Volume 26, Issue 3, March 2014

This experimental note is concerned with a new effect we discovered in the course of studying water hammering phenomena. Namely, the ejecta originating from the solid plate impact on a water surface brings about a liquid rim at its edge with the fluid flowing towards the rim center and forming a singular structure resembling a “pancake.” Here, we present the experimental observations and a qualitative physical explanation for the effect, which proves to be fundamental to the situation when the size and speed of the impacting body are such that the capillary effects become important.
 ARTICLES

 Biofluid Mechanics

Lift and wakes of flying snakes
View Description Hide DescriptionFlying snakes use a unique method of aerial locomotion: they jump from tree branches, flatten their bodies, and undulate through the air to produce a glide. The shape of their body crosssection during the glide plays an important role in generating lift. This paper presents a computational investigation of the aerodynamics of the crosssectional shape. Twodimensional simulations of incompressible flow past the anatomically correct crosssection of the species Chrysopelea paradisi show that a significant enhancement in lift appears at a 35° angle of attack, above Reynolds numbers 2000. Previous experiments on physical models also obtained an increased lift, at the same angle of attack. The flow is inherently threedimensional in physical experiments, due to fluid instabilities, and it is thus intriguing that the enhanced lift also appears in the twodimensional simulations. The simulations point to the lift enhancement arising from the early separation of the boundary layer on the dorsal surface of the snake profile, without stall. The separated shear layer rolls up and interacts with secondary vorticity in the nearwake, inducing the primary vortex to remain closer to the body and thus cause enhanced suction, resulting in higher lift.

Loop subdivision surface boundary integral method simulations of vesicles at low reduced volume ratio in shear and extensional flow
View Description Hide DescriptionUsing an unstructured boundary integral method with curvature determination via Loop subdivision surfaces, we explore a region of moderate reduced volume vesicles in flow that includes prolate, biconcave, and stomatocyte shapes. We validate our Loop subdivision code against previously published spectral method simulations. In shear flow, we report dynamic phase diagrams at reduced volumes ranging from 0.65 to 0.95 and determine the critical viscosity ratio at which the vesicle moves away from tank treading. We examine biconcave shapes and find the elimination of the trembling regime and a tumbling that includes significant stretch in the vorticity direction, as well as a general reduction in shear and normal stresses versus a prolate shape. Finally, we reexamine over a wider range of reduced volume the shape instability originally reported by Zhao and Shaqfeh [“The shape stability of a lipid vesicle in a uniaxial extensional flow,” J. Fluid Mech. 719, 345–361 (2013)] of a vesicle placed in an extensional flow. At sufficiently low reduced volume and high capillary number, we find the steady elongated dumbbell shape is unstable to odd perturbations and the vesicle's dumbbell ends become unequal in size. We also find that the critical capillary number as a function of reduced volume is similar between uniaxial and planar extensional flow.
 Micro and Nanofluid Mechanics

On the damping effect of gas rarefaction on propagation of acoustic waves in a microchannel
View Description Hide DescriptionWe consider the response of a gas in a microchannel to instantaneous (smallamplitude) nonperiodic motion of its boundaries in the normal direction. The problem is formulated for an ideal monatomic gas using the Bhatnagar, Gross, and Krook (BGK) kinetic model, and solved for the entire range of Knudsen (Kn) numbers. Analysis combines analytical (collisionless and continuumlimit) solutions with numerical (lowvariance Monte Carlo and linearized BGK) calculations. Gas flow, driven by motion of the boundaries, consists of a sequence of propagating and reflected pressure waves, decaying in time towards a final equilibrium state. Gas rarefaction is shown to have a “damping effect” on equilibration process, with the time required for equilibrium shortening with increasing Kn. Oscillations in hydrodynamic quantities, characterizing gas response in the continuum limit, vanish in collisionless conditions. The effect of having two moving boundaries, compared to only one considered in previous studies of timeperiodic systems, is investigated. Comparison between analytical and numerical solutions indicates that the collisionless description predicts the system behavior exceptionally well for all systems of the size of the mean free path and somewhat larger, in cases where boundary actuation acts along times shorter than the ballistic time scale. The continuumlimit solution, however, should be considered with care at early times near the location of acoustic wavefronts, where relatively sharp flowfield variations result in effective increase in the value of local Knudsen number.

