Volume 23, Issue 4, April 2011

We study the dynamics of rod shaped particles in twodimensional electromagnetically driven fluid flows. Two separate types of flows that exhibit chaotic mixing are compared: one with timeperiodic flow and the other with constant forcing but nonperiodic flow. Video particle tracking is used to make accurate simultaneous measurements of the motion and orientation of rods along with the carrier fluid velocity field. These measurements allow a detailed comparison of the motion and orientation of rods with properties of the carrier flow.Measured rod rotation rates are in agreement with predictions for ellipsoidal particles based on the measuredvelocity gradients at the center of the rods. There is little dependence on length for the rods we studied (up to 53% of the length scale of the forcing). Rods are found to align weakly with the extensional direction of the strainrate tensor. However, the alignment is much stronger with the direction of Lagrangian stretching defined by the eigenvectors of the Cauchy–Green deformation tensor. A simple model of the stretching process predicts the degree of alignment of rods with the stretching direction.
 AWARD AND INVITED PAPERS


Patterns and dynamics in transitional plane Couette flow
View Description Hide DescriptionNear transition, plane Couette flow takes the form of largescale, oblique, and statistically steady alternating bands of turbulent and laminar flow. Properties of these flows are investigated using direct numerical simulation in a tilted computational domain. Four regimes—uniform, intermittent, periodic, and localized—are characterized. The Fourier spectrum along the direction of variation of the pattern is presented, and the component corresponding to the pattern wavenumber is investigated as an order parameter. The mean flow of a periodic pattern is characterized and shown to lead to a relation between the Reynolds number and the wavelength and angle of a pattern.
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 LETTERS


Lipid membrane instability driven by capacitive charging
View Description Hide DescriptionA new mechanism for lipidmembrane destabilization and poration by electric fields is proposed. When a dc electric field is applied to an insulating planar membrane separating fluids with different conductivities, a capacitive charging current through the membrane in combination with shearing stresses, created by the electric field acting on its own induced free charge, drives electrohydrodynamic flow that modulates the shape and lipid density fluctuations. The instability is transient and decays as the membrane charges. Accordingly, the dynamics depends on the relative magnitude of the time for charging the membranecapacitor and the electrohydrodynamic flow time.

A new scaling for the streamwise turbulence intensity in wallbounded turbulent flows and what it tells us about the “outer” peak
View Description Hide DescriptionOne recent focus of experimental studies of turbulence in high Reynolds number wallbounded flows has been the scaling of the root mean square of the fluctuating streamwise velocity, but progress has largely been impaired by spatial resolutioneffects of hotwire sensors. For the nearwall peak, recent results seem to have clarified the controversy; however, one of the remaining issues in this respect is the emergence of a second (socalled outer) peak at high Reynolds numbers. The present letter introduces a new scaling of the local turbulence intensity profile, based on the diagnostic plot by Alfredsson and Örlü [Eur. J. Mech. B/Fluids42, 403 (2010)], which predicts the location and amplitude of the “outer” peak and suggests its presence as a question of sufficiently large scale separation.
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 ARTICLES

 Biofluid Mechanics

The stability of a homogeneous suspension of chemotactic bacteria
View Description Hide DescriptionThe linear stability of a homogeneous dilute suspension of chemotactic bacteria in a constant chemoattractant gradient is analyzed. The bacteria execute a runandtumble motion, typified by the species E. coli, wherein periods of smooth swimming (runs) are interrupted by abrupt uncorrelated changes in swimming direction (tumbles). Bacteria tumble less frequently when swimming toward regions of higher chemoattractant concentration, leading to a mean bacterial orientation and velocity in the base state. The stability of an unbounded suspension, both with and without a chemoattractant, is controlled by coupled long wavelength perturbations of the fluid velocity and bacterial orientation fields. In the former case, the most unstable perturbations have their wave vector oriented along the chemoattractant gradient. Chemotaxis reduces the critical bacteria concentration, for the onset of collective swimming, compared with that predicted by Subramanian and Koch [“Critical bacterial concentration for the onset of collective swimming,” J. Fluid Mech.632, 359 (2009)] in the absence of a chemoattractant. A part of this decrease may be attributed to the increase in the mean tumbling time in the presence of a chemoattractant gradient. A second destabilizing influence comes from the ability of the shearing motion, associated with a velocity perturbation in which the velocity and chemical gradients are aligned, to sweep prealigned bacteria into the local extensional quadrant thereby creating a stronger destabilizing active stress than in an initially isotropic suspension. The chemoattractant gradient also fundamentally alters the unstable spectrum for any finite wavenumber. In suspensions of bacteria that do not tumble, Saintillan and Shelley [“Instabilities and pattern formation in active particle suspensions: Kinetic theory and continuum simulations,” Phys. Rev. Lett.100, 178103 (2008); “Instabilities, pattern formation and mixing in active suspensions,” Phys. Fluids20, 123304 (2008)] showed that the growth rate has two real solutions (stationary modes) below a critical wavenumber at which the two solutions merge and then bifurcate to form a pair of complex conjugate solutions (propagating modes) for larger wavenumbers. The discrete spectrum terminates at a second critical wavenumber, and beyond this wavenumber, the only remaining solutions are neutrally stable waves comprising the continuous spectrum. In the presence of a chemoattractant gradient, however, the aforementioned perfect bifurcation is broken and a pair of traveling wave solutions is found for all wavenumbers. Furthermore, instead of terminating at a critical wavenumber, the solutions for the growth rate asymptote to the negative of the tumbling frequency at large wavenumbers.

