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Dec 2010

Volume 22, Issue 12, Articles (12xxxx)

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Phys. Fluids 22, 121901 (2010); http://dx.doi.org/10.1063/1.3529236 (9 pages)

J. Sznitman, X. Shen, R. Sznitman, and P. E. Arratia
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Flutter instability of rectangle and trapezoid flags in uniform flow

Zhen Pang, Lai-bing Jia, and Xie-zhen Yin

Phys. Fluids 22, 121701 (2010); http://dx.doi.org/10.1063/1.3525920 (4 pages)

Online Publication Date: 14 December 2010

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An experiment on the flutter instability of rectangle and trapezoid flags is conducted in a low speed wind tunnel and a physical model is proposed to predict the critical velocity of flutter instability of the flags. The nondimensional second moment of area is used to depict the effect of the flag shape on the flutter. The result shows that the method presented in this paper can be used to predict the lower-critical velocity. The change of the flutter envelope and critical velocity is found to be related to the dominant mode.
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47.20.-k Flow instabilities
47.80.Jk Flow visualization and imaging
47.80.Cb Velocity measurements
47.60.-i Flow phenomena in quasi-one-dimensional systems

The thickness of the turbulent/nonturbulent interface is equal to the radius of the large vorticity structures near the edge of the shear layer

Carlos B. da Silva and Rodrigo R. Taveira

Phys. Fluids 22, 121702 (2010); http://dx.doi.org/10.1063/1.3527548 (4 pages) | Cited 8 times

Online Publication Date: 21 December 2010

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Direct numerical simulations at Reynolds numbers ranging from Reλ = 30 to 160 show that the thickness δω of the turbulent/nonturbulent (T/NT) interface in planar jets is of the order of the Taylor scale δω ∼ λ, while in shear free, irrotational/isotropic turbulence is of the order of the Kolmogorov microscale δω ∼ η. It is shown that δω is equal to the radius of the large vorticity structures (LVSs) in this region, δω ≈ RLVS. Thus, the mean shear and the Reynolds number affect the T/NT interface thickness insofar as they define the radial dimension of the LVS near the T/NT interface.
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47.27.-i Turbulent flows
47.27.wg Turbulent jets
47.32.-y Vortex dynamics; rotating fluids
47.11.-j Computational methods in fluid dynamics

Slip length for longitudinal shear flow over a dilute periodic mattress of protruding bubbles

Darren Crowdy

Phys. Fluids 22, 121703 (2010); http://dx.doi.org/10.1063/1.3531683 (4 pages) | Cited 7 times

Online Publication Date: 30 December 2010

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An analytical formula for the frictional slip length associated with transverse shear flow over a bubble mattress comprising a dilute periodic array of parallel circular-arc grooves protruding into the fluid has recently been presented by Davis and Lauga [Phys. Fluids 21, 011701 (2009)] . This letter derives an analytical formula for the slip length associated with longitudinal shear flow over the same surface. The formula is in excellent agreement with a phenomenological result based on finite element simulations given by Teo and Khoo [Microfluid. Nanofluid. 9, 499 (2010)] .
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47.45.Gx Slip flows and accommodation
47.55.D- Drops and bubbles
47.11.Fg Finite element methods
47.10.-g General theory in fluid dynamics
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back to top Biofluid Mechanics

Propulsive force measurements and flow behavior of undulatory swimmers at low Reynolds number

J. Sznitman, X. Shen, R. Sznitman, and P. E. Arratia

Phys. Fluids 22, 121901 (2010); http://dx.doi.org/10.1063/1.3529236 (9 pages) | Cited 7 times

Online Publication Date: 22 December 2010

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The swimming behavior of the nematode Caenorhabditis elegans is investigated in aqueous solutions of increasing viscosity. Detailed flow dynamics associated with the nematode’s swimming motion as well as propulsive force and power are obtained using particle tracking and velocimetry methods. We find that C. elegans delivers propulsive thrusts on the order of a few nanonewtons. Such findings are supported by values obtained using resistive force theory; the ratio of normal to tangential drag coefficients is estimated to be approximately 1.4. Over the range of solutions investigated here, the flow properties remain largely independent of viscosity. Velocity magnitudes of the flow away from the nematode body decay rapidly within less than a body length and collapse onto a single master curve. Overall, our findings support that C. elegans is an attractive living model to study the coupling between small-scale propulsion and low Reynolds number hydrodynamics.
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47.63.Gd Swimming microorganisms
47.80.-v Instrumentation and measurement methods in fluid dynamics
47.15.-x Laminar flows

The impact of uncertainty on shape optimization of idealized bypass graft models in unsteady flow

Sethuraman Sankaran and Alison L. Marsden

Phys. Fluids 22, 121902 (2010); http://dx.doi.org/10.1063/1.3529444 (16 pages) | Cited 2 times

