# Non-steady electro-osmotic flow of a micropolar fluid in a microchannel

TL;DR: In this paper, the initial boundary value problem of non-steady electro-osmotic flow of a micropolar fluid in a rectangular microchannel of height much larger than the Debye length and length much larger the height was formulated.

Abstract: We formulated the initial-boundary-value problem of non-steady electro-osmotic flow of a micropolar fluid in a rectangular microchannel of height much larger than the Debye length and length much larger the height. Solving the governing differential equations numerically when a spatially uniform electric field is applied as an impulse of finite magnitude, we found that the effect is instantaneous on the flow, just as for simple Newtonian fluids. The decay times of the fluid velocity and the microrotation, however, are smaller in micropolar fluids than in simple Newtonian fluids. The maximum magnitude of microrotation decreases as the micropolarity increases. The effect of microrotation on the stress tensor is more dominant than that of the fluid speed, and a threshold effect with respect to the magnitude of the zeta potential is evident in the spatial profile of the couple stress tensor. We expect similar trends even when the applied electric field varies over some finite interval of time.

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TL;DR: In this article, the influence of micropolar nature of fluids in fully developed flow induced by electrokinetically driven peristaltic pumping through a parallel plate microchannel is analyzed.

Abstract: An analysis is presented in this work to assess the influence of micropolar nature of fluids in fully developed flow induced by electrokinetically driven peristaltic pumping through a parallel plate microchannel. The walls of the channel are assumed as sinusoidal wavy to analyze the peristaltic flow nature. We consider that the wavelength of the wall motion is much larger as compared to the channel width to validate the lubrication theory. To simplify the Poisson Boltzmann equation, we also use the Debye-Huckel linearization (i.e. wall zeta potential ≤ 25mV). We consider governing equation for micropolar fluid in absence of body force and couple effects however external electric field is employed. The solutions for axial velocity, spin velocity, flow rate, pressure rise and stream functions subjected to given physical boundary conditions are computed. The effects of pertinent parameters like Debye length and Helmholtz-Smoluchowski velocity which characterize the EDL phenomenon and external electric field, coupling number and micropolar parameter which characterize the micropolar fluid behavior, on peristaltic pumping are discussed through the illustrations. The results show that peristaltic pumping may alter by applying external electric fields. This model can be used to design and engineer the peristalsis-lab-on-chip and micro peristaltic syringe pumps for biomedical applications.

51 citations

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TL;DR: In this paper, the electroosmotic flow of a micropolar fluid in a microchannel bounded by two parallel porous plates undergoing periodic vibration is studied, and the equations for conservation of linear and angular momentums and Gauss's law of charge distribution are solved within the framework of the Debye-Huckel approximation.

Abstract: The electroosmotic flow of a micropolar fluid in a microchannel bounded by two parallel porous plates undergoing periodic vibration is studied. The equations for conservation of linear and angular momentums and Gauss’s law of charge distribution are solved within the framework of the Debye-Huckel approximation. The fluid velocity and microrotation are assumed to depend linearly on the Reynolds number. The study shows that the amplitude of microrotation is highly sensitive to the changes in the magnitude of the suction velocity and the width of the microchannel. An increase in the micropolar parameter gives rise to a decrease in the amplitude of microrotation. Numerical estimates reveal that the microrotation of the suspended microelements in blood also plays an important role in controlling the electro-osmotically actuated flow dynamics in microbio-fluidic devices.

40 citations

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TL;DR: In this article, the electro-osmotic flow of a micropolar bio-fluid was studied between two plates that are in a state of periodic vibrations, and it was shown that electrical double layers formed in the vicinity of the wall can significantly alter the flow dynamics of physiological fluids in micro-biofluidic devices.

Abstract: The paper is devoted to a study of the electro-osmotic flow of a micropolar bio-fluid, when the flow takes place between two plates that are in a state of periodic vibrations. Considering blood as a micropolar fluid, it is found that the amplitude of oscillation of the microparticles of blood increases when the micropolar effect is pronounced more and more and that a rise in Debye- Huckel parameter enhances both the velocity and microrotation gradient. The results provide guidelines for the improvement of design of bio-sensing and micro-fluidic devices. The study leads to the conclusion that electrical double layers formed in the vicinity of the wall can significantly alter the flow dynamics of physiological fluids in micro-bio-fluidic devices.

25 citations

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TL;DR: In this article, the effects of microstructure of fluid particles on the electrokinetic phenomena were investigated analytically based on a micropolar fluid model, where micro-rotation of fluid particle and material parameters like viscosity and angular visccosity coefficients are involved.

