchannel

2019 ◽  
Vol 9 (20) ◽  
pp. 4359 ◽  
Author(s):  
Saima Noreen ◽  
Sadia Waheed ◽  
Abid Hussanan ◽  
Dianchen Lu
Keyword(s):  
Fluid Flow ◽  
Flow Pattern ◽  
Flow Rate ◽  
Electroosmotic Flow ◽  
Linear Problem ◽  
Perturbation Technique ◽  
Volumetric Flow Rate ◽  
Carreau Fluid ◽  
Long Wavelength ◽  
Wide Range

This article explores the heat and transport characteristics of electroosmotic flow augmented with peristaltic transport of incompressible Carreau fluid in a wavy microchannel. In order to determine the energy distribution, viscous dissipation is reckoned. Debye Hückel linearization and long wavelength assumptions are adopted. Resulting non-linear problem is analytically solved to examine the distribution and variation in velocity, temperature and volumetric flow rate within the Carreau fluid flow pattern through perturbation technique. This model is also suitable for a wide range of biological microfluidic applications and variation in velocity, temperature and volumetric flow rate within the Carreau fluid flow pattern.

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