Online Publication Date: 22 December 2010

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It is well known that the fluid mechanics of bypass grafts impacts biomechanical responses and is linked to intimal thickening and plaque deposition on the vessel wall. In spite of this, quantitative information about the fluid mechanics is not currently incorporated into surgical planning and bypass graft design. In this work, we use a derivative-free optimization technique for performing systematic design of bypass grafts. The optimization method is coupled to a three-dimensional pulsatile Navier–Stokes solver. We systematically account for inevitable uncertainties that arise in cardiovascular simulations, owing to noise in medical image data, variable physiologic conditions, and surgical implementation. Uncertainties in the simulation input parameters as well as shape design variables are accounted for using the adaptive stochastic collocation technique. The derivative-free optimization framework is coupled with a stochastic response surface technique to make the problem computationally tractable. Two idealized numerical examples, an end-to-side anastomosis, and a bypass graft around a stenosis, demonstrate that accounting for uncertainty significantly changes the optimal graft design. Results show that small changes in the design variables from their optimal values should be accounted for in surgical planning. Changes in the downstream (distal) graft angle resulted in greater sensitivity of the wall-shear stress compared to changes in the upstream (proximal) angle. The impact of cost function choice on the optimal solution was explored. Additionally, this work represents the first use of the stochastic surrogate management framework method for robust shape optimization in a fully three-dimensional unsteady Navier–Stokes design problem.
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47.85.-g Applied fluid mechanics
47.10.ad Navier-Stokes equations
47.63.-b Biological fluid dynamics
back to top Micro- and Nanofluid Mechanics

Flow regime transition at high capillary numbers in a microfluidic T-junction: Viscosity contrast and geometry effect

Amit Gupta and Ranganathan Kumar

Phys. Fluids 22, 122001 (2010); http://dx.doi.org/10.1063/1.3523483 (11 pages) | Cited 5 times

Online Publication Date: 2 December 2010

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Flow regimes obtained as a consequence of two immiscible fluids interacting at a T-junction are presented for transitional to high capillary numbers and different ratios of the continuous and dispersed phase flow rates and viscosities. Results are presented for the formation of micron-sized droplets using simulations performed based on a three-dimensional lattice Boltzmann method. The influence of viscosity and geometry of the device on the frequency and volume of droplets formed has been examined and the nondimensional drop size correlated with the capillary number and flow rate ratio. This work reveals two important and new physical features: (a) the transition zone separating droplet and jet flows narrows for high capillary numbers and (b) the critical flow rate ratio separating droplet and parallel flows increases as the dispersed to continuous channel width ratio increases, aspects which have been correlated using a simple relation for both transitions from the droplet-at-T-junction to droplet-in-channel and droplet-in-channel to parallel flow. In the droplet-at-T-junction regime, the droplet formation frequency was recorded as a function of the capillary number, flow rate ratio, and the channel width ratio as well. Results show that the transition to stable jets can be delayed and droplets can be formed even at very high flow rate ratios by significantly increasing the viscosity of the continuous phase.
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47.55.db Drop and bubble formation
47.55.nb Capillary and thermocapillary flows
47.60.Dx Flows in ducts and channels
47.60.Kz Flows and jets through nozzles
47.61.Jd Multiphase flows
47.11.Qr Lattice gas

Influence of streaming potential on the elastic response of a compliant microfluidic substrate subjected to dynamic loading

Jeevanjyoti Chakraborty and Suman Chakraborty

Phys. Fluids 22, 122002 (2010); http://dx.doi.org/10.1063/1.3524530 (9 pages) | Cited 6 times

Online Publication Date: 7 December 2010

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In the present study, we investigate the effect of streaming potential on the elastic response of a compliant surface subjected to dynamic loading conditions. For illustrating the pertinent physical phenomena, we analyze in particular the dynamical characteristics of the system on squeezing out of a liquid layer through a narrow gap formed between an elastic fluidic surface and an incipient rigid oscillating sphere. We reveal that the streaming potential effects may amplify the elastic force response of the substrate to a considerable extent. Interestingly and nontrivially, this increment turns out not only to be a function of the pertinent electrokinetic parameters dictating the establishment of the streaming potential, but also a combined consequence of the oscillation frequency and the stiffness of the substrate, consistent with a dynamical interaction between interfacial electrochemical-hydrodynamics and structural responsive characteristics that has hitherto not been emphatically explored.
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47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.60.-i Flow phenomena in quasi-one-dimensional systems
68.03.Kn Dynamics (capillary waves)
47.61.Fg Flows in micro-electromechanical systems (MEMS) and nano-electromechanical systems (NEMS)

Breakup of diminutive Rayleigh jets

Wim van Hoeve, Stephan Gekle, Jacco H. Snoeijer, Michel Versluis, Michael P. Brenner, and Detlef Lohse

Phys. Fluids 22, 122003 (2010); http://dx.doi.org/10.1063/1.3524533 (11 pages) | Cited 10 times

