Volume 26, Issue 7, July 2014

We study the near field of a zeronetmassflux (ZNMF) actuated round jet using direct numerical simulations. The Reynolds number of the jet Re D = 2000 and three ZNMF actuators are used, evenly distributed over a circle, and directed towards the main jet. The actuators are triggered in phase, and have a relatively low momentum coefficient of C μ = 0.0049 each. We study four different control frequencies with Strouhal numbers ranging from St D = 0.165 to St D = 1.32; next to that, also two uncontrolled baseline cases are included in the study. We find that this type of ZNMF actuation leads to strong deformations of the nearfield jet region that are very similar to those observed for noncircular jets. At the end of the jet's potential core (x/D = 5), the jetcolumn cross section is deformed into a hexagramlike geometry that results from strong modifications of the vortex structures. Two mechanisms lead to these modifications, i.e., (i) selfdeformation of the jet's primary vortex rings started by distortions in their azimuthal curvature by the actuation, and (ii) production of side jets by the development and subsequent detachment of secondary streamwise vortex pairs. Further downstream (x/D = 10), the jet transforms into a triangular pattern, as the sharp corner regions of the hexagram entrain fluid and spread. We further investigate the global characteristics of the actuated jets. In particular when using the jet preferred frequency, i.e., St D = 0.33, parameters such as entrainment, centerline decay rate, and mean turbulent kinetic energy are significantly increased. Furthermore, high frequency actuation, i.e., St D = 1.32, is found to suppress the mechanisms leading to large scale structure growth and turbulent kinetic energy production. The simulations further include a passive scalar equation, and passive scalar mixing is also quantified and visualized.
 ANNOUNCEMENTS


Announcement: Changes in the Editorial Organization of Physics of Fluids
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Radiation induces turbulence in particleladen fluids
View Description Hide DescriptionWhen a transparent fluid laden with solid particles is subject to radiative heating, nonuniformities in particle distribution result in local fluid temperature fluctuations. Under the influence of gravity, buoyancy induces vortical fluid motion which can lead to strong preferential concentration, enhancing the local heating and more nonuniformities in particle distribution. By employing direct numerical simulations this study shows that the described feedback loop can create and sustain turbulence. The velocity and length scale of the resulting turbulence is not known a priori, and is set by balance between viscous forces and buoyancy effects. When the particle response time is comparable to a viscous time scale, introduced in our analysis, the system exhibits intense fluctuations of turbulent kinetic energy and strong preferential concentration of particles.
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 ARTICLES

 Biofluid Mechanics

Heat transfer and tear film dynamics over multiple blink cycles
View Description Hide DescriptionWe consider model problems for the tear film over multiple blink cycles with heat transfer from the posterior side of the tear film. A nonlinear partial differential equation governs the film thickness on a moving domain in one space dimension and time. One end of the tear film moves in order to mimic blinking in the eye. The film thickness is coupled with the diffusion of heat from the posterior of the film, where the underlying cornea and aqueous humor are modeled as a rectangular domain. The domain of the tear film is located on one edge of the rectangle. The resulting problem is solved using the method of lines with a Chebyshev spectral method in space. Evaporation is included in the model, with end fluxes specified to compensate for the evaporation from the film. The numerical results reveal a similarity to quantitative in vivo observations of the film dynamics and measured ocular surface temperature. Periodicity in the film and temperature dynamics is explored with different flux conditions and end motions, and a transition between periodic and nonperiodic solutions is analyzed.

Dynamics of swimming bacteria at complex interfaces
View Description Hide DescriptionFlagellated bacteria exploiting helical propulsion are known to swim along circular trajectories near surfaces. Fluid dynamics predicts this circular motion to be clockwise (CW) above a rigid surface (when viewed from inside the fluid) and counterclockwise (CCW) below a free surface. Recent experimental investigations showed that complex physicochemical processes at the nearby surface could lead to a change in the direction of rotation, both at solid surfaces absorbing slipinducing polymers and interfaces covered with surfactants. Motivated by these results, we use a farfield hydrodynamic model to predict the kinematics of swimming near three types of interfaces: clean fluidfluid interface, slipping rigid wall, and a fluid interface covered by incompressible surfactants. Representing the helical swimmer by a superposition of hydrodynamic singularities, we first show that in all cases the surfaces reorient the swimmer parallel to the surface and attract it, both of which are a consequence of the Stokes dipole component of the swimmer flow field. We then show that circular motion is induced by a higherorder singularity, namely, a rotlet dipole, and that its rotation direction (CW vs. CCW) is strongly affected by the boundary conditions at the interface and the bacteria shape. Our results suggest thus that the hydrodynamics of complex interfaces provide a mechanism to selectively stir bacteria.

