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.

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.

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.

Exact Solution of the Start-Up Electroosmotic Flow of Generalized Maxwell Fluids in Triangular Microducts

2021 ◽  
Author(s):  
F.Talay Akyildiz ◽  
Dennis A. Siginer
Keyword(s):  
Exact Solution ◽  
Electroosmotic Flow ◽  
Fractional Derivatives ◽  
Maxwell Fluid ◽  
Solution Technique ◽  
Maxwell Fluids ◽  
Start Up ◽  
Triangular Region ◽  
Overshoot Phenomenon ◽  
Poisson Boltzmann

Abstract Unsteady electroosmotic flow of generalized Maxwell fluids in triangular microducts is investigated. The governing equation is formulated with Caputo-Fabrizio time-fractional derivatives whose orders are distributed in the interval [0, 1). The linear momentum and the Poisson-Boltzmann equations are solved analytically in tandem in the triangular region with the help of the Helmholtz eigenvalue problem and Laplace transforms. The analytical solution developed is exact. The solution technique we use is new, leads to exact solutions, is completely different from those available in the literature and is applicable to other similar problems. The new expression for the velocity field displays experimentally observed 'velocity overshoot' as opposed to existing analytical studies none of which can predict the overshoot phenomenon. We show that when Caputo-Fabrizio time-fractional derivatives approach unity the exact solution for the classical upper convected Maxwell fluid is obtained. The presence of elasticity in the constitutive structure alters the Newtonian velocity profiles drastically. The influence of pertinent parameters on the flow field is explored.

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.

scholarly journals Extended Stokes' Problems for Relatively Moving Porous Half-Planes

2009 ◽  
Vol 2009 ◽  
pp. 1-10 ◽  
Author(s):  
Chi-Min Liu
Keyword(s):  
Exact Solutions ◽  
Integral Transform ◽  
Initial Conditions ◽  
Integral Transforms ◽  
Momentum Equation ◽  
Transform Method ◽  
Stokes Problems ◽  
Flow Phenomena ◽  
Mass Influx ◽  
Mathematical Techniques

A shear flow motivated by relatively moving half-planes is theoretically studied in this paper. Either the mass influx or the mass efflux is allowed on the boundary. This flow is called the extended Stokes' problems. Traditionally, exact solutions to the Stokes' problems can be readily obtained by directly applying the integral transforms to the momentum equation and the associated boundary and initial conditions. However, it fails to solve the extended Stokes' problems by using the integral-transform method only. The reason for this difficulty is that the inverse transform cannot be reduced to a simpler form. To this end, several crucial mathematical techniques have to be involved together with the integral transforms to acquire the exact solutions. Moreover, new dimensionless parameters are defined to describe the flow phenomena more clearly. On the basis of the exact solutions derived in this paper, it is found that the mass influx on the boundary hastens the development of the flow, and the mass efflux retards the energy transferred from the plate to the far-field fluid.

A Selective Determination of the Proton Nuclear Relaxation Times of the Alkaloid Vindoline: An Extension via Fourier Transform Measurements

1974 ◽  
Vol 52 (5) ◽  
pp. 829-832 ◽  
Author(s):  
L. D. Hall ◽  
Caroline M. Preston
Keyword(s):  
Fourier Transform ◽  
Relaxation Times ◽  
Lattice Relaxation ◽  
Spin Lattice Relaxation ◽  
Nuclear Relaxation ◽  
Transform Method ◽  
Fourier Transform Method ◽  
Selective Determination ◽  
Spin Lattice

A Fourier Transform method has been used to measure the spin–lattice relaxation times of essentially all the protons of the alkaloid, vindoline. It is shown that even for a molecule of this size substantial and potentially useful differences exist in the experimental relaxation times which reflect the degree of crowding of each proton by other protons.

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.

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