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.

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.

Electroosmotic Flow and Mass Species Transport in a Microcapillary Under Influences of Joule Heating

2003 ◽  
Author(s):  
Gongyue Tang ◽  
Chun Yang ◽  
Cheekiong Chai ◽  
Haiqing Gong
Keyword(s):  
Joule Heating ◽  
Electroosmotic Flow ◽  
Mathematic Model ◽  
Transfer Coefficients ◽  
Mass Transfer Equation ◽  
Buffer Solution ◽  
Species Transport ◽  
Heat Transfer Coefficients ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation

This study presents a numerical analysis of Joule heating effect on the electroosmotic flow and species transport, which has a direct application in the capillary electrophoresis based BioChip technology. A rigorous mathematic model for describing the Joule heating in an electroosmotic flow including Poisson-Boltzmann equation, modified Navier-Stokers equations and energy equation is developed. All these equations are coupled together through the temperature-dependent parameters. By numerically solving aforementioned equations simultaneously, the electroosmotic flow field and the temperature distributions in a cylindrical microcapillary are obtained. A systematic study is carried out under influences of different geometry sizes, buffer solution concentrations, applied electric field strengths, and heat transfer coefficients. In addition, sample species transport in a microcapillary is also investigated by numerically solving the mass transfer equation with consideration of temperature-dependant diffusion coefficient and electrophoresis mobility. The characteristics of the Joule heating, electroosmotic flow, and sample species transport in microcapillaries are discussed. The simulations reveal that the presence of the Joule heating could have a great impact on the electroosmotic flow and sample species transport.

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.

Groundwater remediation by anionic surfactant micelles - an innovative double layer model applied to Na+ and Mg2+ association with dodecylsulfate micelles

1998 ◽  
Vol 38 (7) ◽  
pp. 99-106 ◽  
Author(s):  
Ching Yuan ◽  
Chung-Hsuang Hung ◽  
Chad T. Jafvert
Keyword(s):  
Anionic Surfactant ◽  
Groundwater Remediation ◽  
Electrical Potential ◽  
Binding Constants ◽  
High Concentration ◽  
Experimental Conditions ◽  
Counterion Binding ◽  
Double Layer Model ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation

The association reactions involving counterions, Na+ and Mg2+, and micelles composed of the anionic surfactant, dodecylsulfate (DS−), were investigated in ultrafiltration experiments. To access the data, an innovative model was developed that considered specific counterion binding within a Stern layer, with binding constant dependent upon the electrical potential as derived by the Poisson-Boltzmann equation and with calculation of the cmc as a function of counterion binding (or association). The experimental and model results both show that magnitude of counterion binding is greater for divalent species, Mg2+, than that for the monovalent species, Na2+. However, high concentration of Na+ compete for surface area diminishing the ability of the DS− to bind either divalent species. At experimental conditions from 0 to 100 mM NaCl addition, the binding ratio (BR) varied only from 0.58 to 0.63. The optimum binding constants, KMg and KNa, were determined to be 0.4 and 1.0 L mol−1, respectively, for the model. The experimental data and model calculated results were generally in good agreement.

Roughness Effect on Pressure Drop for Electroosmotic (EO) Flow in Microtubes

2008 ◽  
Author(s):  
Hossein Shokouhmand ◽  
Maziar Aghvami ◽  
Mostafa Moghadami ◽  
Hamed Babazadeh
Keyword(s):  
Pressure Drop ◽  
Friction Factor ◽  
Electroosmotic Flow ◽  
Body Force ◽  
Momentum Equation ◽  
Wall Roughness ◽  
Roughness Effect ◽  
Isotropic Distribution ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation

This paper presents a theoretical model of the roughness effect on friction factor and pressure drop of fully developed, laminar flow in microtubes by considering the effect of the electrical double layer. The EDL potential distribution is calculated using the Poisson–Boltzmann equation and then the velocity profile is obtained by solving the fluid momentum equation with a body force term. The wall roughness in microtubes is modeled by utilizing a Gaussian, isotropic distribution. It is found that the effect of roughness is to increase the friction factor and pressure drop of the electroosmotic flow in microtubes.

