Volume 26, Issue 4, April 2014

Experimental and analytical results are presented on two identical bioinspired hydrofoils oscillating in a sidebyside configuration. The timeaveraged thrust production and power input to the fluid are found to depend on both the oscillation phase differential and the transverse spacing between the foils. For inphase oscillations, the foils exhibit an enhanced propulsive efficiency at the cost of a reduction in thrust. For outofphase oscillations, the foils exhibit enhanced thrust with no observable change in the propulsive efficiency. For oscillations at intermediate phase differentials, one of the foils experiences a thrust and efficiency enhancement while the other experiences a reduction in thrust and efficiency. Flow visualizations reveal how the wake interactions lead to the variations in propulsive performance. Vortices shed into the wake from the tandem foils form vortex pairs rather than vortex streets. For inphase oscillation, the vortex pairs induce a momentum jet that angles towards the centerplane between the foils, while outofphase oscillations produce vortex pairs that angle away from the centerplane between the foils.
 LETTERS


Vortexinduced drag and the role of aspect ratio in undulatory swimmers
View Description Hide DescriptionDuring cruising, the thrust produced by a selfpropelled swimmer is balanced by a global drag force. For a given object shape, this drag can involve skin friction or form drag, both being welldocumented mechanisms. However, for swimmers whose shape is changing in time, the question of drag is not yet clearly established. We address this problem by investigating experimentally the swimming dynamics of undulating thin flexible foils. Measurements of the propulsive performance together with full recording of the elastic wave kinematics are used to discuss the general problem of drag in undulatory swimming. We show that a major part of the total drag comes from the trailing longitudinal vortices that rollup on the lateral edges of the foils. This result gives a comparative advantage to swimming foils of larger span thus bringing new insight to the role of aspect ratio for undulatory swimmers.

On the extension of the eddy viscosity model to compressible flows
View Description Hide DescriptionIn the paper the authors examine the extension of the eddy viscosity modeling approach to compressible large eddy simulation. On the basis of formal algebraic relations among the generalized central moments and the filtered Favre terms, a new compressible eddy viscosity formulation is derived.

Viscosity of liquid ^{4}He and quantum of circulation: Are they related?
View Description Hide DescriptionIn the vicinity of the superfluid transition in liquid ^{4}He, we explore the relation between two apparently unrelated physical quantities—the kinematic viscosity, ν, in the normal state and the quantum of circulation, κ, in the superfluid state. The model developed here leads to the simple relationship ν ≈ κ/6, and links the classical and quantum flow properties of liquid ^{4}He. We critically examine available data relevant to this relation and find that the prediction holds well at the saturated vapor pressure. Additionally, we predict the kinematic viscosity for liquid ^{4}He along the λline at negative pressures.

The effect of the Basset history force on particle clustering in homogeneous and isotropic turbulence
View Description Hide DescriptionWe study the effect of the Basset history force on the dynamics of small particles transported in homogeneous and isotropic turbulence and show that this term, often neglected in previous numerical studies, reduces the smallscale clustering typical of inertial particles. The contribution of this force to the total particle acceleration is, on average, responsible for about 10% of the total acceleration and particularly relevant during rare strong events. At moderate density ratios, i.e., sand or metal powder in water, its presence alters the balance of forces determining the particle acceleration.
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 ARTICLES

 Biofluid Mechanics

Swimming and pumping of rigid helical bodies in viscous fluids
View Description Hide DescriptionRotating helical bodies of arbitrary crosssectional profile and infinite length are explored as they swim through or transport a viscous fluid. The Stokes equations are studied in a helical coordinate system, and closed form analytical expressions for the forcefree swimming speed and torque are derived in the asymptotic regime of nearly cylindrical bodies. Highorder accurate expressions for the velocity field and swimming speed are derived for helical bodies of finite pitch angle through a double series expansion. The analytical predictions match well with the results of full numerical simulations, and accurately predict the optimal pitch angle for a given crosssectional profile. This work may improve the modeling and design of helical structures used in microfluidic manipulation, synthetic microswimmer engineering, and the transport and mixing of viscous fluids.