Steady streaming: A key mixing mechanism in lowReynoldsnumber acinar flows
View Description Hide DescriptionStudy of mixing is important in understanding transport of submicron sized particles in the acinar region of the lung. In this article, we investigate transport in view of advective mixing utilizing Lagrangian particle tracking techniques: tracer advection, stretch rate and dispersion analysis. The phenomenon of steady streaming in an oscillatory flow is found to hold the key to the origin of kinematic mixing in the alveolus, the alveolar mouth and the alveolated duct. This mechanism provides the common route to folding of material lines and surfaces in any region of the acinar flow, and has no bearing on whether the geometry is expanding or if flow separates within the cavity or not. All analyses consistently indicate a significant decrease in mixing with decreasing Reynolds number (Re). For a given Re, dispersion is found to increase with degree of alveolation, indicating that geometry effects are important. These effects of Re and geometry can also be explained by the streaming mechanism. Based on flow conditions and resultant convective mixing measures, we conclude that significant convective mixing in the duct and within an alveolus could originate only in the first few generations of the acinar tree as a result of nonzero inertia, flow asymmetry, and large Keulegan–Carpenter () number.

Pulsatile flow past an oscillating cylinder
View Description Hide DescriptionA fundamental study to characterize the flow around an oscillating cylinder in a pulsatile flow environment is investigated. This work is motivated by a new proposed design of the total artificial lung (TAL), which is envisioned to provide better gas exchange. The Navier–Stokes computations in a moving frame of reference were performed to compute the dynamic flow field surrounding the cylinder. Cylinder oscillations and pulsatile freestream velocity were represented by two sinusoidal waves with amplitudes A and B and frequencies and , respectively. The Keulegan–Carpenter number was used to describe the frequency of the oscillating cylinder while the pulsatile freestream velocity was fixed by imposing for all cases investigated. The parameters of interest and their values were amplitude , the Keulegan–Carpenter number , and the Reynolds number corresponding to operating conditions of the TAL. It was observed that an increase in amplitude and a decrease in are associated with an increase in vorticity (up to 246%) for every Re suggesting that mixing could be enhanced by the proposed TAL design. The drag coefficient was found to decrease for higher amplitudes and lower for all cases investigated. In some cases the drag coefficient values were found to be lower than the stationary cylinder values (, , and and 20). A lockin phenomenon (cylinder oscillating frequency matched the vortex shedding frequency) was found when for all cases. This lockin condition was attributed to be the cause of the rise in drag observed in that operating regime. For optimal performance of the modified TAL design it is recommended to operate the device at higher fiber oscillation amplitudes and lower (avoiding the lockin regime).

Numerical study on the shape oscillation of an encapsulated microbubble in ultrasound field
View Description Hide DescriptionThe shape oscillation of an encapsulated microbubble in an ultrasound field is numerically investigated. To predict the nonlinear process, the continuity equation and the Navier–Stokes equation are directly solved by means of a boundaryfitted finitevolume method on an orthogonal curvilinear coordinate system. The mechanics of neoHookean membrane is incorporated into the dynamic equilibrium at the bubblesurface. The numerical results show that the membrane raises the natural frequency of an encapsulated bubble especially for small bubble, whereas this effect is attenuated as the initial bubble size grows. For a small encapsulated bubble of which the natural frequency is sufficiently higher than the driving frequency, the oscillation is stable, namely, the oscillatory amplitude is small; besides, the radial mode and shape modes are out of resonance so that no deformation emerges. As the bubble becomes larger, the natural frequencies of encapsulated and gas bubbles get closer, leading to the less apparent difference in oscillatory amplitude between them. Furthermore, shape modes of an encapsulated bubble are prone to be induced when twice of the higherorder natural frequency is approximately equal to the frequency of radial mode particularly when the bubble is at radial resonance for which the largeamplitude pulsation enhances the compressive stress developing in the membrane. In contrast, the shape oscillation is less likely to occur for a gas bubble with micrometer size since the surface tension suppresses the developments of nonspherical shape modes.