Abstract: The effects of microstructure of fluid particles on the electrokinetic phenomena are investigated analytically based on a micropolar fluid model, where micro-rotation of fluid particles and material parameters like viscosity and angular viscosity coefficients are involved. Meanwhile, the influences of velocity slip at the surface of a nanofluidic channel and overlapped electrical double layers (EDLs) are incorporated. Results indicate that the introduction of micropolarity will significantly affect the electrokinetic effects, especially in the case of overlapped EDLs. Qualitatively, it leads to evident reductions in the flow rate, streaming current, and streaming potential relative to Newtonian fluids. The velocity slip is an opposing and competitive mechanism which tends to increase the flow rate, streaming current, and potential. Furthermore, the interplay between the micropolarity and slip effects is studied in detail. The influence of micropolarity on the electrokinetic energy conversion (EKEC) efficiency depends on the ionic Peclet number R. For small values of R (e.g., R = 0.1), the EKEC efficiency for micropolar fluids may exceed that for Newtonian fluids in some range of parameter K in the case of overlapped EDLs for nanochannels. However, for R ≥ 0.2, the EKEC efficiency for micropolar fluids is always less than that for Newtonian fluids.

22 citations

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TL;DR: In this paper, the effects of the related dimensionless parameters, e.g., the micropolar parameter, the frequency, the electrokinetic width, and the wall zeta potential ratio of the upper plate to the lower plate, on the electroosmotic velocity and microrotation are investigated.

Abstract: The time periodic electroosmotic flow of an incompressible micropolar fluid between two infinitely extended microparallel plates is studied. The analytical solutions of the velocity and microrotation are derived under the Debye-H¨uckel approximation. The effects of the related dimensionless parameters, e.g., the micropolar parameter, the frequency, the electrokinetic width, and the wall zeta potential ratio of the upper plate to the lower plate, on the electroosmotic velocity and microrotation are investigated. The results show that the amplitudes of the velocity and the volume flow rate will drop to zero when the micropolar parameter increases from 0 to 1. The effects of the electrokinetic width and the frequency on the velocity of the micropolar fluid are similar to those of the Newtonian fluid. However, the dependence of the microrotation on the related parameters mentioned above is complex. In order to describe these effects clearly, the dimensionless microrotation strength and the penetration depth of the microrotation are defined, which are used to explain the variation of the microrotation. In addition, the effects of various parameters on the dimensionless stress tensor at the walls are studied.

15 citations

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01 Jan 1992

TL;DR: In this article, the Taylor series is used to model the wave equation and the Laplace equation in the context of linear algebraic equations, eigenproblems, polynomial approximation and interpolation, and difference formulas numerical integration.

Abstract: Part I Basic tools of numerical analysis: systems of linear algebraic equations eigenproblems solution of nonlinear equations polynomial approximation and interpolation numerical differention and difference formulas numerical integration. Part II Ordinary differential equations: solution of one-dimensional initial-value problems solution of one-dimensional boundary-value problems. Part III Partial differential equations: elliptic partial differential equations - the Laplace equation finite difference methods for propagation problems parabolic partial differential equations - the convection equation coordinate transformations and grid generation parabolic partial differential equations - the convection-diffusion equation hyperbolic partial differential equations - the wave equation. Appendix: the Taylor series.

1,202 citations

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TL;DR: This Review gives an overview of selected recent developments and applications of nanomedicine.

Abstract: The application of nanotechnology concepts to medicine joins two large cross-disciplinary fields with an unprecedented societal and economical potential arising from the natural combination of specific achievements in the respective fields. The common basis evolves from the molecular-scale properties relevant to the two fields. Local probes and molecular imaging techniques allow surface and interface properties to be characterized on a nanometer scale at predefined locations, while chemical approaches offer the opportunity to elaborate and address surfaces, for example, for targeted drug delivery, enhanced biocompatibility, and neuroprosthetic purposes. However, concerns arise in this cross-disciplinary area about toxicological aspects and ethical implications. This Review gives an overview of selected recent developments and applications of nanomedicine.

1,101 citations

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01 Jan 1989

TL;DR: In this article, the authors introduce the Transport in Fluids Equations of Change (TUE) model for the transport of uncharged molecules and particles in a fluid and discuss its application in the field of particle capture.

Abstract: Preface to the Paperback Edition Preface to the Second Edition Preface to the First Edition Acknowledgments for the First Edition Introduction Transport in Fluids Equations of Change Solutions of Uncharged Molecules Solutions of Uncharged Macromolecules and Particles Solutions of Electrolytes Solutions of Charged Macromolecules and Particles Suspension Stability and Particle Capture Rheology and Concentrated Suspensions Surface Tension Appendix A SI Units and Physical Constants Appendix B Symbols Author Index Subject Index

1,062 citations