Online Publication Date: 8 December 2010

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Discharging a liquid from a nozzle at sufficient large velocity leads to a continuous jet that due to capillary forces breaks up into droplets. Here we investigate the formation of microdroplets from the breakup of micron-sized jets with ultra high-speed imaging. The diminutive size of the jet implies a fast breakup time scale τc = math of the order of 100 ns, and requires imaging at 14×106 frames/s. We directly compare these experiments with a numerical lubrication approximation model that incorporates inertia, surface tension, and viscosity [ J. Eggers and T. F. Dupont, J. Fluid Mech. 262, 205 (1994) ; X. D. Shi, M. P. Brenner, and S. R. Nagel, Science 265, 219 (1994) ]. The lubrication model allows to efficiently explore the parameter space to investigate the effect of jet velocity and liquid viscosity on the formation of satellite droplets. In the phase diagram, we identify regions where the formation of satellite droplets is suppressed. We compare the shape of the droplet at pinch-off between the lubrication approximation model and a boundary-integral calculation, showing deviations at the final moment of the pinch-off. In spite of this discrepancy, the results on pinch-off times and droplet and satellite droplet velocity obtained from the lubrication approximation agree with the high-speed imaging results.
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47.55.db Drop and bubble formation
47.55.df Breakup and coalescence
47.60.Kz Flows and jets through nozzles
47.55.nb Capillary and thermocapillary flows
47.80.Jk Flow visualization and imaging
68.03.Cd Surface tension and related phenomena

Transport of Brownian particles confined to a weakly corrugated channel

Xinli Wang and German Drazer

Phys. Fluids 22, 122004 (2010); http://dx.doi.org/10.1063/1.3527546 (10 pages) | Cited 2 times

Online Publication Date: 21 December 2010

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We investigate the average velocity of Brownian particles driven by a constant external force when constrained to move in two-dimensional, weakly corrugated channels. We consider both the geometric confinement of the particles between solid walls as well as the soft confinement induced by a periodic potential. Using perturbation methods we show that the leading order correction to the marginal probability distribution of particles in the case of soft confinement is equal to that obtained in the case of geometric confinement, provided that the (configuration) integral over the cross-section of the confining potential is equal to the width of the solid channel. We then calculate the probability distribution and average velocity in the case of a sinusoidal variation in the width of the channels. The reduction on the average velocity is larger in the case of soft channels at small Péclet numbers and for relatively narrow channels and the opposite is true at large Péclet numbers and for wide channels. In the limit of large Péclet numbers the convergence to bulk velocity is faster in the case of soft channels. The leading order correction to the average velocity and marginal probability distribution agree well with Brownian Dynamics simulations for the two types of confinement and over a wide range of Péclet numbers.
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05.40.Jc Brownian motion
02.50.Cw Probability theory
47.60.Dx Flows in ducts and channels
47.55.-t Multiphase and stratified flows
47.10.A- Mathematical formulations
05.60.-k Transport processes

Effects of convection and solid wall on the diffusion in microscale convection flows

Jun Zhang, Jing Fan, and Fei Fei

Phys. Fluids 22, 122005 (2010); http://dx.doi.org/10.1063/1.3528310 (9 pages) | Cited 3 times

Online Publication Date: 21 December 2010

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The diffusive transport properties in microscale convection flows are studied by using the direct simulation Monte Carlo method. The effective diffusion coefficient D∗ is computed from the mean square displacements of simulated molecules based on the Einstein diffusion equation D∗ = 〈Δx2(t)〉/2t. Two typical convection flows, namely, thermal creep convection and Rayleigh–Bénard convection, are investigated. The thermal creep convection in our simulation is in the noncontinuum regime, with the characteristic scale of the vortex varying from 1 to 100 molecular mean free paths. The diffusion is shown to be enhanced only when the vortex scale exceeds a certain critical value, while the diffusion is reduced when the vortex scale is less than the critical value. The reason for phenomenon of diffusion reduction in the noncontinuum regime is that the reduction effect due to solid wall is dominant while the enhancement effect due to convection is negligible. A molecule will lose its memory of macroscopic velocity when it collides with the walls, and thus molecules are hard to diffuse away if they are confined between very close walls. The Rayleigh–Bénard convection in our simulation is in the continuum regime, with the characteristic length of 1000 molecular mean free paths. Under such condition, the effect of solid wall on diffusion is negligible. The diffusion enhancement due to convection is shown to scale as the square root of the Péclet number in the steady convection regime, which is in agreement with previous theoretical and experimental results. In the oscillation convection regime, the diffusion is more strongly enhanced because the molecules can easily advect from one roll to its neighbor due to an oscillation mechanism.
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47.61.Cb Non-continuum effects
47.55.P- Buoyancy-driven flows; convection
47.11.-j Computational methods in fluid dynamics
back to top Interfacial Flows

Numerical study of a droplet migration induced by combined thermocapillary-buoyancy convection

Huy-Bich Nguyen and Jyh-Chen Chen

Phys. Fluids 22, 122101 (2010); http://dx.doi.org/10.1063/1.3524822 (9 pages) | Cited 3 times