Probing interfacial dynamics and mechanics using submerged particle microrheology. I. Theory
View Description Hide DescriptionMicrorheology relies on tracking the thermal or driven motion of microscopic particles in a soft material. It is well suited to the study of materials that have no threedimensional realization, which makes them difficult to study using a macroscopic rheometer. For this reason, microrheology is becoming an important rheological probe of Langmuir monolayers and membranes. Interfacial microrheology, however, has been difficult to reconcile quantitatively with more traditional macroscopic approaches. We suggest that uncertainties in accounting for the mechanical coupling of the tracer particle to the interface or membrane are responsible for these discrepancies. To resolve them, we propose a new noncontact approach to interfacial microrheology that uses particles submerged in the subphase a known distance below the interface. In this first of two papers, we present calculations of the response function (and thus the equilibrium fluctuation spectrum) of a spherical particle submerged below a viscoelastic surface that has a finite surface tension and/or bending modulus. In the second paper, we compare these results to submerged particle microrheology in a few example systems, showing quantitative agreement.

Probing interfacial dynamics and mechanics using submerged particle microrheology. II. Experiment
View Description Hide DescriptionA noncontact microrheological technique to probe the mechanics of the air/water interface is explored. Polystyrene spheres dissolved in water are trapped with an optical tweezer near the free surface of water, allowing the response functions of the particles to be measured as a function of the distance from the air/water interface. These measurements show that at the surface, the imaginary part of the response function increases by approximately 30% from the Stokes value measured in the bulk. As the particle is moved away from the surface via an optical trap, the response function returns to the bulk value. The method is tested by comparing the response function of particles near a rigid wall to the theory developed by Faxèn. A newly developed hydrodynamic theory is used to explain the results at the free interface through a calculation of the linear response function as a function of depth. These results show a range of sensitivity that can be utilized to study the microrheology of a Langmuir monolayer without distorting its structure.

Motor characteristics determine the rheological behavior of a suspension of microswimmers
View Description Hide DescriptionA suspension of motile cells exhibits complex rheological properties due to their collective motion. We measure the shear viscosity of a suspension of Escherichia coli strains varying in motor characteristics such as duration of run and tumble. At low cell densities, all strains irrespective of their motor characteristics exhibit a linear increase in viscosity with cell density suggesting that the cells behave as a suspension of passive rods with an effective aspect ratio set by the motor characteristics of the bacteria. As the cell density is increased beyond a critical value, the viscosity drops sharply signaling the presence of strongly coordinated motion among bacteria. The critical density depends not only on the magnitude of shear but also the motor characteristics of individual cells. High shear rate disrupts the coordinated motion reducing its behavior, once again, to a suspension of inactive particles.

Liftdrag and flow structures associated with the “clap and fling” motion
View Description Hide DescriptionThe present study focuses on the analysis of the fluid dynamics associated with the flapping motion of finitethickness wings. A twodimensional numerical model for one and twowinged “clap and fling” stroke has been developed to probe the aerodynamics of insect flight. The influence of kinematic parameters such as the percentage overlap between translational and rotational phase ξ, the separation between two wings δ and Reynolds numbers Re on the evolvement of lift and drag has been investigated. In addition, the roles of the leading and trailing edge vortices on lift and drag in clap and fling type kinematics are highlighted. Based on a surrogate analysis, the overlap ratio ξ is identified as the most influential parameter in enhancing lift. On the other hand, with increase in separation δ, the reduction in drag is far more dominant than the decrease in lift. With an increase in Re (which ranges between 8 and 128), the mean drag coefficient decreases monotonously, whereas the mean lift coefficient decreases to a minimum and increases thereafter. This behavior of lift generation at higher Re was characterized by the “wingwake interaction” mechanism which was absent at low Re.

