Electroosmosis modulated peristaltic biorheological flow through an asymmetric microchannel : mathematical model

A theoretical study is presented of peristaltic hydrodynamics of an aqueous electrolytic nonNewtonian Jeffrey bio-rheological fluid through an asymmetric microchannel under an applied axial electric field. An analytical approach is adopted to obtain the closed form solution for velocity, volumetric flow, pressure difference and stream function. The analysis is also restricted under the low Reynolds number assumption and lubrication theory approximations. Debye-Hückel linearization (i.e. wall zeta potential ≤ 25mV) is also considered. Streamline plots are also presented for the different electro-osmotic parameter, varying magnitudes of the electric field (both aiding and opposing cases) and for different values of the ratio of relaxation to retardation time parameter. Comparisons are also included between the Newtonian and general non-Newtonian Jeffrey fluid cases. The results presented here may be of fundamental interest towards designing lab-on-a-chip devices for flow mixing, cell manipulation, micro-scale pumps etc. Trapping is shown to be more sensitive to an electric field (aiding, opposing and neutral) rather than the electro-osmotic parameter and viscoelastic relaxation to retardation ratio parameter. The results may also help towards the design of organ-on-a-chip like devices for better drug design

Numerical Simulation of Electroosmotic Flow of Viscoelastic Fluid in Microchannel

Electroosmotic flow (EOF) has been widely used in various biochemical microfluidic applications, many of which often involve the use of viscoelastic non-Newtonian fluids. Due to the existence of the elastic effect, the viscoelastic EOF develops into chaotic flow under extremely low Reynolds numbers, which is known as elastic turbulence. The mechanism of elastic turbulence in electroosmotic flow remains unclear. Numerical simulation plays an important role in understanding the mechanisms of elastic turbulence. This dissertation is aimed to study the EOF of viscoelastic fluids in constriction microchannels under various direct current (DC) and alternating current (AC) electric fields. First, the EOF of viscoelastic fluid in a straight contraction microchannel is investigated. The influences of the polymer concentration and the applied DC electric field on the elastic instabilities are analyzed. The flow fluctuations and secondary upstream vortices before the entrance of the microchannel are found to be related to the induced elastic stress within the microchannel. The polymer concentration shows a more significant influence on the elastic instability. A flow map in polymer concentration and electric field domain is formed as guidance for further studies. Then, the study is extended to the viscoelastic EOF in a microchannel with 90◦ bends under the combination of DC and AC electric fields. The elastic turbulence is identified from the fluctuation of the velocity field and upstream vortices. The energy spectra of the velocity fluctuation show power-law decay over a wide range of frequencies, which is a typical characteristic of elastic turbulence. The 90◦ bends show influence on the dye concentration profile in cross sections of the microchannel. A more even dye concentration distribution is obtained with an increasing number of 90◦ bends. Moreover, the opening angle of the particle trace at the exit of the contraction microchannel show dependency on the frequency of the AC electric field, which is related to the characteristic frequency of the viscoelastic EOF. The study is then focused on the influence of the frequency of the AC electric field on the viscoelastic EOF. Short contraction microchannels are adopted for the frequency study. The peak in the energy spectra of the velocity fluctuation under DC electric field indicates the characteristic frequency of the viscoelastic EOF. Under AC electric field, the highest amplitude of the energy spectra is obtained when the frequency of AC electric field is close to the characteristic frequency. The same trend is also observed in the statistical results of the average velocity. However, when the frequency is relatively high, both the amplitude of the energy spectra and the average velocity decrease to a level even lower than under a DC electric field, which indicates the existence of an optimal frequency of the AC electric field in order to achieve the highest flow rate

Further developments on theoretical and computational rheology

Tese financiada pela FCT - Fundação para a Ciência e a Tecnologia, Ciência.Inovação2010, POPH, União Europeia FEDERTese de doutoramento. Engenharia Química e Biológica. Faculdade de Engenharia. Universidade do Porto. 201