Comparison of erythrocyte dynamics in shear flow under different stressfree configurations
View Description Hide DescriptionAn open question that has persisted for decades is whether the cytoskeleton of a red blood cell is stressfree or under a stress. This question is important in the context of theoretical modeling of cellular motion under a flowing condition where it is necessary to make an assumption about the stressfree state. Here, we present a 3D numerical study to compare the cell dynamics in a simple shear flow under two different stressfree states, a biconcave discocyte representing the resting shape of the cell, and a nearly spherical oblate shape. We find that whether the stressfree states make a significant difference or not depends on the viscosity of the suspending medium. If the viscosity is close to that of blood plasma, the two stressfree states do not show any significant difference in cell dynamics. However, when the suspending medium viscosity is well above that of the physiological range, as in many in vitro studies, the shear rate separating the tanktreading and tumbling dynamics is observed to be higher for the biconcave stressfree state than the spheroidal state. The former shows a strong shape oscillation with repeated departures from the biconcave shape, while the latter shows a nearly stable biconcave shape. It is found that the cell membrane in the biconcave stressfree state is under a compressive stress and a weaker bending force density, leading to a periodic compression of the cell. The shape oscillation then leads to a higher energy barrier against membrane tanktread leading to an early transition to tumbling. However, if the cells are released with a large offshear plane angle, the oscillations can be suppressed due to an azimuthal motion of the membrane along the vorticity direction leading to a redistribution of the membrane points and lowering of the energy barrier, which again results in a nearly similar behavior of the cells under the two different stressfree states. A variety of offshear plane dynamics is observed, namely, rolling, kayaking, precession, and a new dynamics termed “hovering.” For the physiological viscosity range, the shearplane tumbling appears to be relatively less common, while the rolling is observed to be more stable.

Propulsive performance of unsteady tandem hydrofoils in a sidebyside configuration
View Description Hide DescriptionExperimental and analytical results are presented on two identical bioinspired hydrofoils oscillating in a sidebyside configuration. The timeaveraged thrust production and power input to the fluid are found to depend on both the oscillation phase differential and the transverse spacing between the foils. For inphase oscillations, the foils exhibit an enhanced propulsive efficiency at the cost of a reduction in thrust. For outofphase oscillations, the foils exhibit enhanced thrust with no observable change in the propulsive efficiency. For oscillations at intermediate phase differentials, one of the foils experiences a thrust and efficiency enhancement while the other experiences a reduction in thrust and efficiency. Flow visualizations reveal how the wake interactions lead to the variations in propulsive performance. Vortices shed into the wake from the tandem foils form vortex pairs rather than vortex streets. For inphase oscillation, the vortex pairs induce a momentum jet that angles towards the centerplane between the foils, while outofphase oscillations produce vortex pairs that angle away from the centerplane between the foils.

Oscillating motions of neutrally buoyant particle and red blood cell in Poiseuille flow in a narrow channel
View Description Hide DescriptionTwo motions of oscillation and vacillating breathing (swing) of red blood cell with a stiffened membrane have been observed in bounded Poiseuille flows [L. Shi, T.W. Pan, and R. Glowinski, “Deformation of a single blood cell in bounded Poiseuille flows,” Phys. Rev. E85, 16307 (2012)]. To understand such motions, we have compared them with the oscillating motion of a neutrally buoyant particle of the same shape in Poiseuille flow in a narrow channel since a suspended cell is actually a neutrally buoyant entity. In a narrow channel, the particle can be held in the central region for a while with its mass center moving up and down if it is placed at the centerline initially. Its inclination angle oscillates at the beginning; but its range of oscillation keeps increasing and at the end the particle tumbles when the particle migrates away from the centerline due to the inertia effect. When the particle mass center is restricted to move only on the channel centerline, the inclination angle has been locked to a fixed angle without oscillation. Since the mass center of a deformable cell always migrates toward the channel central region in Poiseuille flow, its inclination angle behaves similar to the aforementioned oscillating motion of the particle as long as the cell keeps the long body shape and moves up and down. But when the upanddown oscillation of the cell mass center damps out, the oscillating motion of the inclination angle also damps out and the cell inclination angle also approaches to a fixed angle.