On the absence of asymmetric wakes for periodically plunging finite wings
View Description Hide DescriptionIt has previously been shown that, at high Strouhal numbers, oscillating airfoils can produce deflected jets that can create very high liftcoefficients for otherwise symmetric scenarios. These deflected jets form through pairing of the trailingedge vortices to create asymmetric vortex couples that selfpropel at an angle to the freestream, resulting in an asymmetric flow field and nonzero lift. In this paper results are presented that indicate these highlift deflected jets cannot form for finite wings. Instead of the straight vortex tubes that pair and convect at an angle to the freestream observed for effectively infinite wings, finite wings exhibit vortex tubes that break into two branches near the tip forming double helix structures. One branch connects with the last vortex; one branch connects with the next vortex. This creates a long “daisy chain” of interconnected trailing edge vortices forming a long series of vortex loops. These symmetric flow fields are shown to persist for finite wings even to Strouhal numbers more than twice those required to produce asymmetric wakes on plunging airfoils. Two contributing reasons are discussed for why deflected jets are not observed. First the tip vortex creates threedimensionality that discourages vortex coupling. Second, the symmetry of the circulation of the interconnected vortex loops, which has been confirmed by the experiments, is a natural consequence of the vortex topology. Therefore, the asymmetry in trailing edge vortex strength previously observed as characteristic of deflected jets cannot be supported for finite wings.
 Micro and Nanofluid Mechanics

Fluid structure in the immediate vicinity of an equilibrium threephase contact line and assessment of disjoining pressure models using density functional theory
View Description Hide DescriptionWe examine the nanoscale behavior of an equilibrium threephase contact line in the presence of longranged intermolecular forces by employing a statistical mechanics of fluids approach, namely, density functional theory (DFT) together with fundamental measure theory (FMT). This enables us to evaluate the predictive quality of effective Hamiltonian models in the vicinity of the contact line. In particular, we compare the results for mean field effective Hamiltonians with disjoining pressures defined through (i) the adsorption isotherm for a planar liquid film, and (ii) the normal force balance at the contact line. We find that the height profile obtained using (i) shows good agreement with the adsorption film thickness of the DFTFMT equilibrium density profile in terms of maximal curvature and the behavior at large film heights. In contrast, we observe that while the height profile obtained by using (ii) satisfies basic sum rules, it shows little agreement with the adsorption film thickness of the DFT results. The results are verified for contact angles of 20°, 40°, and 60°.

Does liquid slippage within a rough channel always increase the flow rate?
View Description Hide DescriptionSlippage of liquid over rough superhydrophobic surfaces that induce the CassieBaxter state decreases frictional force on the flow. This may easily lead to a hasty conclusion that liquid slip enhances the flow rate in rough channels. Here, we show that flow rates can be rather reduced by roughening and hydrophobizing microchannel walls to support liquid slippage, depending on the topography of the roughness. We consider theoretical models that predict liquid flow rates in channels of different roughness and wetting conditions, to construct criteria for the surface structure that determine whether slip or noslip would be advantageous in enhancing flow rates. It is shown that liquid slips are advantageous only in channels with highly hydrophobic, short, sparsely distributed protrusions. We corroborate our theoretical predictions with microchannels decorated with micropillars of varying wettabilities.

Method of determining kinetic boundary conditions in net evaporation/condensation
View Description Hide DescriptionThe aim of the present study is to develop the method of determining the kinetic boundary condition (KBC) at a vaporliquid interface in net evaporation/condensation. We proposed a novel method for determining the KBC by combining the numerical simulations of the mean field kinetic theory and the molecular gas dynamics. The method was evaluated on steady vapor flow between two liquid slabs at different temperatures. A uniform net mass flux in the vapor phase induced by net evaporation and condensation is obtained from the numerical simulation of the mean field kinetic theory for both vapor and liquid phases. The KBC was specified by using the uniform net mass flux, and the numerical simulation of the molecular gas dynamics was conducted for the vapor phase. Comparing the macroscopic variables in the vapor phase obtained from both numerical simulations, we can validate the KBC whether the appropriate solutions are obtained. Moreover, the evaporation and condensation coefficients were estimated uniquely. The results showed that the condensation and evaporation coefficients were identical and constant in net evaporation. On the other hand, in net condensation, the condensation coefficient increased with the collision molecular mass flux. We also presented the applicable limit of the KBC which is assumed to be the isotropic Gaussian distribution at the liquid temperature. From these results, the KBCs in net evaporation and condensation, which enable the exact macroscopic variables to be determined, were proposed.
 Interfacial Flows