Online Publication Date: 7 December 2010

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Numerical computations have been performed to study the effects of thermocapillary convection and buoyancy convection, and free surface deformation induced by gravity on the migration behavior of a liquid droplet on a horizontal solid surface subjected to a uniform temperature gradient. Investigations are carried out by solving the Navier–Stokes equations coupled with the energy equation through the finite element method. The combined thermocapillary and buoyancy force driven convection produces complex dynamic behavior of fluid motion inside the droplet. The net momentum generated by a pair of asymmetric thermocapillary convection vortices inside the droplet drives the droplet to move in both small and middle droplet sized regimes. In the small sized regime, the quasisteady migration speed of the droplet is mostly linearly proportional to its size because of the stronger net thermocapillary momentum. When the droplet is in the middle sized regime, its quasisteady migration speed reaches a maximum, but this is gradually reduced as the droplet size increases due to the suppression of the net thermocapillary momentum by the buoyancy force. In the large droplet sized regime, two pairs of convection vortices exist inside the droplet as a result of the appearance of the buoyancy-driven convection accompanying the thermocapillary convection. The quasisteady migration speed quickly diminishes mainly due to the reduction of the net thermocapillary momentum from the stronger buoyancy convection.
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47.55.db Drop and bubble formation
47.55.dm Thermocapillary effects
47.55.nb Capillary and thermocapillary flows
47.10.ad Navier-Stokes equations
47.11.Fg Finite element methods
02.70.Dh Finite-element and Galerkin methods

Electrohydrodynamic instabilities in thin liquid trilayer films

Scott A. Roberts and Satish Kumar

Phys. Fluids 22, 122102 (2010); http://dx.doi.org/10.1063/1.3520134 (15 pages) | Cited 9 times

Online Publication Date: 9 December 2010

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Experiments by Dickey et al. [Langmuir 22, 4315 (2006)] and Leach et al. [Chaos 15, 047506 (2005)] show that novel pillar shapes can be generated from electrohydrodynamic instabilities at the interfaces of thin polymer/polymer/air trilayer films. In this paper, we use linear stability analysis to investigate the effect of free charge and ac electric fields on the stability of trilayer systems. Our work is also motivated by our recent theoretical study [ S. A. Roberts and S. Kumar, J. Fluid Mech. 631, 255 (2009) ] which demonstrates how ac electric fields can be used to increase control over the pillar formation process in thin liquid bilayer films. For perfect dielectric films, the effect of an ac electric field can be understood by considering an equivalent dc field. Leaky dielectric films yield pillar configurations that are drastically different from perfect dielectric films, and ac fields can be used to control the location of free charge within the trilayer system. This can alter the pillar instability modes and generate smaller diameter pillars when conductivities are mismatched. The results presented here may be of interest for the creation of complex topographical patterns on polymer coatings and in microelectronics.
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47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.50.Gj Instabilities
47.20.-k Flow instabilities
68.15.+e Liquid thin films
77.55.-g Dielectric thin films
77.84.Nh Liquids, emulsions, and suspensions; liquid crystals

The influence of capillary flow on the fate of evaporating wetted imprint of the sessile droplet in porous medium

B. Markicevic and H. K. Navaz

Phys. Fluids 22, 122103 (2010); http://dx.doi.org/10.1063/1.3527547 (16 pages) | Cited 2 times

Online Publication Date: 14 December 2010

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The fate of a wetting liquid sessile droplet imbibed by a porous medium is formulated as a multiphase flow problem and a numerical solution is developed using the capillary network model with a microforce balance at the liquid∣gas interface. The liquid phase capillary flow and evaporation are solved simultaneously. An exclusive evidence for a multiphase flow is already found in the capillary flow, as a liquid wets a much larger volume of porous medium compared to the wetted volume, calculated by assuming that the medium imbibes the liquid in the single-phase flow. The physics of the multiphase capillary flow includes the formation of local gas clusters and liquid ganglia. The clusters and ganglia distribution is further altered by evaporation. The evaporation tends to shrink the ganglia sizes and open the gas clusters, both due to the liquid mass loss from the porous medium. Still, the capillarity tends to disperse the liquid back into the regions from where the liquid previously evaporated. These changes in the liquid saturation produce the changes in vapor concentration within the porous medium and changes in the mass fluxes. The imprint shape varies, where, for more spherical imprints, the evaporation is enhanced due to the capillary flow. The opposite is true for the elongated imprints for which the capillarity hinders the evaporation rate. Comparing the spherical and elongated imprints, the liquid dispersion differs and the capillary flow the into protrusion direction is pronounced for the elongated imprints. The changes in the liquid dispersion and imprint shape influence the vapor concentration within the porous medium, vapor phase mass fluxes, and liquid persistence time. Finally, the previous behavior is observed for hazardous materials and warfare agents, where predicting the fate of such kind of liquids and their vapors become especially important due to their harmful effects.
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47.55.Ca Gas/liquid flows
68.08.Bc Wetting
47.56.+r Flows through porous media
47.55.nb Capillary and thermocapillary flows
47.60.Dx Flows in ducts and channels

Building water bridges in air: Electrohydrodynamics of the floating water bridge

Álvaro G. Marín and Detlef Lohse

Phys. Fluids 22, 122104 (2010); http://dx.doi.org/10.1063/1.3518463 (9 pages) | Cited 11 times

