Study of the Transient Electroosmotic Flow of Maxwell Fluids in Square Cross-Section Microchannels

2015 ◽  
Author(s):  
Edson M. Jiménez ◽  
Juan P. Escandón ◽  
Oscar E. Bautista
Keyword(s):  
Cross Section ◽  
Electroosmotic Flow ◽  
Separation Of Variables ◽  
Fluid Velocity ◽  
Microfluidic Devices ◽  
Maxwell Model ◽  
Momentum Equation ◽  
Oscillatory Behavior ◽  
Viscous Effects ◽  
Maxwell Fluids

Several kinds of fluids with non-Newtonian behavior are manipulated in microfluidic devices for medical, chemical and biological applications. This work presents an analytical solution for the transient electroosmotic flow of Maxwell fluids in square cross-section microchannels. The appropriate combination of the momentum equation with the rheological Maxwell model derives in a mathematical model based in a hyperbolic partial differential equation, that permits to determine the velocity profile. The flow field is solved using the Green’s functions for the steady-state regime, and the method of separation of variables for the transient phenomenon in the electroosmotic flow. Taking in to account the normalized form of the governing equations, we predict the influence of the main dimensionless parameters on the velocity profiles. The results show an oscillatory behavior in the transient stage of the fluid flow, which is directly controlled by the dimensionless relaxation time, this parameter is an indicator of the competition between elastic and viscous effects. Hence, this investigation about the characteristics of the fluid rheology on the fluid velocity of the transient electroosmotic flow are discussed in order to contribute to the understanding the different tasks and design of microfluidic devices.

scholarly journals Start-Up Electroosmotic Flow of Multi-Layer Immiscible Maxwell Fluids in a Slit Microchannel

Micromachines ◽  
2020 ◽  
Vol 11 (8) ◽  
pp. 757
Author(s):  
Juan Escandón ◽  
David Torres ◽  
Clara Hernández ◽  
René Vargas
Keyword(s):  
Electroosmotic Flow ◽  
Relaxation Times ◽  
Solution Process ◽  
Momentum Equation ◽  
Oscillatory Behavior ◽  
Liquid Interfaces ◽  
Transform Method ◽  
Maxwell Fluids ◽  
Start Up ◽  
Density Ratios

In this investigation, the transient electroosmotic flow of multi-layer immiscible viscoelastic fluids in a slit microchannel is studied. Through an appropriate combination of the momentum equation with the rheological model for Maxwell fluids, an hyperbolic partial differential equation is obtained and semi-analytically solved by using the Laplace transform method to describe the velocity field. In the solution process, different electrostatic conditions and electro-viscous stresses have to be considered in the liquid-liquid interfaces due to the transported fluids content buffer solutions based on symmetrical electrolytes. By adopting a dimensionless mathematical model for the governing and constitutive equations, certain dimensionless parameters that control the start-up of electroosmotic flow appear, as the viscosity ratios, dielectric permittivity ratios, the density ratios, the relaxation times, the electrokinetic parameters and the potential differences. In the results, it is shown that the velocity exhibits an oscillatory behavior in the transient regime as a consequence of the competition between the viscous and elastic forces; also, the flow field is affected by the electrostatic conditions at the liquid-liquid interfaces, producing steep velocity gradients, and finally, the time to reach the steady-state is strongly dependent on the relaxation times, viscosity ratios and the number of fluid layers.

Transient AC Electro-Osmotic Flow of Generalized Maxwell Fluids through Microchannels

2014 ◽  
Vol 548-549 ◽  
pp. 216-223
Author(s):  
Ze Yin ◽  
Yong Jun Jian ◽  
Long Chang ◽  
Ren Na ◽  
Quan Sheng Liu
Keyword(s):  
Reynolds Number ◽  
Relaxation Time ◽  
Electroosmotic Flow ◽  
Momentum Equation ◽  
Parallel Channel ◽  
Maxwell Fluids ◽  
Transient Velocity ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Electro Osmotic Flow

In this paper, we represent analytical solutions of transient velocity for electroosmotic flow (EOF) of generalized Maxwell fluids through both micro-parallel channel and micro-tube using the method of Laplace transform. We solve the problem including the linearized Poisson-Boltzmann equation, the Cauchy momentum equation and generalized Maxwell constitutive equation. By numerical calculation, the results show that the EOF velocity is greatly depends on oscillating Reynolds number and normalized relaxation time.

