Low Reynolds Number Fluid Research Articles

AC Dielectrophoresis Using Elliptic Electrode Geometry

This paper presents negative AC dielectrophoretic investigations using elliptic electrode geometry. Simulations of the electric field gradient variation using various ratios of the semimajor and the semiminor axis were carried out to determine the optimum elliptic geometry for the dielectrophoretic electrokinetics of specimen in an assay with laminar (low Reynolds number) fluid flow. Experimental setup of the elliptic electrode assembly using PCB fabrication and electrokinetic accumulation of specimen in a dielectrophoretic cage is also being reported. Using an actuating signal between 1 kHz and 1 MHz, successful trapping of 45 μm polystyrene beads suspended in distilled water was demonstrated due to negative dielectrophoresis near 100 kHz using the novel elliptic electrode.

A novel miniature virus-inspired swimming robot for biomedical applications

This paper proposes a novel concept of virus-like swimming robot in the range of nano to micro scales for biomedical applications. Viruses are submicroscopic, intracellular parasites that consist of nucleic acid genome and protein capsid. Their shapes help them to move within the infected host organisms and attach to host cells. In this paper, main geometrical features of the viral structure are utilized for conceptual design of the virus-inspired swimming robot and resultant thorny spherical shaped body is equipped with a new inclined and concentric multi-flagella propulsion system for operation in low Reynolds number fluid flow environment. In off-propulsion situation a theoretical formula is derived for thrust value estimation. On the other hand, to investigate the robot behavior in the fluid media in on-propulsion condition, flow field around the robot is simulated using a numerical strategy consisting of surface methods of regularized Stokeslet and Rotlet theory. For propulsion control of the robot a multilayer artificial neural network is designed and employed then flow field of the robot wake is analyzed using Lagrangian Coherent Structure (LCS) concept. Furthermore, potential characteristics and specific features of this kind of miniature robots are discussed as well as its application. The results indicate the capability of the miniature robot to perform complex missions in low Reynolds number fluid flow environment especially bodily fluid systems including lymphatic, urinary and cerebrospinal fluid (CSF) systems.

The immersed boundary method for advection–electrodiffusion with implicit timestepping and local mesh refinement

We describe an immersed boundary method for problems of fluid–solute-structure interaction. The numerical scheme employs linearly implicit timestepping, allowing for the stable use of timesteps that are substantially larger than those permitted by an explicit method, and local mesh refinement, making it feasible to resolve the steep gradients associated with the space charge layers as well as the chemical potential, which is used in our formulation to control the permeability of the membrane to the (possibly charged) solute. Low Reynolds number fluid dynamics are described by the time-dependent incompressible Stokes equations, which are solved by a cell-centered approximate projection method. The dynamics of the chemical species are governed by the advection–electrodiffusion equations, and our semi-implicit treatment of these equations results in a linear system which we solve by GMRES preconditioned via a fast adaptive composite-grid (FAC) solver. Numerical examples demonstrate the capabilities of this methodology, as well as its convergence properties.

Assessment of fetal canine cardiac myocyte survival in a dual‐side flow bioreactor with modeled hypoxia/reperfusion injury

The present study introduces a new experimental model of hypoxia/reperfusion injury using a newly developed bioreactor system. The injury is introduced and kept localized via fluid dynamic manipulation. Using low Reynolds number fluid flow, regions of the culture can be injured while maintaining physiological conditions in the remaining culture. This approach enables both normal and injured cells within the same monolayer to be investigated side-by-side. The current study evaluated the ability of the model to induce localized reperfusion injury in a monolayer of fetal canine cardiomyocytes (FCCs). Significant apoptosis was found in the hypoxia/reperfusion-injured but not normal-flow regions of the myocyte cultures. The model holds the potential to help elucidate the fundamental mechanisms of hypoxic/reperfusion insults in myocardium.

Acoustic properties of sintered FeCrAlY foams with open cells (II): Sound attenuation

Open-celled metal foams fabricated through metal sintering offers novel mechanical, thermal and acoustic properties. Previously, polymer foams were used as a means of absorbing acoustic energy. However, the structural applications of these foams are inherently limited. The metal sintering approach provides a cost-effective means for the mass-production of open-cell foams from a range of materials, including high-temperature steel alloys. The low Reynolds number fluid properties of sintered steel alloy (FeCrAlY) foams were investigated in a previous study. The static flow resistance of the foams was modeled based on a cylinder and a sphere arranged in a periodic lattice at general incidence to the flow, with the resulting predictions correlating well to measurements. The application of the flow resistance in an acoustic model is the primary focus of the present study. The predictions for the static flow resistance of the sintered foams are first used in a theoretical model to determine the characteristic impedances, as well as the propagation constants of the foams. Subsequently, the predicted acoustic performance of the foams is compared to experimental results. Finally, the design space for a simple acoustic absorber incorporating sintered foams is examined, with the effects of absorber size, foam selection, and foam spacing explored.