Dynamics of vesicles in shear and rotational flows: Modal dynamics and phase diagram
View Description Hide DescriptionDespite the recent upsurge of theoretical reduced models for vesicle shape dynamics, comparisons with experiments have not been accomplished. We review the implications of some of the recently proposed models for vesicledynamics, especially the tumblingtrembling domain regions of the phase plane, and show that they all fail to capture the essential behavior of real vesicles for excess areas greater than 0.4. We emphasize new observations of shape harmonics and the role of thermal fluctuations.
 Micro and Nanofluid Mechanics

Ferrohydrodynamic pumping of a ferrofluid or electrohydrodynamic pumping of a polar liquid through a planar duct
View Description Hide DescriptionFerrohydrodynamic pumping of a ferrofluid through a planar duct by means of a running magnetic wave is studied to second order in the amplitude of the exciting current density. The theory for electrohydrodynamic pumping of a polar liquid by means of a running electric wave is shown to be nearly identical. For the given fluid parameters, the net flow rate can be optimized by suitable choice of wavenumber and frequency of the running wave.

Folded microthreads: Role of viscosity and interfacial tension
View Description Hide DescriptionThe shape and evolution of periodically folded threads are experimentally examined in a microfluidic network. The fluidic system is designed for the production and lubricated transport of very uniform folds. To investigate the influence of viscosity and interfacial tension on buckling deformations, multiphase flows are scrutinized using both miscible and immiscible fluid pairs. The parameters used to analyze folding morphologies include thread diameter, arclength, fold amplitude, and wavelength. When fluids are immiscible, the onset of viscous folding is characterized as a function of the capillary number and the phenomenon of “capillary unfolding” where a corrugated thread straightens along the flow direction is demonstrated. The spatial transition from folding to coilinglike flow behavior of highviscosity capillary threads is also shown.

Manipulation of confined bubbles in a thin microchannel: Drag and acoustic Bjerknes forces
View Description Hide DescriptionBubbles confined between the parallel walls of microchannels experience an increased drag compared to freestanding bubbles. We measure and model the additional friction from the walls, which allows the calibration of the drag force as a function of velocity. We then develop a setup to apply locally acoustic waves and demonstrate the use of acoustic forces to induce the motion of bubbles. Because of the bubble pulsation, the acoustic forces—called Bjerknes forces—are much higher than for rigid particles. We evaluate these forces from the measurement of bubble drift velocity and obtain large values of several hundreds of nanonewtons. Two applications have been developed to explore the potential of these forces: asymmetric bubble breakup to produce very well controlled bidisperse populations and intelligent switching at a bifurcation.

Mass flow rate measurements in microtubes: From hydrodynamic to near free molecular regime
View Description Hide DescriptionAn experimental investigation of the reflection/accommodation process at the wall in a single silica microtube and isothermal stationary flow conditions was carried out. Several gases and different diameters were studied through various regimes. Especially for helium, the Knudsen number range was investigated as far as the free molecular regime. This kind of investigation requires a powerful experimental platform to measure mass flow rates, which we have carried out. An analytic expression of the mass flow rate, based on the Navier–Stokes equations with second order boundary condition, was used to yield the tangential momentum accommodation coefficient (TMAC) in the 0.003–0.3 Knudsen number range. Otherwise, the experimental results of the mass flow rate were compared with theoretical values calculated from kinetic approaches using variable TMAC as parameter over the 0.3–30 Knudsen number range, and an overall agreement appears through the comparison. Finally, whatever the theoretical approach the TMAC obtained from gas (nitrogen, xenon, argon, and helium)surface (fused silica) pairs is similar and lower than unity. A tendency of the TMAC values seems to appear according to the molecular mass of the gases. In addition for each gas, the second order slip coefficient magnitude seems to decrease when the tube diameter increases.
 Interfacial Flows

