Thermally Fully Developed Electroosmotic Flow of Power-Law Fluids in a Circular Microchannel

2013 ◽  
Vol 29 (4) ◽  
pp. 609-616 ◽  
Author(s):  
Y.-J. Sun ◽  
Y.-J. Jian ◽  
L. Chang ◽  
Q.-S. Liu
Keyword(s):  
Power Law ◽  
Joule Heating ◽  
Electroosmotic Flow ◽  
Flow Behavior ◽  
Mathematic Model ◽  
Dimensionless Temperature ◽  
Fluid Temperature ◽  
Navier Stokes Equation ◽  
Power Law Fluids ◽  
Behavior Index

ABSTRACTThis study presents a thermally fully developed electroosmotic flow of the non-Newtonian power-law fluids through a circle microchannel. A rigorous mathematic model for describing the Joule heating in an electroosmotic flow including the Poisson Boltzmann equation, the modified Navier Stokes equation and the energy equation is developed. The semi-analytical solutions of normalized velocity and temperature are derived. The velocity profile is computed by numerical integrate, and the temperature distribution is obtained by finite difference method. Results show that the velocity profiles depend greatly on the fluid behavior index n and the nondimensional electrokinetic width K. For a specified value of K, the axial velocity increases with a decrease in n, and the same trend for the effect of K on the velocity can be found for a specified value of n. Moreover, the dimensionless temperature is governed by three parameters, namely, the flow behavior index n, the nondimensional electrokinetic width K, and the dimen-sionless Joule heating parameter G. The variations of radial fluid temperature distributions with different parameters are investigated.

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.

Electrokinetic Transport of Power Law Fluid Through a Micro-Channel With Hydrodynamic Slippage

2019 ◽  
Author(s):  
Ainul Haque ◽  
Ameeya Kumar Nayak ◽  
Bernhard Weigand
Keyword(s):  
Viscous Dissipation ◽  
Power Law ◽  
Joule Heating ◽  
Electroosmotic Flow ◽  
Staggered Grid ◽  
Micro Channel ◽  
Coupling Effects ◽  
Advantages And Disadvantages ◽  
Power Law Fluids ◽  
Flow Enhancement

Abstract A pressure driven electroosmotic flow (EOF) is numerically studied in a slit micro-channel with alternating hydrodynamic slip patches. The coupled Poisson-Boltzman-Navier Stokes equations dealt with external electric potential are solved for the flow enhancement of non-Newtonian fluids in microfluidic domain, which is a big challenge in the transportation and mixing of fluids in BioMEMS devices as the drag effect is very strong along the walls. This effect can be minimized with the use of slip boundary conditions by the coupling effects of liquid-liquid or gas-liquid interface positioning. In the present article, the fluid is considered to be a power-law fluids which is driven due to the coupling effects of two superimposed electric fields: the externally imposed electric field and the induced potential. An additional pressure gradient is created by the electrokinetic pumping to generate a higher velocity gradient in the presence of viscous dissipation and Joule heating effects. The analytical quantification of the electroosmotic flow velocity and temperature distribution is made and compared with the numerical results due to the staggered grid based finite volume method. The results are presented in terms of flow enhancement factor (Ef) (provides maximum species transport) and the average entropy generation due to fluid friction, viscous dissipation and Joule heating effect. The advantages and disadvantages of utilizing slip conditions are discussed which has large scale applications on drug delivery, DNA analysis and sequencing and especially biomedical applications, since cell damage due to pumping will be minimized compared to the micro pumps with moving valves, blades and pistons.

Solutions of Laminar Jet Flow Problems for Non-Newtonian Power-Law Fluids

1978 ◽  
Vol 100 (3) ◽  
pp. 363-366 ◽  
Author(s):  
E. M. Mitwally
Keyword(s):  
Power Law ◽  
Flow Behavior ◽  
Flow Behavior Index ◽  
Free Jets ◽  
Free Jet ◽  
Laminar Jet ◽  
Flow Problems ◽  
Power Law Fluids ◽  
Flow Configurations ◽  
Behavior Index

Solutions are presented for laminar flow of non-Newtonian power-law fluids. The flow configurations cover the two-dimensional plane and radial free jets, the axisymmetrical (circular) free jet, and the plane and radial wall jets. When the flow behavior index is unity, the present results agree well with those already published for the case of Newtonian fluids.

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.

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.

Mixed Electroosmotic Pressure Driven Flow and Heat Transfer of Power Law Fluid in a Hydrophobic Microchannel

2017 ◽  
Author(s):  
Ainul Haque ◽  
Ameeya Kumar Nayak
Keyword(s):  
Heat Transfer ◽  
Power Law ◽  
Joule Heating ◽  
Scientific Data ◽  
Channel Height ◽  
Flow And Heat Transfer ◽  
Power Law Fluids ◽  
Hydrophobic Microchannel ◽  
Pressure Driven Flow ◽  
Pressure Driven

In this paper, a mathematical model has been developed to analyze the combined electroosmotic and pressure driven flow of power law fluids in a micro channel in the presence of Joule heating effects. The effects of Navier slip boundary condition and thermal radiation is examined for effective heat transfer in a hydrophobic microchannel. The analytical treatment has been performed for fluid flow and heat transfer effects in terms of flow governing parameters. This study highlights the effect of channel height to the electric double layer thickness and observed the flow variation due to heat transfer effect with the available scientific data. For a pure EOF, velocity slip have more significant role to get a maximum flow rate as expected. For both pseudo-plastic and dilatent fluids Nusselt number is decreased with the increment of the hydrophobic parameter and dimensionless pressure gradient where as increment in Joule heating effect enhance the heat transfer rate.

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