A WEAKLY NONLINEAR INSTABILITY OF MISCIBLE DISPLACEMENTS IN A RECTILINEAR POROUS MEDIA FLOW

1994 ◽  
Vol 04 (05) ◽  
pp. 1319-1328 ◽  
Author(s):  
WILLIAM B. ZIMMERMAN
Keyword(s):  
Linear Theory ◽  
Landau Equation ◽  
Separation Of Variables ◽  
Finite Amplitude ◽  
Linear Stability Theory ◽  
Porous Media Flow ◽  
Perturbation Scheme ◽  
Viscous Effects ◽  
Regular Perturbation ◽  
Displacement Front

The linear stability theory of Tan & Homsy [1986] is extended to include the effects of weak nonlinear coupling between mass flux and viscous effects when the viscous fingers grow from a slowly diffusing, nearly flat displacement front. A regular perturbation scheme combined with a similarity-separation of variables technique leads to a Landau equation for the amplitude of the disturbance. The Landau constant has a simple pole for a given wavenumber within the linear theory cutoff wavenumber for growth. An argument is given that this pole leads to pairing of fingers while the instability remains small. Comparison of the length scale of the pole of the Landau constant with experimental measurements of finger scale shows good agreement where plausibly finite-amplitude effects might come into play, but with the linear theory otherwise.

The Design and Simulation for a Novel Electroosmotic Micromixer

2006 ◽  
Author(s):  
Hongjun Song ◽  
Xie-Zhen Yin ◽  
Dawn J. Bennett
Keyword(s):  
Electric Field ◽  
Cross Section ◽  
Chemical Reactions ◽  
Electroosmotic Flow ◽  
Chaotic Advection ◽  
Microfluidic Systems ◽  
Mixing Effect ◽  
Passive Mixers ◽  
The Cross ◽  
External Forces

The analysis of fluid mixing in microfluidic systems is useful for many biological and chemical applications at the micro scale such as the separation of biological cells, chemical reactions, and drug delivery. The mixing of fluids is a very important factor in chemical reactions and often determines the reaction velocity. However, the mixing of fluids in microfluidics tends to be very slow, and thus the need to improve the mixing effect is a critical challenge for the development of the microfluidic systems. Micromixers can be classified into two types, active micromixers and passive micromixers. Passive micromixers depend on changing the structure and shape of microchannels in order to generate chaotic advection and to increase the mixing area. Thus, the mixing effect is enhanced without any help from external forces. Although passive micromixers have the advantage of being easily fabricated and requiring no external energy, there are also some disadvantages. For example, passive mixers often lack flexibility and power. Passive mixers rely on the geometrical properties of the channel shapes to induce complicated fluid particle trajectories thereby enhancing the mixing effect. On the other hand, active micromixers induce a time-dependent perturbation in the fluid flow. Active micromixers mainly use external forces for mixing including ultrasonic vibration, dielectrophoresis, magnetic force, electrohydrodynamic, and electroosmosis force. However, the complexity of their fabrication limits the application of active micromixers. In this paper we present a novel electroosmotic micromixer using the electroosmotic flow in the cross section to enhance the mixing effect. A DC electric field is applied to a pair of electrodes which are placed at the bottom of the channel. A transverse flow is generated in the cross section due to electroosmotic flow. Numerical simulations are investigated using a commercial software Fluent® which demonstrates how the device enhances the mixing effect. The mixing effect is increased when the magnitude of the electric field increased. The influences of Pe´clet number are also discussed. Finally, a simple fabrication using polymeric materials such as SU-8 and PDMS is presented.