Linear instability mechanisms leading to optimally efficient locomotion with flexible propulsors
View Description Hide DescriptionWe present the linear stability analysis of experimental measurements obtained from unsteady flexible pitching panels. The analysis establishes the connections among the wake dynamics, propulsor dynamics, and Froude efficiency in flexible unsteady propulsion systems. Efficiency is calculated from direct thrust and power measurements and wake flowfields are obtained using particle image velocimetry. It is found that for flexible propulsors every peak in efficiency occurs when the driving frequency of motion is tuned to a wake resonant frequency, not a structural resonant frequency. Also, there exists an optimal flexibility that globally maximizes the efficiency. The optimal flexibility is the one where a structural resonant frequency is tuned to a wake resonant frequency. The optimally tuned flexible panels demonstrate an efficiency enhancement of 122%–133% as compared to an equivalent rigid panel and there is a broad spectrum of wake resonant frequencies allowing high efficiency swimming over a wide range of operating conditions. At a wake resonant frequency we find that the entrainment of momentum into the timeaveraged velocity jet is maximized.
 Micro and Nanofluid Mechanics

Role of solution conductivity in reaction induced charge autoelectrophoresis
View Description Hide DescriptionCatalytic bimetallic Janus particles swim by a bipolar electrochemical propulsion mechanism that results from electroosmotic fluid slip around the particle surface. The flow is driven by electrical body forces which are generated from a coupling of a reactioninduced electric field and net charge in the diffuse layer surrounding the particle. This paper presents simulations, scaling, and physical descriptions of the experimentally observed trend that the swimming speed decays rapidly with increasing solution conductivity. The simulations solve the full PoissonNernstPlanckStokes equations with multiple ionic species, a cylindrical particle in an infinite fluid, and nonlinear ButlerVolmer boundary conditions to represent the electrochemical surface reactions. The speed of bimetallic particles is reduced in highconductivity solutions because of reductions in the induced electric field in the diffuse layer near the rod, the total reaction rate, and the magnitude of the rod zeta potential. This work suggests that the autoelectrophoretic mechanism is inherently susceptible to speed reductions in higher ionic strength solutions.

Stability of bubbly liquids and its connection to the process of cavitation inception
View Description Hide DescriptionThis paper presents a potential energy approach for the investigation of the stability of bubbly liquids. Using the system's free energy variations with respect to the void fraction as a stability criterion for the whole system, we consider that sudden bubble expansion occurs only when the bubble cluster expansion is energetically favorable. The results obtained provide new insight into the behavior of prenucleated liquids when the inception point is reached as well as a simple method to estimate the energy exchanges between a bubble cluster and its environment when the kinetic energy is negligible compared to the elastic energy stored during tension and compression processes. In addition to the radius of the initial nuclei, the concentration and polydispersity are shown to exert an important influence on the response of the system after inception.
 Interfacial Flows

Interfacial stress balances in structured continua and free surface flows in ferrofluids
View Description Hide DescriptionInterfacial linear and internal angular momentum balances are obtained for a structured continuum and for the special case of a ferrofluid, a suspension of magnetic nanoparticles in a Newtonian fluid. The interfacial balance equations account for the effects of surface tension and surface tension gradient, magnetic surface excess forces, antisymmetric stresses, and couple stresses in driving interfacial flows in ferrofluids. Application of the interfacial balance equations is illustrated by obtaining analytical expressions for the translational and spin velocity profiles in a thin film of ferrofluid on an infinite flat plate when a rotating magnetic field is applied with axis of rotation parallel to the ferrofluid/air interface. The cases of zero and nonzero spin viscosity are considered for small applied magnetic field amplitude. Expressions for the maximum translational velocity, slope of the translational velocity profile at the ferrofluid/air interface, and volumetric flow rate are obtained and their use to test the relevance of spin viscosity and couple stresses in the flow situation under consideration is discussed.