Three-layered electro-osmosis modulated blood flow through a micro-channel

Electrokinetic peristaltic multi-layered transport is considered in a micro-channel under the action of an axial electrical field. Three different layers i.e. the core layer, intermediate layer and peripheral layer are simulated with three different viscosities for each fluid layer. The unsteady two-dimensional conservation equations for mass and momentum with electrokinetic body forces, are transformed from the wave frame to the laboratory frame and the electrical field terms are rendered into electrical potential terms via the Poisson-Boltzmann equation, Debye length approximation and ionic Nernst Planck equation. The dimensionless emerging linearized electrokinetic boundary value problem is solved using integral methods. Closed-form expressions are derived for stream functions in the core, intermediate and peripheral layers. Expressions are also derived for the core-intermediate interface shape and the intermediate-peripheral interface shape. Maximum pressures are also computed. To study bolus migration, the range of the trapping limit is also determined in the peripheral layer. It is found that in the core layer larger boluses are computed in the case of lower intermediate layer viscosity relative to peripheral layer viscosity although the number of boluses is greater when the intermediate layer viscosity exceeds the peripheral layer viscosity. Furthermore, in the intermediate layer, stronger concentration of streamlines is computed in the lower half space with positive Helmholtz-Smoluchowski velocity. Also, negative Helmholtz-Smoluchowski velocity reduces the core layer (H1) interface shape whereas it enhances the peripheral layer (H) and intermediate layer (H2) shapes. At lower values of volume flow rate ratio, hydromechanical efficiency is maximum for positive Helmholtz-Smoluchowski velocity whether intermediate layer viscosity is less or greater than peripheral layer viscosity. Finally, greater with greater peristaltic wave amplitude and also for positive Helmholtz-Smoluchowski velocity there is an increase in time-averaged flow rate, whether intermediate layer viscosity is less or greater than peripheral layer viscosity. The analysis is relevant to electro-kinetic hemodynamics and bio-micro-fluidics

Electroosmotic Flow of Viscoelastic Fluid in a Nanochannel Connecting Two Reservoirs

Electroosmotic flow (EOF) of viscoelastic fluid with Linear Phan-Thien–Tanner (LPTT) constitutive model in a nanochannel connecting two reservoirs is numerically studied. For the first time, the influence of viscoelasticity on the EOF and the ionic conductance in the micro-nanofluidic interconnect system, with consideration of the electrical double layers (EDLs), is investigated. Regardless of the bulk salt concentration, significant enhancement of the flow rate is observed for viscoelastic fluid compared to the Newtonian fluid, due to the shear thinning effect. An increase in the ionic conductance of the nanochannel occurs for the viscoelastic fluid. The enhancement of the ionic conductance is significant under the overlapping EDLs condition

Slip and hall current effects on Jeffrey fluid suspension flow in a peristaltic hydromagnetic blood micropump

The magnetic properties of blood allow it to be manipulated with an electromagnetic field. Electromagnetic blood flow pumps are a robust technology which provide more elegant and sustainable performance compared with conventional medical pumps. Blood is a complex multi-phase suspension with non-Newtonian characteristics which are significant in micro-scale transport. Motivated by such applications, in the present article a mathematical model is developed for magnetohydrodynamic (MHD) pumping of blood in a deformable channel with peristaltic waves. A Jeffery’s viscoelastic formulation is employed for the rheology of blood. A twophase fluid-particle (“dusty”) model is utilized to better simulate suspension characteristics (plasma and erythrocytes). Hall current and wall slip effects are incorporated to achieve more realistic representation of actual systems. A two-dimensional asymmetric channel with dissimilar peristaltic wave trains propagating along the walls is considered. The governing conservation equations for mass, fluid and particle momentum are formulated with appropriate boundary conditions. The model is simplified using of long wavelength and creeping flow approximations. The model is also transformed from the fixed frame to the wave frame and rendered non-dimensional. Analytical solutions are derived. The resulting boundary value problem is solved analytically and exact expressions are derived for the fluid velocity, particulate velocity, fluid/particle fluid and particulate volumetric flow rates, axial pressure gradient, pressure rise and skin friction distributions are evaluated in detail. Increasing Hall current parameter reduces bolus growth in the channel, particle phase velocity and pressure difference in the augmented pumping region whereas it increases fluid phase velocity, axial pressure gradient and pressure difference in the pumping region. Increasing the hydrodynamic slip parameter accelerates both particulate and fluid phase flow at and close to the channel walls, enhances wall skin friction, boosts pressure difference in the augmented pumping region and increases bolus magnitudes. Increasing viscoelastic parameter (stress relaxation time to retardation time ratio) decelerates the fluid phase flow, accelerates the particle phase flow, decreases axial pressure gradient, elevates pressure difference in the augmented pumping region and reduces pressure difference in the pumping region. Increasing drag particulate suspension parameter decelerates the particle phase velocity, accelerates the fluid phase velocity, strongly elevates axial pressure gradient and reduces pressure difference (across one wavelength) in the augmented pumping region. Increasing particulate volume fraction density enhances bolus magnitudes in both the upper and lower zones of the channel and elevates pressure rise in the augmented pumping region