Electroosmotic flow of Maxwell fluid in a microchannel of isosceles right triangular cross section

2021 ◽  
Vol 33 (12) ◽  
pp. 123113
Author(s):  
Xu Yang ◽  
Shaowei Wang ◽  
Moli Zhao ◽  
Yue Xiao
Keyword(s):  
Cross Section ◽  
Electroosmotic Flow ◽  
Maxwell Fluid ◽  
Triangular Cross Section

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.

Lack of null controllability of viscoelastic flows

2019 ◽  
Vol 25 ◽  
pp. 60
Author(s):  
Debayan Maity ◽  
Debanjana Mitra ◽  
Michael Renardy
Keyword(s):  
Approximate Controllability ◽  
Momentum Equation ◽  
Null Controllability ◽  
Viscoelastic Flow ◽  
Viscoelastic Flows ◽  
Relaxation Mode ◽  
Maxwell Fluids ◽  
Linear Viscoelastic ◽  
Exact Null Controllability

We consider controllability of linear viscoelastic flow with a localized control in the momentum equation. We show that, for Jeffreys fluids or for Maxwell fluids with more than one relaxation mode, exact null controllability does not hold. This contrasts with known results on approximate controllability.

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.

The generation of internal waves by vibrating elliptic cylinders. Part 2. Approximate viscous solution

1997 ◽  
Vol 351 ◽  
pp. 119-138 ◽  
Author(s):  
D. G. HURLEY ◽  
G. KEADY
Keyword(s):  
Approximate Solution ◽  
Circular Cylinder ◽  
Flow Field ◽  
Cross Section ◽  
Similarity Solution ◽  
Internal Gravity Waves ◽  
Approximate Theory ◽  
Viscous Effects ◽  
Typical Dimension ◽  
Viscous Solution

An approximate theory is given for the generation of internal gravity waves in a viscous Boussinesq fluid by the rectilinear vibrations of an elliptic cylinder. A parameter λ which is proportional to the square of the ratio of the thickness of the oscillatory boundary layer that surrounds the cylinder to a typical dimension of its cross-section is introduced. When λ[Lt ]1 (or equivalently when the Reynolds number R[Gt ]1), the viscous boundary condition at the surface of the cylinder may to first order in λ be replaced by the inviscid one. A viscous solution is proposed for the case λ[Lt ]1 in which the Fourier representation of the stream function found in Part 1 (Hurley 1997) is modified by including in the integrands a factor to account for viscous dissipation. In the limit λ→0 the proposed solution becomes the inviscid one at each point in the flow field.For ease of presentation the case of a circular cylinder of radius a is considered first and we take a to be the typical dimension of its cross-section in the definition of λ above. The accuracy of the proposed approximate solution is investigated both analytically and numerically and it is concluded that it is accurate throughout the flow field if λ is sufficiently small, except in a small region near where the characteristics touch the cylinder where viscous effects dominate.Computations indicate that the velocity on the centreline on a typical beam of waves, at a distance s along the beam from the centre of the cylinder, agrees, within about 1%, with the (constant) inviscid values provided λs/a is less than about 10−3. This result is interpreted as indicating that those viscous effects which originate from the characteristics that touch the cylinder (places where the inviscid velocity is singular) reach the centreline of the beam when λs/a is about 10−3. For larger values of s, viscous effects are significant throughout the beam and the velocity profile of the beam changes until it attains, within about 1% when λs/a is about 2, the value given by the similarity solution obtained by Thomas & Stevenson (1972). For larger values of λs/a, their similarity solution applies.In an important paper Makarov et al. (1990) give an approximate solution for the circular cylinder that is very similar to ours. However, it does not reduce to the inviscid one when the viscosity is taken to be zero.Finally it is shown that our results for a circular cylinder apply, after small modifications, to all elliptical cylinders.

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