Online Publication Date: 15 December 2010

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The interaction of electrical fields and liquids can lead to a phenomenon that defies intuition. Some famous examples can be found in electrohydrodynamics as Taylor cones, whipping jets, or noncoalescing drops. A less famous example is the floating water bridge: a slender thread of water held between two glass beakers in which a high voltage difference is applied. Surprisingly, the water bridge defies gravity even when the beakers are separated at distances up to 2 cm. In this paper, experimental measurements and simple models are proposed and discussed for the stability of the bridge and the source of the flow, revealing an important role of polarization forces on the stability of the water bridge. On the other hand, the observed flow can only be explained due to the non-negligible free charge present in the surface. In this sense, the floating water bridge can be considered as an extreme case of a leaky dielectric liquid [ J. R. Melcher and G. I. Taylor, Annu. Rev. Fluid Mech. 1, 111 (1969) ].
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47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.55.nb Capillary and thermocapillary flows
47.80.Jk Flow visualization and imaging
47.20.-k Flow instabilities
47.55.df Breakup and coalescence

Wavelength selection in the crown splash

Li V. Zhang, Philippe Brunet, Jens Eggers, and Robert D. Deegan

Phys. Fluids 22, 122105 (2010); http://dx.doi.org/10.1063/1.3526743 (9 pages) | Cited 12 times

Online Publication Date: 22 December 2010

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The impact of a drop onto a liquid layer produces a splash that results from the ejection and dissolution of one or more liquid sheets, which expand radially from the point of impact. In the crown splash parameter regime, secondary droplets appear at fairly regularly spaced intervals along the rim of the sheet. By performing many experiments for the same parameter values, we measure the spectrum of small-amplitude perturbations growing on the rim. We show that for a range of parameters in the crown splash regime, the generation of secondary droplets results from a Rayleigh–Plateau instability of the rim, whose shape is almost cylindrical. In our theoretical calculation, we include the time dependence of the base state. The remaining irregularity of the pattern is explained by the finite width of the Rayleigh-Plateau dispersion relation. Alternative mechanisms, such as the Rayleigh–Taylor instability, can be excluded for the experimental parameters of our study.
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47.55.db Drop and bubble formation
47.80.Jk Flow visualization and imaging
68.15.+e Liquid thin films
47.20.Lz Secondary instabilities
47.54.De Experimental aspects

Axial dispersion in segmented gas-liquid flow: Effects of alternating channel curvature

Metin Muradoglu

Phys. Fluids 22, 122106 (2010); http://dx.doi.org/10.1063/1.3531742 (8 pages) | Cited 2 times

Online Publication Date: 30 December 2010

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The effects of channel curvature on the axial dispersion in segmented gas-liquid flows are studied computationally in a two-dimensional setting using a finite-volume/front-tracking method. Passive tracer particles are used to visualize and quantify the axial dispersion. The molecular diffusion is modeled by random walk of tracer particles. It is found that there is significant axial dispersion in serpentine channels even in the absence of molecular diffusion. The lubricating thin liquid layer that persists on the wall of a straight channel is periodically broken in the serpentine channel leading to enhanced axial dispersion. It is also found that the axial dispersion is always larger in the serpentine channel than that in the straight channel but the effects of channel curvature are more pronounced at high Peclet numbers, i.e., Pe>104. A model is proposed based on the difference between the liquid film thicknesses on the inner and outer side of the bend in the limit as Pe→∞. Good agreement is found between the computational results and the model when the liquid slug is well mixed by the chaotic advection.
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47.60.Dx Flows in ducts and channels
47.11.Df Finite volume methods
68.15.+e Liquid thin films
47.55.Kf Particle-laden flows
47.85.mf Lubrication flows
47.52.+j Chaos in fluid dynamics
back to top Viscous and Non-Newtonian Flows

Mixing of passive tracers in the decay Batchelor regime of a channel flow

Yonggun Jun and Victor Steinberg

Phys. Fluids 22, 123101 (2010); http://dx.doi.org/10.1063/1.3522400 (15 pages) | Cited 6 times