Travelling wave dipolophoresis of ideally polarizable nanoparticles with overlapping electric double layers in cylindrical pores
View Description Hide DescriptionWe provide a general integral formulation for the dipolophoretic transport of a polarizable colloid in a likewise polarizable nanochannel which takes into account electric double layer (EDL) overlap between the channel walls and resultant background flow as well as the overlap between the wall EDL and that of the particle. The analysis is based on extension of the Lorentz reciprocal theorem for Stokes flows and necessitates the solving of two auxiliary problems; the background inducedcharge electroosmotic flow in the channel and the Stokesian motion of a nanoparticle under confinement. To demonstrate our general methodology, we provide a closed form analytical solution for the specific case of a polarizable spherical colloid, located at the axis of a cylindrical nanopore whose walls are subject to a travellingwave alternatingcurrent electric signal. We quantify the level of EDL overlap via the introduction of a new parameter, ξ which represents the undefined ionic density at the centerline under Boltzmann distribution and depends on the EDL thickness, λ0. Both the background electroosmotic flow and the phoretic velocity of the particle are found to be a function of the frequency of the applied field, while displaying distinct dispersion characteristics. In the thin EDL limit, maximum velocity and mass transport are obtained in the kiloHertz range.

Airwater centrifugal convection
View Description Hide DescriptionA sealed cylindrical container is filled with air and water. The container rotation and the axial gradient of temperature induce the steady axisymmetric meridional circulation of both fluids due to the thermal buoyancy and surfacetension (Marangoni) effects. If the temperature gradient is small, the water circulation is onecellular while the air circulation can be one or twocellular depending on water fraction Wf. The numerical simulations are performed for the cylinder lengthtoradius ratio l = 1 and l = 4. The l = 4 results and the analytical solution for l → ∞ agree in the cylinder's middle part. As the temperature gradient increases, the water circulation becomes one, two, or threecellular depending on Wf. The results are of fundamental interest and can be applied for bioreactors.

Bag breakup of low viscosity drops in the presence of a continuous air jet
View Description Hide DescriptionThis work examines the breakup of a single drop of various low viscosity fluids as it deforms in the presence of continuous horizontal air jet. Such a fragmentation typically occurs after the bulk liquid has disintegrated upon exiting the atomizer and is in the form of an ensemble of drops which undergo further breakup. The drop deformation and its eventual disintegration is important in evaluating the efficacy of a particular industrial process, be it combustion in automobile engines or pesticide spraying in agricultural applications. The interplay between competing influences of surface tension and aerodynamic disruptive forces is represented by the Weber number, We, and Ohnesorge number, Oh, and used to describe the breakup morphology. The breakup pattern considered in our study corresponds to that of a bag attached to a toroidal ring which occurs from ∼12 < We < ∼16. We aim to address several issues connected with this breakup process and their dependence on We and Oh which have been hitherto unexplored. The We boundary at which breakup begins is theoretically determined and the expression obtained, , is found to match well with experimental data {[L.P. Hsiang and G. M. Faeth, Int. J. Multiphase Flow21(4), 545–560 (1995)] and [R. S. Brodkey, “Formation of drops and bubbles,” in The Phenomena of Fluid Motions (AddisonWesley, Reading, 1967)]}. An exponential growth in the radial extent of the deformed drop and the streamline dimension of the bag is predicted by a theoretical model and confirmed by experimental findings. These quantities are observed to strongly depend on We. However, their dependence on Oh is weak.

Postbreakup solutions of NavierStokes and Stokes threads
View Description Hide DescriptionWe consider the breakup of a fluid thread, neglecting the effect of the outside fluid (or air). After breakup, the solution of the fluid equations consists of two threads, receding rapidly from the point of breakup. We show that the bulk of each thread is described by a similarity solution of slender geometry (which we call the thread solution), but which breaks down near the tip. Near the tip of the thread the thread solution can be matched to a solution of Stokes' equation, which consists of a finger of constant spatial radius, rounded at the end. Very close to breakup, the thread solution balances inertia, viscosity, and surface tension (NavierStokes case). If however the fluid viscosity is large (as measured by the dimensionless Ohnesorge number), some time after breakup the thread solution consists of a balance of surface tension and viscosity only (Stokes case), and the thread profile can be described analytically.