Steadystate liquid sloshing in a rectangular tank with a slattype screen in the middle: Quasilinear modal analysis and experiments
View Description Hide DescriptionTwodimensional resonant liquid sloshing in a rectangular tank equipped with a central slattype screen is studied theoretically and experimentally with focus on nonsmallsolidity ratios of the screen , nonlarge number of slots , and steadystate conditions. The tank is horizontally and harmonically excited with frequencies in a range covering the two lowest primaryexcited natural sloshing resonance frequencies in the corresponding clean tank. The liquid depth is finite. Theoretical analysis is based on the multimodal method with linear freesurface conditions and a quadratic pressure drop condition at the screen expressing an “integral” effect of the screeninduced crossflow separation (or jet flow). New experimental data on the maximum wave elevations at the wall are compared with the theoretical predictions. Very good agreement is shown for the smallest forcing amplitudes (the forcing amplitudetotank width ratio is ≈0.001). Increasing the nondimensional forcing amplitude to ≈0.01 leads to discrepancies due to secondary resonance causing the energy context from the two primaryexcited antisymmetric modes to other, first of all, symmetric modes. A further increase of the nondimensional forcing amplitude to 0.03 leads to more complex secondary resonance effects. Specific surface wave phenomena, e.g., wave breaking, are experimentally observed and documented by photographs and videos.

An analysis of headon droplet collision with large deformation in gaseous medium
View Description Hide DescriptionA theoretical analysis was performed for the headon collision of two identical droplets in a gaseous environment, with the attendant bouncing and coalescence outcomes, for situations in which the extent of droplet deformation upon collision is comparable to the original droplet radius, corresponding to of the droplet Weber number. The model embodies the essential physics that describes the substantial amount of droplet deformation, the viscous loss through droplet internal motion induced by the deformation, the dynamics and rarefied nature of the gas film between the interfaces of the colliding droplets, and the potential destruction and thereby merging of these interfaces due to the van der Waals attraction force. The theoreticalmodel was applied to investigate collisions involving hydrocarbon and water droplets at sub and superatmospheric pressures. The results agree well with previous experimental observations in that as the Weber number increases in the range of , collision of hydrocarbon droplets at one atmospheric pressure results in the nonmonotonic coalescencebouncingcoalescence transition, that while bouncing is absent for water droplets at atmospheric pressure, it occurs at higher pressures, and that while bouncing is observed for hydrocarbon droplets at atmospheric pressure, it is absent at lower pressures.

Linear stability analysis of ice growth under supercooled water film driven by a laminar airflow
View Description Hide DescriptionWe propose a theoretical model for icegrowth under a winddriven supercooled waterfilm. The thickness and surface velocity of the water layer are variable by changing the air stream velocity. For a given water supply rate, linear stability analysis is carried out to study the morphological instability of the icewater interface. In this model, water and air boundary layers are simultaneously disturbed due to the change in ice shape, and the effect of the interaction between air and waterflows on the growth condition of the icewater interface disturbance is taken into account. It is shown that as the wind speed increases, the amplification rate of the disturbance is significantly affected by variable stresses exerted on the waterair interface by the air flow as well as restoring forces due to gravity and surface tension. We predict that an ice pattern of a centimeterscale in wavelength appears and the wavelength decreases as the wind speed increases, and that the ice pattern moves in the direction opposite to the waterflow. The effect of the air stress disturbance on the heat transfer coefficient at the waterair interface is also investigated for various wind speeds.
 Viscous and NonNewtonian Flows

Shorttime pressure response during the startup of a constantrate production of a high pressure gas well
View Description Hide DescriptionThe startup flow of a constantrate production of a high pressure gas well is studied, with emphasis on the effect of gas acceleration. Gas acceleration is important in the near wellbore region for a high pressure gas in a high permeability formation. It is shown that when gas acceleration is important, the system of governing equations for the porous mediaflow becomes hyperbolic. In response to an impulsively imposed mass flowrate, a steep pressure front is created at the wellbore and it propagates into the formation. This steep pressure front is trailed by large amplitude pressure waves. As they travel away from the wellbore, the pressure front becomes less steep and the amplitude of the trailing waves decreases due to viscous damping. It is found that the pressure drawdown experiences a rapid increase followed by an oscillatory behavior in short times before approaching the classical logarithmic rise regime. The pressure gradient at the wellbore wall can grow to a large magnitude in the early times, which can cause a tensile failure of the rock materials near the wellbore.

Modeling and simulations of the spreading and destabilization of nematic droplets
View Description Hide DescriptionA series of experiments [C. Poulard and A. M. Cazabat, “Spontaneous spreading of nematic liquid crystals,” Langmuir21, 6270 (2005)] on spreading droplets of nematic liquid crystal(NLC) reveals a surprisingly rich variety of behaviors. Small droplets can either be arrested in their spreading, spread stably, destabilize without spreading (corrugated surface), or spread with a fingering instability and corrugated free surface. In this work, we discuss the problem of NLCdrops spreading in a simplified twodimensional (2D) geometry. The model that we present is based on a longwavelength approach for NLCs by Ben Amar and Cummings [“Fingering instabilities in driven thin nematic films,” Phys. Fluids13, 1160 (2001); L. J. Cummings, “Evolution of a thin film of nematic liquid crystal with anisotropic surface energy,” Eur. J. Appl. Math.15, 651 (2004)]. The improvements in the model here permit fully nonlinear timedependent simulations. These simulations, for the appropriate choice of parameter values, exhibit 2D versions of most of the phenomena mentioned above.