Online Publication Date: 7 December 2010

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We report detailed quantitative studies of passive scalar mixing in a curvilinear channel flow, where elastic turbulence in a dilute polymer solution of high molecular weight polyacrylamide in a high viscosity water-sugar solvent was achieved. For quantitative investigation of mixing, a detailed study of the profiles of mean longitudinal and radial components of the velocity in the channel as a function of Wi was carried out. Besides, a maximum of the average value as well as a rms of the longitudinal velocity was used to determine the threshold of the elastic instability in the channel flow. The rms of the radial derivatives of the longitudinal and radial velocity components was utilized to define the control parameters of the problem, the Weissenberg Wiloc and the Péclet Pe numbers. The main result of these studies is the quantitative test of the theoretical prediction about the value of the mixing length in the decay Batchelor regime. The experiment shows large quantitative discrepancy, more than 200 times in the value of the coefficient C, which appears in the theoretical expression for the mixing length, but with the predicted scaling relation. There are two possible reasons to this discrepancy. First is the assumption made in the theory about the δ-correlated velocity field, which is in odds with the experimental observations. Second, and probably a more relevant suggestion for the significantly increased mixing length and thus reduced mixing efficiency, is the observed jets, the rare, localized, and vigorous ejection of the scalar trapped near the wall, which protrudes into the peripheral region as well as the bulk. They are first found in the recent numerical calculations and then observed in the experiment reported. The jets definitely strongly reduce the mixing efficiency in particular in the peripheral region and so can lead to considerable increase of the mixing length. We hope that this result will initiate further numerical calculations of the mixing length. Finally, we analyze statistical properties of the mixing in the decay Batchelor regime by studying the power spectra, the decay exponents scaling, the structure functions of a tracer and moments of PDF of passive scalar increments, and the temporal and spatial correlation functions and find rather satisfactory agreement with theory.
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47.27.wj Turbulent mixing layers
47.60.Dx Flows in ducts and channels
47.27.nd Channel flow
47.57.Ng Polymers and polymer solutions
47.27.nb Boundary layer turbulence
47.27.wg Turbulent jets

Viscous evolution of point vortex equilibria: The collinear state

Fangxu Jing, Eva Kanso, and Paul K. Newton

Phys. Fluids 22, 123102 (2010); http://dx.doi.org/10.1063/1.3516637 (12 pages) | Cited 4 times

Online Publication Date: 7 December 2010

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We describe the viscous evolution of a collinear three-vortex structure that corresponds initially to an inviscid point vortex fixed equilibrium, with the goal of elucidating some of the main transient dynamical features of the flow. Using a multi-Gaussian “core-growth” type of model, we show that the system immediately begins to rotate unsteadily, a mechanism we attribute to a “viscously induced” instability. We then examine in detail the qualitative and quantitative evolution of the system as it evolves toward the long-time asymptotic Lamb–Oseen state, showing the sequence of topological bifurcations that occur both in a fixed reference frame and in an appropriately chosen rotating reference frame. The evolution of passive particles in this viscously evolving flow is shown and interpreted in relation to these evolving streamline patterns.
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47.32.cd Vortex stability and breakdown
47.32.Ef Rotating and swirling flows
47.20.Ky Nonlinearity, bifurcation, and symmetry breaking
02.50.-r Probability theory, stochastic processes, and statistics

Pair collisions of fluid-filled elastic capsules in shear flow: Effects of membrane properties and polymer additives

Pratik Pranay, Samartha G. Anekal, Juan P. Hernandez-Ortiz, and Michael D. Graham

Phys. Fluids 22, 123103 (2010); http://dx.doi.org/10.1063/1.3524531 (17 pages) | Cited 6 times

Online Publication Date: 8 December 2010

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The dynamics and pair collisions of fluid-filled elastic capsules during Couette flow in Newtonian fluids and dilute solutions of high-molecular weight (drag-reducing) polymers are investigated via direct simulation. Capsule membranes are modeled using either a neo-Hookean constitutive model or a model introduced by Skalak et al. [“Strain energy function of red blood-cell membranes,” Biophys. J. 13, 245 (1973)] , which includes an energy penalty for area changes. This model was developed to capture the elastic properties of red blood cells. Polymer molecules are modeled as bead-spring trimers with finitely extensible nonlinearly elastic springs; parameters were chosen to loosely approximate 4000 kDa poly(ethylene oxide). Simulations are performed with a novel Stokes flow formulation of the immersed boundary method for the capsules, combined with Brownian dynamics for the polymer molecules. The results for isolated capsules in shear indicate that at the very low concentrations considered here, polymers have a little effect on the capsule shape. In the case of pair collisions, the effect of polymer is strongly dependent on the elastic properties of the capsules’ membranes. For neo-Hookean capsules or for Skalak capsules with only a small penalty for area change, the net displacement in the gradient direction after collision is virtually unaffected by the polymer. For Skalak capsules with a large penalty for area change, polymers substantially decrease the net displacement when compared to the Newtonian case and the effect is enhanced upon increasing the polymer concentration. The differences between the polymer effects in the various cases are associated with the extensional flow generated in the region between the capsules as they leave the collision. The extension rate is highest when there is a strong resistance to a change in the membrane area and is substantially decreased in the presence of polymer.
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87.85.gf Fluid mechanics and rheology
47.63.Cb Blood flow in cardiovascular system
47.57.Ng Polymers and polymer solutions
47.15.-x Laminar flows
47.11.-j Computational methods in fluid dynamics
87.16.dp Transport, including channels, pores, and lateral diffusion

Experimental study of dispersion and miscible viscous fingering of initially circular samples in Hele-Shaw cells

R. Maes, G. Rousseaux, B. Scheid, M. Mishra, P. Colinet, and A. De Wit

Phys. Fluids 22, 123104 (2010); http://dx.doi.org/10.1063/1.3528039 (12 pages) | Cited 4 times