A numerical study of droplet trapping in microfluidic devices
View Description Hide DescriptionMicrofluidic channels are powerful means of control of minute volumes such as droplets. These droplets are usually conveyed at will in an externally imposed flow which follows the geometry of the microchannel. It has recently been pointed out by Dangla et al. [“Trapping microfluidic drops in wells of surface energy,” Phys. Rev. Lett.107(12), 124501 (2011)] that the motion of transported droplets may also be stopped in the flow, when they are anchored to grooves which are etched in the channels top wall. This feature of the channel geometry explores a direction that is usually uniform in microfluidics. Herein, this anchoring effect exploiting the three spatial directions is studied combining a depth averaged fluid description and a geometrical model that accounts for the shape of the droplet in the anchor. First, the presented method is shown to enable the capture and release droplets in numerical simulations. Second, this tool is used in a numerical investigation of the physical mechanisms at play in the capture of the droplet: a localized reduced Laplace pressure jump is found on its interface when the droplet penetrates the groove. This modified boundary condition helps the droplet cope with the linear pressure drop in the surrounding fluid. Held on the anchor the droplet deforms and stretches in the flow. The combination of these ingredients leads to recover the scaling law for the critical capillary number at which the droplets exit the anchors where h is the channel height and R the droplet undeformed radius.

Vapor bubble nucleation by rubbing surfaces: Molecular dynamics simulations
View Description Hide DescriptionWe propose a new mechanism for bubble nucleation triggered by the rubbing of solid surfaces immersed in a liquid, in which the fluid molecules squeezed between the solids are released with high kinetic energy into the bulk of the liquid, resulting in the nucleation of a vapor bubble. Molecular dynamics simulations with a superheated LennardJones fluid are used to evidence this mechanism. Nucleation is observed at the release of the squeezed molecules, for squeezing pressures above a threshold value and for all the relative velocities between the solids that we investigate. We show that the total kinetic energy of the released molecules for a single release event is proportional to the number of molecules released, which depends on the squeezing pressure, but is independent of the velocity.
 Interfacial Flows

Insight into instabilities in burning droplets
View Description Hide DescriptionThe complex multiscale physics of nanoparticle laden functional droplets in a reacting environment is of fundamental and applied significance for a wide variety of applications ranging from thermal sprays to pharmaceutics to modern day combustors using new brands of biofuels. Formation of homogenous nucleated bubbles at the superheat limit inside vaporizing droplets (with or without nanoparticles) represents an unstable system. Here we show that selfinduced boiling in burning functional pendant droplets can produce severe volumetric shape oscillations. Internal pressure buildup due to ebullition activity ejects bubbles from the droplet domain causing undulations on the droplet surface and oscillations in bulk. Through experiments, we establish that the degree of droplet deformation depends on the frequency and intensity of these bubble expulsion events. In a distinct regime of single isolated bubble residing in the droplet, however, preejection transient time is identified by DarrieusLandau evaporative instability, where bubbledroplet system behaves as a synchronized driverdriven system with bulk bubbleshape oscillations being imposed on the droplet. The agglomeration of nanophase additives modulates the flow structures within the droplet and also influences the bubble inception and growth leading to different levels of instabilities.

Experimental sloshing pressure impacts in ensemble domain: Transient and stationary statistical characteristics
View Description Hide DescriptionThe present paper focuses on the analysis of impact pressure registrations from repeated model scale sloshing experiments under harmonic rotational excitation. A series of more than 100 experiments, each one encompassing more than 100 impact events, has been conducted seeking the highest feasible repeatability. Different excitation periods, that cover the main features of the impact dynamics, have been considered in a preliminary screening, describing the main features of the impact dynamics. Since, even under a nominally deterministic excitation, the pressure at each impact is characterized by a high variability, a statistical approach is used treating the impact pressure as a stochastic process. For one selected excitation period, the statistical analysis focuses on the ensemble distribution of the maximum pressure during each impact event. Particular attention is given to the evolution of such distributions, in order to detect the variations in the statistical characteristics of the process. This is achieved by, first, identifying the presence and the length of the transient phase and, second, by characterizing the process at stationary state. The statistics of impact pressure for different peaks are discussed mostly in the ensemble domain. Linking the latter with the time domain analysis is made by checking that the problem can be considered “practically ergodic.” The “practical ergodicity” of the process is dealt with by checking to what extent steady state ensemble statistical information can be obtained from a single long run experiment. Statistical checks for correlation and independence of maximum impact pressures are also carried out to test the hypothesis of independent identically distributed random variables. The method of analysis presented in this paper through the considered example case is general in nature and is considered to be highly portable. In particular, it is considered to allow for a more thorough understanding of nondeterministic events such as those considered herein, by looking at them from a sound statistical perspective. The thorough description of the whole experimental setup makes the presented data suitable for comparison purposes and for validation of theoretical/numerical approaches.