Free surface due to a flow driven by a rotating disk inside a vertical cylindrical tank: Axisymmetric configuration
View Description Hide DescriptionThe flow driven by a rotating disk at the bottom of an open fixed cylindrical cavity is studied numerically and experimentally. The steady axisymmetric NavierStokes equations projected onto a curvilinear coordinate system are solved by a NewtonRaphson algorithm. The free surface shape is computed by an iterative process in order to satisfy a zero normal stress balance at the interface. In previous studies, regarding the free surface deflection, there is a significant disagreement between a firstorder approximation [M. Piva and E. Meiburg, “Steady axisymmetric flow in an open cylindrical container with a partially rotating bottom wall,” Phys. Fluids17, 063603 (2005)] and a full numerical simulation [R. Bouffanais and D. Lo Jacono, “Unsteady transitional swirling flow in the presence of a moving free surface,” Phys. Fluids21, 064107 (2009)]. For a small deflection, the firstorder approximation matches with our numerical simulation and for a large deflection a good agreement is found with experimental measurements.

Behavior of oscillatory tube flow at liquidgas interfaces
View Description Hide DescriptionOscillatory flow in a long tube is characterized by an annular axial velocity profile far away from the boundaries for which an analytical solution exists. The radial velocity component is zero. Near the entrance or free surface region, this analytic solution does not hold due to the boundary conditions. Herein, the flow behavior at a liquidgas as well as liquidwall interface is investigated in detail by means of flow visualization measurements and Particle Image Velocimetry. The results suggest an additional radial velocity component due to the influence of the boundary. An investigation of the phase locked flow depicts the generation of steady streaming below the free surface which could be identified by vortex rings. Their shape and velocities vary according to the boundary conditions. For low frequencies, the streaming patterns are similar for cases with liquidgas and liquidwall interface denoting that the surface tension does not play a role for these cases. The oscillatory amplitude dominates streaming strength. As the Womersley number increases the free surface becomes unstable and Faraday waves occur which are further analysed here. This instability interacts with the steady streaming patterns which causes a change in shape and increases the streaming strength.

Flow around a corner in the water impact problem
View Description Hide DescriptionIn this work, we study the local flow in the vicinity of a flat sector of arbitrary angle α in the water impact problem as motivated by recent experimental observations in the author's laboratory. The key question is as to why the ejecta formed during the impact at zero deadrise angle is considerably higher along a straight edge of the sector compared to that near a sharp corner α < π, e.g., if the impacting body is a rectangular plate. Resolving this question is made possible by the discovered here mathematical equivalence of the problem to electromagnetic diffraction phenomena. The main result of the present study is the revealed and quantified influence of the geometry of a flat plate corner on the fluid flow around it, which also contributes to the understanding of certain threedimensional effects in the water impact problem and provides a generalization of the classical twodimensional results on the impact at zero deadrise angle. The offered theoretical solution is also qualitatively supported with the help of particle image velocimetry measurements.

The water entry of slender axisymmetric bodies
View Description Hide DescriptionWe present a study of the forces, velocities, and trajectories of slender (length/diameter = 10) axisymmetric projectiles using an embedded inertial measurement unit (IMU). Three nose shapes (cone, ogive, and flat) were used. Projectiles were tested at vertical and oblique impact angles with different surface treatments. The trajectory of a halfhydrophobic and halfhydrophilc case impacting vertically was compared to the trajectory of symmetrically coated projectiles impacting the free surface at oblique angles. The oblique impact cases showed significantly more final lateral displacement than the halfandhalf case over the same depth. The amount of lateral displacement was also affected by the nose shape, with the cone nose shape achieving the largest lateral displacement for the oblique entry case. Instantaneous lift and drag coefficients were calculated using data from the IMU for the vertical, halfandhalf, and oblique entry cases. Impact forces were calculated for each nose shape and the flat nose shape experienced the largest impulsive forces up to 37 N when impacting vertically. The impact force of the flat nose decreased for the oblique entry case. The location of the center of pressure was determined at discrete time steps using a theoretical torque model and values from the IMU. Acoustic spectrograms showed that the sound produced during the water entry event predominately arises from the pinchoff for the cone and ogive nose shapes, with additional sound production from impact for the flat nose shape. Each test run was imaged using two Photron SA3 cameras.