Online Publication Date: 22 December 2010

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Experimental studies are conducted to analyze dispersion and miscible viscous fingering of initially circular samples of a given solution displaced linearly at constant speed U by another solution in horizontal Hele-Shaw cells (two glass plates separated by a thin gap). In the stable case of a dyed water sample having the same viscosity as that of displacing nondyed water, we analyze the transition between dispersive and advective transport of the passive scalar displaced linearly. At low displacement speed and after a certain time, the length of the sample increases as a square root of time allowing to compute the value of a dispersion coefficient. At larger injection speed, the displacement remains advective for the duration of the experiment, with a length of the sample increasing linearly in time. A parametric study allows to gain insight into the switch from one regime to another as a function of the gap width of the cell. In the unstable case of viscous glycerol samples displaced by dyed water, the rear interface of the sample where less viscous water pushes more viscous glycerol is unstable with regard to viscous fingering. The interface deforms into fingers, the number and size of which depend on the viscosity ratio between the two solutions and on the displacement speed. We study the influence of these viscous fingering phenomena on the increased spreading of the sample for various mobility ratios and injection speeds.
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47.55.nd Spreading films
47.57.-s Complex fluids and colloidal systems
68.08.Bc Wetting
47.60.-i Flow phenomena in quasi-one-dimensional systems
back to top Particulate, Multiphase, and Granular Flows

Droplet motion in a microconfined shear flow via a three-dimensional spectral boundary element method

Mohammad A. Khan and Yechun Wang

Phys. Fluids 22, 123301 (2010); http://dx.doi.org/10.1063/1.3525357 (13 pages) | Cited 1 time

Online Publication Date: 9 December 2010

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A 3D spectral boundary element method is employed to compute the dynamics of a single droplet in a microconfined shear flow. Comparisons have been made for the motion of an initially spherical droplet near a single wall and that between two parallel plates. Investigations are conducted for the influences of the capillary number, viscosity ratio, and initial location of the droplet on the droplet deformation, orientation, velocities, as well as the transition between the initial rapid deformation and the subsequent relaxation stage. Computational results for the deformation and velocities are compared with analytical predictions. It is found that the analytical predictions are limited for small deformations, large droplet-wall distances, and near equiviscous droplets.
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47.85.Np Fluidics
47.11.Hj Boundary element methods
47.55.D- Drops and bubbles
47.61.-k Micro- and nano- scale flow phenomena

Capsule dynamics and rheology in shear flow: Particle pressure and normal stress

Jonathan R. Clausen and Cyrus K. Aidun

Phys. Fluids 22, 123302 (2010); http://dx.doi.org/10.1063/1.3483207 (11 pages) | Cited 6 times

Online Publication Date: 9 December 2010

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In this paper, we examine the dynamics of an isolated capsule using a hybrid lattice-Boltzmann/finite-element method, with a focus on how the capsule dynamics affects the rheology of capsule suspensions. We study initially spherical capsules undergoing a “tank-treading” behavior in which the particle assumes an ellipsoidal shape at a steady orientation while the capsule’s membrane rotates. Of particular interest is the calculation of the particle pressure and a full characterization of the normal stresses. To date, results on capsule rheology only consider normal stress differences, which are insufficient to explain particle migration using the suspension balance model [P. R. Nott and J. F. Brady, “Pressure-driven suspension flow: Simulation and theory,” J. Fluid Mech. 275, 157 (1994) ] . We also extend the results of R. Roscoe [“On the rheology of a suspension of viscoelastic spheres in a viscous liquid,” J. Fluid Mech. 28, 273 (1967)] using the solution for ellipsoidal particles of G. B. Jeffery [“The motion of ellipsoidal particles immersed in a viscous fluid,” Proc. R. Soc. London, Ser. A 102, 161 (1922)] to predict the particle-phase pressure of deformable particles. Both analytical modeling and numerical results show a negative (tensile) particle pressure, in contrast with the case of an isolated sphere, which shows no particle pressure.
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47.11.Qr Lattice gas
47.27.N- Wall-bounded shear flow turbulence
47.57.Qk Rheological aspects
47.11.Fg Finite element methods

A formula for the wall-amplified added mass coefficient for a solid sphere in normal approach to a wall and its application for such motion at low Reynolds number

F.-L. Yang

Phys. Fluids 22, 123303 (2010); http://dx.doi.org/10.1063/1.3518764 (13 pages) | Cited 4 times