Thinliquidfilm flow on a topographically patterned rotating cylinder
View Description Hide DescriptionThe flow of thin liquid films on rotating surfaces is directly relevant to the coating of discrete objects. To begin understanding how surface topography influences such flows, we consider a model problem in which a thin liquid film flows over a rotating cylinder patterned with a sinusoidal surface topography. Lubrication theory is applied to develop a partial differential equation that governs the film thickness as a function of time and the angular coordinate. Static situations are considered first in order to determine the parameter regime in which the lubrication approximation is expected to be valid. When gravitational forces are relatively weak, cylinder rotation leads to the formation of droplets connected by very thin films. The number of droplets is equal to the pattern frequency at low and high rotation rates, with the droplets located at the pattern troughs at low rotation rates and the pattern crests at high rotation rates. When gravitational forces become significant, the film thickness never reaches a steady state, in contrast to the case of an unpatterned cylinder. The results of this work clearly establish that the flow of thin liquid films on rotating surfaces can be very sensitive to the presence of surface topography.

Jet orientation of a collapsing bubble near a solid wall with an attached air bubble
View Description Hide DescriptionThe interaction between a cavitation bubble and a nonoscillating air bubble attached to a horizontal polyvinyl chloride plate submerged in deionized water is investigated using a lowvoltage sparkdischarge setup. The attached air bubble is approximately hemispherical in shape, and its proximity to a sparkinduced oscillating bubble (represented by the dimensionless standoff distance H ^{′}) determines whether or not a jet is formed in the oscillating bubble during its collapse. When the oscillating bubble is created close to the plate, it jets towards or away from the plate. The ratio of oscillating bubble oscillation time and the wallattached bubble oscillation time (T ^{′}) is found to be an important parameter for determining the jet direction. This is validated with numerical simulations using an axialsymmetrical boundary element model. Our study highlights prospects in reducing cavitation damage with a stationary bubble, and in utilizing a cavitation collapse jet by controlling the jet's direction.

Jet impingement and the hydraulic jump on horizontal surfaces with anisotropic slip
View Description Hide DescriptionThis paper presents an analysis that describes the dynamics of laminar liquid jet impingement on horizontal surfaces with anisotropic slip. Due to slip at the surface and the anisotropy of its magnitude, the overall behavior departs notably from classical results. For the scenario considered the slip length varies as a function of the azimuthal coordinate and describes superhydrophobic surfaces micropatterned with alternating ribs and cavities. The thin film dynamics are modeled by a radial momentum analysis for a given jet Reynolds number and specified slip length and the influence of slip on the entire flow field is significant. In an average sense the thin film dynamics exhibit similarities to behavior that exists for a surface with isotropic slip. However, there are also important deviations that are a direct result of the azimuthally varying slip and these become more pronounced at higher Reynolds numbers and at greater slip lengths. The analysis also allows determination of the azimuthally varying radial location of the hydraulic jump that forms due to an imposed downstream depth. Departure from the no slip case and from the scenario of isotropic slip is characterized over a range of jet Reynolds numbers and realistic slip length values. The results show that for all cases the hydraulic jump is elliptical, with eccentricity increasing as the Reynolds number or slip length increases, or as the downstream depth decreases. The radial location of the hydraulic jump is greatest in the direction of greatest slip (parallel to the microribs), while it is a minimum in the direction transverse to the rib/cavity structures. The model results for the hydraulic jump radial position are compared to experimental measurements with good agreement.

Linear stability analysis of thin liquid film flow over a heterogeneously heated substrate
View Description Hide DescriptionThe linear stability of a thin film of volatile liquid flowing over a surface with embedded, regularly spaced heaters is investigated. The temperature gradients at the upstream edges of the heaters induce gradients in surface tension that create a pronounced nonuniformity in the film profile due to the formation of capillary ridges. The Governing equations for the evolution of the film thickness are derived within the lubrication approximation, and three important parameters that affect the dynamics and stability of the film are identified. The computed twodimensional, steady solutions for the local film thickness reveal that due to evaporation there is a slight change in the height of capillary ridge at subsequent heaters downstream. Using a linear stability analysis, it is shown that, as for a single heater, the film is susceptible to two types of instabilities. A rivulet instability leads to spanwiseperiodic rivulets, and an oscillating thermocapillary instability leads to streamwise, timeperiodic oscillations in the film thickness. The critical Marangoni number is calculated for both types of instability for a range of parameter values. The effect of the number of heaters, heater width, and gap between the heaters on the critical Marangoni number is computed and analyzed. For small evaporation rates and less volatile films, the presence of multiple heaters has almost no noticeable effect on the film stability. For larger evaporation rates and more volatile films, additional heaters decrease the Marangoni number at instability onset. The destabilizing effect of multiple heaters is sensitive to the heater geometry and spacing. Furthermore, the limitations of streamwise periodic boundary conditions for analyzing the stability of such flows are discussed. Computations on the transient and nonlinear growth of perturbations are also presented and indicate that the results of eigenanalysis are physically determinant.