Acoustic properties of sintered FeCrAlY foams with open cells (I): Static flow resistance

Open celled metal foams fabricated through the route of metal sintering are a new class of material that offers novel mechanical and acoustic properties. The metal sintering approach offers a cost-effective means for the mass-production of open-cell foams from a range of materials, including high-temperature steel alloys. The mechanical properties of open-celled steel alloy (FeCrAlY) foams have been characterized in previous studies, with focus placed on the influence of processing defects on stiffness and strength. In this work, the low-Reynolds number fluid properties of FeCrAlY foams were investigated both theoretically and experimentally. Specifically, the static flow resistance of the sintered foams important for heat transfer, filtration and sound absorption was modeled based on a cylinder and a sphere arranged in a periodic lattice at general incidence to the flow. Experimental measurements were subsequently carried out to validate theoretical predictions, with good agreement achieved.

Cooperativity and hydrodynamic interactions in externally driven semiflexible filaments

We describe a simple simulation method that describes the hydrodynamics of semiflexible filaments immersed in a low Reynolds number fluid and analyze how multiple body cooperativity emerges due to the presence of hydrodynamic interactions (HI). We study the sedimentation of ensembles of filaments under an external force and also consider the propulsion of filaments subject to simple periodic driving. In both cases the dynamics shows qualitative differences due to the presence of HI. For sedimentation, the effects include cooperative velocity and instabilities that can be understood from the interplay of deformations due to flexibility and hydrodynamic forces. The motion of swimmers is more complex, and shows both positive and negative cooperation depending on distance, frequency of drive, and flexibility.

Numerical analysis of fluid mixing in T-Type micro mixer

Micro fluidic system holds promise for many novel applications within chemistry, biology and medicine. Mixing at micro scale with in a reasonable time period and length scale is important, but despite a large number of studied, no systematic study has been carried out so far to understand the effect of flow mechanism and geometry on micro fluidic mixing. Present study analyze the mixing of low Reynolds number (< 25) fluids in T-type passive micro mixer under various geometric and flow conditions to analyze their relative effects on mixing by diffusion and dispersion. CFD base steady state numerical simulations were carried out using finite element method. Results from this study shows that required mixing length increases with the increase of Reynolds number and mixing channel width, while there is a considerable decrease in mixing length with the increase of diffusion coefficient and mixing channel aspect ratio.

Effect of heat generation on low Reynolds number fluid and mass transport in a single lymphatic blood vessel with uniform magnetic field

The paper studies fluid and mass transfer flow of blood in a single blood vessel. Blood is modeled as a Newtonian fluid of constant properties while the blood vessel is modeled as a long tube of circular section of slowly varying radius. The coupled governing equations are solved using a series expansion about a small parameter ε, ( ε ≪ 1) characterizing the radius variation, and expressions are obtained for the velocity, temperature, concentration, shear stress and species transfer at the wall of the blood vessel. Results obtained show that the concentration of species in blood vessels drifts from the axis towards the walls of the blood vessel in qualitative agreement with existing clinical observations.

Metachronal waves for deterministic switching two-state oscillators with hydrodynamic interaction.

We employ a model system, called rowers, as a generic physical framework to define the problem of the coordinated motion of cilia (the metachronal wave) as a far from equilibrium process. Rowers are active (two-state) oscillators in a low Reynolds number fluid, and interact solely through the forces of hydrodynamic origin. In this work, we consider the case of fully deterministic dynamics, find analytical solutions of the equation of motion in the long-wavelength (continuum) limit, and investigate numerically the short-wavelength limit. We prove the existence of metachronal waves below a characteristic wavelength. Such waves are unstable and become stable only if the sign of the coupling is reversed. We also find that with normal hydrodynamic interaction, the metachronal pattern has the form of stable trains of traveling wave packets sustained by the onset of anti-coordinated beating of consecutive rowers.