Online Publication Date: 13 December 2010

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This work re-examines the potential flow theory for a sphere in normal approach to a wall, based on the classical results derived by Lamb [Hydrodynamics (Dover, New York, 1932)] and Milne-Thomson [Theoretical Hydrodynamics, 5th ed. (Dover, New York, 1968)] . These authors generated an expression in which the kinetic energy for a sphere in an unbounded fluid is augmented by a wall correction function in terms of an infinite series that depends on the scaled center-to-wall distance, h∗ = h/a, with a denoting the sphere radius. By truncating the series at the order of h∗−3, the resulting one-term correction function, 3/8h∗−3, is widely employed to approximate the wall-amplified added mass coefficient, CAM(h∗), in multiphase flow research. Nonetheless, this work shows that this one-term correction deviates greatly from corrections including higher order terms when the interstitial gap drops below the half sphere radius. Thus, an explicit formula is developed, for all h∗, using a near-wall Padé approximation, an intermediate bridging function, and a far-field approximation. This proposed formula provides an efficient and reasonable approximation to the infinite series and thus may serve as an improved wall correction function as compared to the one-term formula. The developed formula is applied to compute the unsteady approach of a nonrotating sphere toward a wall in a viscous fluid at low Reynolds number condition. In addition to Brenner’s wall correction on the quasisteady viscous force [ H. Brenner, “The slow motion of a sphere through a viscous fluid towards a plane surface,” Chem. Eng. Sci. 16, 242 (1961) ], the current formula is employed to modify both the added mass coefficient, from 1/2, and the history force. This latter force is modified by integrating the wall-modified potential flow theory with the boundary layer theory. If the one-term correction is used in the equation of motion, underestimation of the sphere motion and the force magnitudes are observed. Lastly, the limiting value of the infinite series derived by Lamb and Milne-Thomson as h→a is analytically evaluated, leading to a result in terms of the generalized zeta function, ζ(3,1). When this limiting value is compared to the one-term correction at h = a, a 38% deficiency of the wall-augmented kinetic energy is revealed, resulting in an underestimated CAM(h∗) that plays a crucial role in presenting the near-wall normal approach.
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47.15.Cb Laminar boundary layers
47.15.G- Low-Reynolds-number (creeping) flows
47.10.A- Mathematical formulations

Settling-induced heat transport

François Blanchette, William Douandju, and Sydney M. Montroy

Phys. Fluids 22, 123304 (2010); http://dx.doi.org/10.1063/1.3531743 (7 pages) | Cited 2 times

Online Publication Date: 30 December 2010

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We investigate the influence of settling particles on heat transport within suspensions. We focus on particles that equilibrate their temperature with the surrounding fluid much faster than their typical settling time. Such particles act as heat carriers and heat transport therefore occur through both diffusion and particle settling. We quantify this effect by deriving the relevant governing equations. We show the effect of particle settling on heat transport as the governing parameter, ϕ(κs/κf)(L/R)Pes, increases, where ϕ is the particle concentration, L is the vertical extent of the domain, R is the particle radius, κs and κf are the thermal conductivity of the solid and fluid phases, respectively, and Pes is the particle Péclet number. We investigate the stabilizing effect this enhanced transport has on unstable density gradients via a linear stability analysis. We conclude by discussing systems where this effect is important, such as rivers coming into the ocean, magma chambers, and when large concentrations of volcanic and forest fire ashes are present in the atmosphere.
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47.27.te Turbulent convective heat transfer
47.57.eb Diffusion and aggregation
47.20.-k Flow instabilities
47.11.-j Computational methods in fluid dynamics
47.27.tb Turbulent diffusion
47.55.Kf Particle-laden flows
back to top Instability and Transition

Onset of double-diffusive convection in a rectangular cavity with stress-free upper boundary

Zhi-Wu Chen, Jie-Min Zhan, Yok-Sheung Li, and Yu-Hua Nie

Phys. Fluids 22, 124101 (2010); http://dx.doi.org/10.1063/1.3517296 (10 pages) | Cited 4 times

Online Publication Date: 1 December 2010

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Double-diffusive buoyancy convection in an open-top rectangular cavity with horizontal temperature and concentration gradients is considered. Attention is restricted to the case where the opposing thermal and solutal buoyancy effects are of equal magnitude (buoyancy ratio Rρ = −1). In this case, a quiescent equilibrium solution exists and can remain stable up to a critical thermal Grashof number Grc. Linear stability analysis and direct numerical simulation show that depending on the cavity aspect ratio A, the first primary instability can be oscillatory, while that in a closed cavity is always steady. Near a codimension-two point, the two leading real eigenvalues merge into a complex coalescence that later produces a supercritical Hopf bifurcation. As Gr further increases, this complex coalescence splits into two real eigenvalues again. The oscillatory flow consists of counter-rotating vortices traveling from right to left and there exists a critical aspect ratio below which the onset of convection is always oscillatory. Neutral stability curves showing the influences of A, Lewis number Le, and Prandtl number Pr are obtained. While the number of vortices increases as A decreases, the flow structure of the eigenfunction does not change qualitatively when Le or Pr is varied. The supercritical oscillatory flow later undergoes a period-doubling bifurcation and the new oscillatory flow soon becomes unstable at larger Gr. Random initial fields are used to start simulations and many different subcritical steady states are found. These steady states correspond to much stronger flows when compared to the oscillatory regime. The influence of Le on the onset of steady flows and the corresponding heat and mass transfer properties are also investigated.
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47.55.pd Multidiffusive convection
47.55.pb Thermal convection
47.32.cd Vortex stability and breakdown
47.20.Bp Buoyancy-driven instabilities (e.g., Rayleigh-Benard)
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.20.Ky Nonlinearity, bifurcation, and symmetry breaking
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