Variational formulation of oscillating fluid clusters and oscillatorlike classification. I. Theory
View Description Hide DescriptionThe present work develops the theoretical framework to describe oscillations of fluid clusters. The basic physical phenomena are presented and justified assumptions lead to the final set of equations for different types of oscillations (pinned/sliding). The special combination of a liquid cluster surrounded by a rigid solid matrix and a gas is investigated in more detail. Furthermore, a classification of oscillating fluid clusters is presented using a onedimensional oscillator model. This classification includes three dynamic properties: mass, eigenfrequency, and damping whereas conceptual implementation and limitations for use in multiphase theories are clearly indicated. The frequency dependent flow profile leads to frequency dependence of the dynamic parameters. This is discussed and represented by dimensionless numbers.

Variational formulation of oscillating fluid clusters and oscillatorlike classification. II. Numerical study of pinned liquid clusters
View Description Hide DescriptionA numerical study of pinned, oscillating water clusters is presented. Two main models represent a liquid bridge between the walls of two particles and a water column enclosed in a slender pore channel, respectively. Variations include material properties (density, viscosity, surface tension, contact angle) and geometric properties (volume, slenderness, winding, interfacial areas). They are initially based on water clusters in 1 mm porespace, which are weakly damped at eigenfrequencies around a few hundred Hz. Stiffness and damping are characterized by eigenfrequency and damping coefficient of an equivalent 1dim. harmonicoscillator model. Finally, frequency dependence of the dynamical properties is demonstrated. The comprehensive quantitative analysis extends and explains relationships between geometric and material properties and the response to harmonic stimulation. Furthermore, interpolation functions of characteristic dynamic properties are provided for use in multiphase theories. The frequency dependence of cluster stiffness and damping was proven and of limited influence on the stimulation of two typical, weakly damped liquid clusters.

Stability of a swirled liquid film entrained by a fast gas stream
View Description Hide DescriptionWe study the liquid flow inside a recessed gascentered swirl coaxial injector, where a swirled liquid flowing against an outer wall is destabilized by a central fast gas stream. We present measurements of the liquid intact length inside the injector, as a function of swirl number and dynamic pressure ratio. We propose a simple model to account for the effect of these parameters. We next study the surface instability inside the injector: its frequency is measured for several swirl angles, and as a function of gas velocity. Results are first confronted to the predictions of an inviscid linear stability analysis including swirl, and second to the predictions of a viscous linear stability analysis where swirl is not included. The viscous analysis captures the experimental frequency.

Selfhealing dynamics of surfactant coatings on thin viscous films
View Description Hide DescriptionWe investigate the dynamics of an insoluble surfactant on the surface of a thin viscous fluid spreading inward to fill a surfactantfree region. During the initial stages of surfactant selfhealing, Marangoni forces drive an axisymmetric ridge inward to coalesce into a growing central distension; this is unlike outward spreading, in which the ridge only decays. In later dynamics, the distension slowly decays and the surfactant concentration equilibrates. We present results from experiments in which we simultaneously measure the surfactant concentration (using fluorescently tagged lipids) and the fluid height profile (via laser profilometry). We compare the results to simulations of a mathematical model using parameters from our experiments. For surfactant concentrations close to but below the critical monolayer concentration, we observe agreement between the height profiles in the numerical simulations and the experiment, but disagreement in the surfactant distribution. In experiments at lower concentrations, the surfactant spreading and formation of a Marangoni ridge are no longer present, and a persistent lipidfree region remains. This observation, which is not captured by the simulations, has undesirable implications for applications where uniform coverage is advantageous. Finally, we probe the generality of the effect, and find that distensions of similar size are produced independent of initial fluid thickness, size of initial clean region, and surfactant type.