Effective pseudo-potentials of hydrodynamic origin

It is shown that low Reynolds number fluid flows can cause suspended particles to respond as though they were in an equilibrium system with an effective potential. This general result follows naturally from the fact that different methods of moving particles in viscous fluids give rise to very different long-range flows. Two examples are discussed: electrophoretic ‘levitation’ of a heavy charged sphere, for which a hydrodynamic ‘pseudo-potential’ can be written in closed form, and quasi-two-dimensional crystals of like-charged colloidal spheres which form near charged walls, whose apparent attraction arises not from a force but from persistent fluid flows.

A Hybrid Method for Low Reynolds Number Flow Past an Asymmetric Cylindrical Body

Low Reynolds number fluid flow past a cylindrical body of arbitrary shape in an unbounded, two‐dimensional domain is a singular perturbation problem involving an infinite logarithmic expansion in the small parameter ε, representing the Reynolds number. We apply a hybrid asymptotic–numerical method to compute the drag coefficient, CD and lift coefficient CL to within all logarithmic terms. The hybrid method solution involves a matrix M, depending only on the shape of the body, which we compute using a boundary integral method. We illustrate the hybrid method results on an elliptic object and on a more complicated profile.

The fluid physics of signal perception by mate-tracking copepods.

Within laboratory-induced swarms of the marine copepod Temora longicornis, the male exhibits chemically mediated trail-following behaviour, concluding with fluid mechanical provocation of the mate-capture response. The location and structure of the invisible trail were determined by examining the specific behaviour of the female copepods creating the signal, the response of the male to her signal, and the fluid physics of signal persistence. Using the distance of the mate-tracking male from the ageing trail of the female, we estimated that the molecular diffusion coefficient of the putative pheromonal stimulant was 2.7 x 10(-5) cm2 s-1, or 1000 times slower than the diffusion of momentum. Estimates of signal strength levels, using calculations of diffusive properties of odour trails and attenuation rates of fluid mechanical signals, were compared to the physiological and behavioural threshold detection levels. Males find trails because of strong across-plume chemical gradients; males sometimes go the wrong way because of weak along-plume gradients; males lose the trail when the female hops because of signal dilution; and mate-capture behaviour is elicited by suprathreshold flow signals. The male is stimulated by the female odour to accelerate along the trail to catch up with her, and the boundary layer separating the signal from the chemosensitive receptors along the copepod antennule thins. Diffusion times, and hence reaction times, shorten and behavioural orientation responses can proceed more quickly. While 'perceptive' distance to the odour signal in the trail or the fluid mechanical signal from the female remains within 1-2 body lengths (< 5 mm), the 'reactive' distance between males and females was an order of magnitude larger. Therefore, when nearest-neighbour distances are 5 cm or less, as in swarms of 10(4) copepods m-3, mating events are facilitated. The strong similarity in the structure of mating trails and vortex tubes (isotropic, millimetre-centimetre scale, 10:1 aspect ratio, 10s persistence), indicates that these trails are constrained by the same physical forces that influence water motion in a low Reynolds number fluid regime, where viscosity limits forces to the molecular scale. The exploratory reaches of mating trails appear inscribed within Kolmogorov eddies and may represent a measure of eddy size. Biologically formed mating trails, however, are distinct in their flow velocity and chemical composition from common small-scale turbulent features; and mechanoreceptive and chemoreceptive copepods use their senses to discriminate these differences. Zooplankton are not aimless wanderers in a featureless environment. Their ambit is replete with clues that guide them in their efforts for survival in the ocean.

Shape Optimization Analysis of Flow Field. (Growth-Strain Method Approach).

A new analytical approach for optimizing shapes of the flow field is presented. The reshaping is accomplished by the growth-strain method which was first developed using the finite-element calculation of the deformation of shapes by generating bulk strain for solid problems. The generation law of the bulk strain is given as a function of a distributed parameter to be made uniform. For solid problems, the validity of the use of the shear strain energy density to maximize the strength based on the Mises criterion or the strain energy density to maximize the stiffness for the distributed parameter has been confirmed. In the present paper, we propose the use of the dissipation energy density for the distributed parameter to minimize the total energy dissipated due to the viscosity of the fluid. Numerical results for abruptly enlarged channel problems in steady state assuming low Reynolds number and incompressible viscous fluid shows the validity of the present approach.