scholarly journals Modeling Microtubule Counterion Distributions and Conductivity Using the Poisson-Boltzmann Equation

2021 ◽  
Vol 8 ◽  
Author(s):  
Boden B. Eakins ◽  
Sahil D. Patel ◽  
Aarat P. Kalra ◽  
Vahid Rezania ◽  
Karthik Shankar ◽  
...  
Keyword(s):  
Boltzmann Equation ◽  
Electrical Properties ◽  
Ionic Currents ◽  
Ionic Concentration ◽  
Buffer Solution ◽  
Physiological Concentration ◽  
Poisson Boltzmann ◽  
The Subject ◽  
Poisson Boltzmann Equation ◽  
The Impact

Microtubules are highly negatively charged proteins which have been shown to behave as bio-nanowires capable of conducting ionic currents. The electrical characteristics of microtubules are highly complicated and have been the subject of previous work; however, the impact of the ionic concentration of the buffer solution on microtubule electrical properties has often been overlooked. In this work we use the non-linear Poisson Boltzmann equation, modified to account for a variable permittivity and a Stern Layer, to calculate counterion concentration profiles as a function of the ionic concentration of the buffer. We find that for low-concentration buffers ([KCl] from 10 μM to 10 mM) the counterion concentration is largely independent of the buffer's ionic concentration, but for physiological-concentration buffers ([KCl] from 100 to 500 mM) the counterion concentration varies dramatically with changes in the buffer's ionic concentration. We then calculate the conductivity of microtubule-counterion complexes, which are found to be more conductive than the buffer when the buffer's ionic concentrations is less than ≈100 mM and less conductive otherwise. These results demonstrate the importance of accounting for the ionic concentration of the buffer when analyzing microtubule electrical properties both under laboratory and physiological conditions. We conclude by calculating the basic electrical parameters of microtubules over a range of ionic buffer concentrations applicable to nanodevice and medical applications.

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 Peristaltically Induced Electroosmotic Flow of Jeffrey Fluid with Zeta Potential and Navier-Slip at the Wall

2019 ◽  
Vol 8 (10) ◽  
pp. 1324-1329
Keyword(s):  
Zeta Potential ◽  
Electrical Potential ◽  
Slip Boundary Condition ◽  
Jeffrey Fluid ◽  
Long Wavelength ◽  
Navier Slip ◽  
Slip Boundary ◽  
Fluid Parameter ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation

This paper concern with the electro-osmotically modulated peristaltic of Jeffrey fluid with zeta potential and Navier-slip boundary condition at the channel wall. The Poisson-Boltzmann equation for electrical potential distribution is assumed to accommodate the electrical double layer. Poisson-Boltzmann equations are simplified by using Debye-Huckel linearization approximation. The closed form analytical solutions are calculated by using low Reynolds number and long wavelength assumptions. Influence of various parameters like electro-osmotic, Jeffrey fluid parameter, Slip parameter and Zeta potential on the flow are discussed through the nature of graphs

Non-Newtonian Fluid Flow and Heat Transfer in Microchannels

2013 ◽  
Vol 275-277 ◽  
pp. 462-465 ◽  
Author(s):  
Chien Hsin Chen ◽  
Yunn Lin Hwang ◽  
Shen Jenn Hwang
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Joule Heating ◽  
Flow Behavior ◽  
Debye Length ◽  
Dimensionless Temperature ◽  
Flow And Heat Transfer ◽  
Power Law Fluids ◽  
Wide Range ◽  
Analytical Expressions

Convective heat transfer of non-Newtonian power-law fluids in a microchannel is investigated. The governing parameters include the flow behavior index, the length scale ratio (ratio of Debye length to half channel height), the Joule heating parameter (ratio of Joule heating to surface heat flux), and the Brinkman number. Analytical expressions are presented for velocity and temperature profiles, as well as the Nusselt number. The flow and heat transfer parameters can be obtained by numerical integrations of the analytical expressions. The dimensionless temperature distribution across the microchannel and the fully-developed Nusselt number are illustrated for a wide range of governing parameters.

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