Debye-Hückel solution for steady electro-osmotic flow of micropolar fluid in cylindrical microcapillary
01 Nov 2013-Applied Mathematics and Mechanics-english Edition (Springer Berlin Heidelberg)-Vol. 34, Iss: 11, pp 1305-1326
TL;DR: In this paper, the authors derived analytical expressions for speed, flux, microrotation, stress, and couple stress in a micropolar fluid exhibiting a steady, symmetric, and one-dimensional electro-osmotic flow in a uniform cylindrical microcapillary.
Abstract: Analytic expressions for speed, flux, microrotation, stress, and couple stress in a micropolar fluid exhibiting a steady, symmetric, and one-dimensional electro-osmotic flow in a uniform cylindrical microcapillary were derived under the constraint of the Debye-Huckel approximation, which is applicable when the cross-sectional radius of the microcapillary exceeds the Debye length, provided that the zeta potential is sufficiently small in magnitude. Since the aciculate particles in a micropolar fluid can rotate without translation, micropolarity affects the fluid speed, fluid flux, and one of the two non-zero components of the stress tensor. The axial speed in a micropolar fluid intensifies when the radius increases. The stress tensor is confined to the region near the wall of the microcapillary, while the couple stress tensor is uniform across the cross-section.
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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, a theoretical analysis for electro-osmotic flow of blood in a hydrophobic micro-channel with externally applied magnetic field is presented, where the lumen of micro-channels is assumed to be porous medium in addition to the consideration of permeability of the channel walls.
Abstract: A theoretical analysis is presented for electro-osmotic flow (EOF) of blood in a hydrophobic micro-channel with externally applied magnetic field. The lumen of micro-channels is assumed to be porous medium in addition to the consideration of permeability of the channel walls. The effects of slip velocity and thermal-slip are taken into consideration. The governing equations in the electrical double layer (EDL) together with the Poisson–Boltzmann equation and the body force exerted by the applied potential are furthermore considered. The flow is governed by the non-Newtonian viscoelastic fluid model. These equations along with the thermal energy equation are approximated by assuming that the channel height is much greater than the thickness of electrical double layer consisting the stern and diffusive layers. The problem is solved analytically and the computed results have presented graphically for various values of the dimensionless parameters. The results presented here have significant impact on the therapeutic treatment in hyperthermia as well as in controlling blood flow and heat transfer in micro-channels.
37 citations
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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TL;DR: In this paper, the boundary value problem (BVP) comprising partial differential equations (PDEs), of steady flow for plane, laminar jet of a micropolar fluid was formulated.
Abstract: In this study, it was formulated the boundary-value-problem (BVP), comprising partial differential equations (PDEs), of steady flow for plane, laminar jet of a micropolar fluid. A new similarity transformation/solution was derived which is valid not only for the Newtonian fluids but also for the micropolar fluids. Obviously, this transformation will be transformed the PDEs into the ordinary differential equations (ODEs). These ODEs were solved numerically by the finite difference method. The obtained results were compared with existing results [1, 12] for the Newtonian fluids. The comparison was favourable. As the aciculate particles in a micropolar fluid can rotate without translation, the micropolarity effects must have influence on fluid-speed, microrotation, stresses, couple stresses and discharge. This influence was highlighted in the present study. If viscosity coupling parameter K1 (being the measure of micropolarity) increases then microrotation, fluid-flux, stresses and couple stresses intensify in the vicinity of the jet along y-direction. The fluid-flux, , for a fixed value of K1 and for the micropolar as well as Newtonian fluids. In addition, the stress and the couple stress tensors are non-symmetric.
2 citations
Cites background from "Debye-Hückel solution for steady el..."
...with respect to the following constitutive equations [21-22];...
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...We shall not survey the history here but we shall refer [2, 7, 10-11, 21-22] for the reader who has interest to know their history....
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"Debye-Hückel solution for steady el..." refers background or result in this paper
...kBT . (18) Here, k1 couples the two viscosity coefficients, k2 and k3 are normalized micropolar parameters, Re may be called the Reynolds number, Romay be called the microrotation Reynolds number [12], and αois the ionic-energy parameter [20]. The Gauss law (10) can now be written as ∇2ψ(r) = −ρe(r). (19) The general condition of radial symmetry implies that ∂/∂θ≡ 0. As the length of the microcapi...
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...osed on microrotation are: vθ(1) = βo dVz(ρ) dρ ρ=1 , vθ(0) = 0 (33) where βo ∈ [−1,0] is some constant. Although some researchers have ignored microrotation effects near a solid wall by setting βo= 0 [12,21], others have held that that βo<0 because the existence of the boundary layer requires that the shear and couple stresses on a wall must be high in magnitude in comparison to locations elsewhere [2...
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...g effects are small enough to be ignored; and (ix) Ris much greater than the Debye length λD. Under these conditions, our starting point comprises the following three equations of micropolar2 fluid flow [12]: ∇′ • V′(r′) = 0, (3) ∇′ • σ′(r′)+ρ′ e(r ′)E′ app= ρm[V ′(r′) • ∇′]V′(r′), (4) ∇′ • m′(r′) +I • × σ′(r′) = ρ mjo[V ′(r′) • ∇′]v′(r′). (5) Introducing Eqs. (1) and (2) in these three equations, we get...
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...troids [10,11]. Therefore, not only is stress asymmetric in micropolar fluids but they also sustain body couples. Micropolar fluids are exemplified by colloidal suspensions, liquid crystals, and epoxies [12]. Blood too is micropolar [13,14], along with other body fluids containing particulate materials. As body fluids are subjected to electric fields in labs-on-a-chip [15], electro-osmotic flows of micropola...
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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.
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