A note on very low reynolds number fluid flow through screens

Extensive experimental results on the pressure loss associated with Newtonian fluid flow through a screen are reported. It is shown that the use of two dimensionless groups, namely, the loss coefficient and the Reynolds number, provides an adequate representation of the data over wide ranges of conditions of Reynolds number, size of screens, etc. There appears to be no influence of the screen aperture/column diameter ratio on the loss coefficient in the range 100–1200.

Simulation of bacterial attraction and adhesion to falling particles in an aquatic environment

Chemosensory movement of bacteria toward the cloud of leaked material around planktonic algae has been suggested as an important aspect of bacterial nutrition in aquatic ecosystems. Inability of bacteria to keep pace with falling algae has been suggested as inhibiting such interactions. The interaction between bacteria and falling particles, including microalgae, is explored with a simulation model of bacterial chemotaxis that incorporates low Reynolds number fluid flow and resulting substrate spatial distributions. Results show that although bacteria cannot maintain a position relative to a falling particle unless the particle is extremely large, such as a marine snow aggregate, chemosensory response does allow them to stay in the high substrate environment of the leaky particle longer than if they did not have it. The ecological significance for bacterial metabolism depends on several factors, including the frequency of contact between algae and bacteria and the relative concentrations of substrate at the cell surface and in the background. Optimal enhancement should occur in eutrophic conditions of large algal cells present in high abundances. Presently available values for the ratio of substrate concentration next to the algal cell relative to that in solution are not large enough to suggest that the microzones around algal cells provide significant enhancement of bacterial nutrition.Chemotaxis should enhance interactions with large marine snow aggregates, both by allowing bacteria to stay for significant periods around them and by enhancing the rates at which bacteria attach to the aggregate surfaces. This enhancement is greater for surfaces in which there is a lower probability of sticking.

Adsorption of interacting Brownian particles onto surfaces: I. General formulation of the macroscopic diffusion equation and results for nonhydrodynamic force interactions

Previous studies on the adsorption or deposition of Brownian particles onto surfaces have been carried out in the limit of infinite particle dilution. In the present study we have examined the effects of finite particle concentrations on the transport and adsorption of Brownian particles onto surfaces. A macroscopic diffusion equation for the collection of particles in a nonuniform host fluid is derived beginning with the n-particle Fokker-Planck equation. Both hydrodynamic interparticle interactions and hydrodynamic interactions of the particles with the adsorbing surface are included in the theoretical formulation. In agreement with previous methods, the resulting convective-diffusion equation is similar in form to the single-particle equation (Smoluchowski equation) with the Einstein diffusion coefficient replaced by the mutual diffusion tensor for the interacting Brownian particles. Solutions to the convective-diffusion equation were carried out for the problem of Brownian particle adsorption onto a large sphere under the conditions of low Reynolds number fluid motion and large particle Peclet numbers. In this first study, we have neglected the effects of hydrodynamic interactions on the solution behavior, and have thus focused our attention on the effects of attractive- and repulsive-type colloidal force interactions on the transport and deposition of Brownian particles onto a spherical collector. Our semianalytic solutions to the convective-diffusion equation show a general behavior of interparticle interactions: attractive-type interactions lead to a decrease in the total particle number flux to the sphere surface as compared to the noninteracting case, whereas repulsive-type interactions result in a relative increase in the flux. This behavior is explained by examining the “force environment” of a particle near the collecting sphere surface. The effects of colloidal interaction forces were further quantified by considering two specific interaction potentials: hard-sphere and electric double-layer interactions. Typical parameters of this latter potential show a most dramatic change in the total particle number flux, resulting in some cases in as much as a 100% increase over the noninteracting case at a particle volume fraction of 10 −2. Finally, we have also summarized our assumptions which have led to the results reported here, including the neglect of hydrodynamic interactions to be investigated in the second part of this study.

Low Reynolds number fluid flow induced by settling aerosol and detected by the particle Doppler shift spectrometer

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTLow Reynolds number fluid flow induced by settling aerosol and detected by the particle Doppler shift spectrometerRobert A. Fletcher, David S. Bright, and Ilan ChabayCite this: J. Phys. Chem. 1980, 84, 12, 1611–1614Publication Date (Print):June 1, 1980Publication History Published online1 May 2002Published inissue 1 June 1980https://doi.org/10.1021/j100449a035RIGHTS & PERMISSIONSArticle Views53Altmetric-Citations2LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (475 KB) Get e-Alerts