Viscous fingering of a miscible reactive interface for an infinitely fast chemical reaction: Nonlinear simulations
View Description Hide DescriptionNonlinear dynamics of miscibleviscous fingering is analyzed numerically for a reactive system when a solution containing a reactant is displacing another misciblesolution containing another reactant . A simple reaction takes place upon contact of the solutions. The viscosity of the fluid depends on the concentration of the various chemicals. The nonlinear fingering dynamics is studied numerically for an infinite Damköhler number , i.e., for an infinitely fast reaction as a function of the logmobility ratios and quantifying the viscosity ratios of the solutions of and , respectively, versus that of the solution of . If , i.e., if the system is genuinely viscously unstable because the displacing solution of is less viscous than the displaced solution of , we analyze the changes to classical nonreactive viscous fingering induced by the reaction. If on the contrary , which corresponds to a hydrodynamically stable case in absence of reactions, we study chemically driven viscous fingering occurring when the chemical reaction triggers a nonmonotonic viscosity profile. Comparison between the present simulation results and corresponding linear stability analysis and experiments is also conducted.
 Particulate, Multiphase, and Granular Flows

Some exact solutions for debris and avalanche flows
View Description Hide DescriptionExact analytical solutions to simplified cases of nonlinear debris avalanchemodelequations are necessary to calibrate numerical simulations of flow depth and velocity profiles on inclined surfaces. These problemspecific solutions provide important insight into the full behavior of the system. In this paper, we present some new analytical solutions for debris and avalancheflows and then compare these solutions with experimental data to measure their performance and determine their relevance. First, by combining the mass and momentum balance equations with a Bagnold rheology, a new and special kinematic wave equation is constructed in which the flux and the wave celerity are complex nonlinear functions of the pressure gradient and the flow depth itself. The new model can explain the mechanisms of wave advection and distortion, and the quasiasymptotic front bore observed in many natural and laboratory debris and granular flows. Exact timedependent solutions for debris flow fronts and associated velocity profiles are then constructed. We also present a novel semiexact twodimensional plane velocity field through the flow depth. Second, starting with the force balance between gravity, the pressure gradient, and Bagnold’s graininertia or macroviscous forces, we construct a simple and very special nonlinear ordinary differential equation to model the steady state debris front profile. An empirical pressure gradient enhancement factor is introduced to adequately stretch the flow front and properly model nonhydrostatic pressure in granular and debris avalanches. An exact solution in explicit form is constructed, and is expressed in terms of the Lambert–Euler omega function. Third, we consider rapid flows of frictional granular materials down a channel. The steady state mass and the momentum balance equations are combined together with the Coulomb friction law. The Chebyshev radicals are employed and the exact solutions are developed for the velocity profile and the debris depth. Similarly, Bagnold’s fluids are also used to construct alternative exact solutions. Many interesting and important aspects of all these exact solutions, their applications to realflow situations, and the influence of model parameters are discussed in detail. These analytical solutions, although simple, compare very well with experimental data of debris flows, granular avalanches, and the wave tips of dam break flows. A new scaling law for Bagnold’s fluids is established to relate the settlement time of debris deposition. It is found analytically that the macroviscous fluid settles (comes to a standstill) considerably faster than the graininertia fluid, as manifested by dispersive pressure.

Rotation and alignment of rods in twodimensional chaotic flow
View Description Hide DescriptionWe study the dynamics of rod shaped particles in twodimensional electromagnetically driven fluid flows. Two separate types of flows that exhibit chaotic mixing are compared: one with timeperiodic flow and the other with constant forcing but nonperiodic flow. Video particle tracking is used to make accurate simultaneous measurements of the motion and orientation of rods along with the carrier fluid velocity field. These measurements allow a detailed comparison of the motion and orientation of rods with properties of the carrier flow.Measured rod rotation rates are in agreement with predictions for ellipsoidal particles based on the measuredvelocity gradients at the center of the rods. There is little dependence on length for the rods we studied (up to 53% of the length scale of the forcing). Rods are found to align weakly with the extensional direction of the strainrate tensor. However, the alignment is much stronger with the direction of Lagrangian stretching defined by the eigenvectors of the Cauchy–Green deformation tensor. A simple model of the stretching process predicts the degree of alignment of rods with the stretching direction.