Transient Electro-osmotic Slip Flow of an Oldroyd-B Fluid with Time-fractional Caputo-Fabrizio Derivative

In this article, the electro-osmotic flow of Oldroyd-B fluid in a circular micro-channel with slip boundary condition is considered. The corresponding fractional system is represented by using a newly defined time-fractional Caputo-Fabrizio derivative without singular kernel. Closed form solutions for the velocity field are acquired by means of Laplace and finite Hankel transforms. Additionally, Stehfest’s algorithm is used for inverse Laplace transform. The solutions for fractional Maxwell, ordinary Maxwell and ordinary Newtonian fluids are obtained as limiting cases of the obtained solution. Finally, the influence of fractional and some important physical parameters on the fluid flow are spotlighted graphically

Electro-Osmotic Flow of MHD Jeffrey Fluid in a Rotating Microchannel by Peristalsis: Thermal Analysis

In this study, we examine the rotating and heat transfer on the peristaltic and electro-osmatic flow of a Jeffery fluid in an asymmetric microchannel with slip impact. A pressure gradient and anal axially imposed electric field work together to impact the electro-osmotic flow (EOF). Mathematical modeling is imported by employing the low Reynolds number and long wavelength approximation. The exact solution has been simplified for the stream function, temperature, and velocity distributions. The effects of diverse egress quantities on the gush virtue are exhibited and discussed with the help of graphs. The shear stress and trapping phenomena have been investigated. The characterization of results has been resolved for the flow governing ingrained appropriate parameters by employing the table. Our findings can be summarized as follows: (i) Debye length has a strong influence on the conducting viscous fluid of EOF in non-uniform micro-channel. (ii) The temperature field is enhanced through the elevated values of the rotation parameter and EOF. (iii) The shear stress has oscillatory behavior and the heat transmission rate increases with the magnitude of larger values of EOF. Finally, there is good agreement between the current results and those that have already been published. This model applies to the study of chemical fraternization/separation procedures and bio-microfluidic devices for the resolution of diagnosis

Electro-magneto-hydrodynamics Flows of Burgers' Fluids in Cylindrical Domains with Time Exponential Memory

This paper investigates the axial unsteady flow of a generalized Burgers’ fluid with fractional constitutive equation in a circular micro-tube, in presence of a time-dependent pressure gradient and an electric field parallel to flow direction and a magnetic field perpendicular on the flow direction. The mathematical model used in this work is based on a time-nonlocal constitutive equation for shear stress with time-fractional Caputo-Fabrizio derivatives; therefore, the histories of the velocity gradient will influence the shear stress and fluid motion. Thermal transport is considered in the hypothesis that the temperature of the cylindrical surface is constant. Analytical solutions for the fractional differential momentum equation and energy equation are obtained by employing the Laplace transform with respect to the time variable t and the finite Hankel transform with respect to the radial coordinate r. It is important to note that the analytical solutions for many particular models such as, ordinary/fractional Burgers fluids, ordinary/fractional Oldryd-B fluids, ordinary/fractional Maxwell fluids and Newtonian fluids, can be obtained from the solutions for the generalized fractional Burgers' fluid by particularizing the material coefficients and fractional parameters. By using the obtained analytical solutions and the Mathcad software, we have carried out numerical calculations in order to analyze the influence of the memory parameters and magnetic parameter on the fluid velocity and temperature. Numerical results are presented in graphical illustrations. It is found that ordinary generalized Burgers’ fluids flow faster than the fractional generalized Burgers’ fluids