Two dimensional Leidenfrost droplets in a HeleShaw cell
View Description Hide DescriptionWe experimentally and theoretically investigate the behavior of Leidenfrost droplets inserted in a HeleShaw cell. As a result of the confinement from the two surfaces, the droplet has the shape of a flattened disc and is thermally isolated from the surface by the two evaporating vapor layers. An analysis of the evaporation rate using simple scaling arguments is in agreement with the experimental results. Using the lubrication approximation we numerically determine the shape of the droplets as a function of its radius. We furthermore find that the droplet width tends to zero at its center when the radius reaches a critical value. This prediction is corroborated experimentally by the direct observation of the sudden transition from a flattened disc into an expending torus. Below this critical size, the droplets are also displaying capillary azimuthal oscillating modes reminiscent of a hydrodynamic instability.

Three dimensional microbubble dynamics near a wall subject to high intensity ultrasound
View Description Hide DescriptionDynamics of cavitation microbubbles due to high intensity ultrasound are associated with important applications in biomedical ultrasound, ultrasonic cleaning, and sonochemistry. Previous numerical studies on this phenomenon were for an axisymmetric configuration. In this paper, a computational model is developed to simulate the three dimensional dynamics of acoustic bubbles by using the boundary integral method. A bubble collapses much more violently subjected to high intensity ultrasound than when under normal constant ambient pressure. A few techniques are thus implemented to address the associated numerical challenge. In particular, a high quality mesh of the bubble surface is maintained by implementing a new hybrid approach of the Lagrangian method and elastic mesh technique. It avoids the numerical instabilities which occur at a sharp jet surface as well as generates a fine mesh needed at the jet surface. The model is validated against the RayleighPlesset equation and an axisymmetric model. We then explore microbubble dynamics near a wall subjected to high intensity ultrasound propagating parallel to the wall, where the Bjerknes forces due to the ultrasound and the wall are perpendicular to each other. The bubble system absorbs the energy from the ultrasound and transforms the uniform momentum of the ultrasound parallel to the wall to the highly concentrated momentum of a highspeed liquid jet pointing to the wall. The liquid jet forms towards the end of the collapse phase with a significantly higher speed than without the presence of ultrasound. The jet direction depends mainly on the dimensionless standoff distance γ = s/R max of the bubble from the wall, where s is the distance between the wall and the bubble centre at inception and R max is the maximum bubble radius. The jet is approximately directed to the wall when γ is 1.5 or smaller and rotates to the direction of the ultrasound as γ increases. When γ is about 10 or larger, the wall effect is negligible and the jet is along the acoustic wave direction. When the amplitude of the ultrasound increases, the jet direction does not change significantly but its width and velocity increase obviously.

Circulation within confined droplets in HeleShaw channels
View Description Hide DescriptionLiquid droplets flowing through a rectangular microfluidic channel develop a vortical flow field due to the presence of shear forces from the surrounding fluid. In this paper, we present an experimental and computational study of droplet velocities and internal flow patterns in a rectangular pressuredriven flow for droplet diameters ranging from 0.1 to 2 times the channel height. Our study shows excellent agreement with asymptotic predictions of droplet and interfacial velocities for infinitesimally small droplets. As the droplet diameter nears the size of the channel height, the droplet velocity slows significantly, and the changing external flow field causes a qualitative change in the location of internal vortices. This behavior is relevant for future studies of mass transfer in microfluidic devices.

The influence of inertia and contact angle on the instability of partially wetting liquid strips: A numerical analysis study
View Description Hide DescriptionThe stability of a thread of fluid deposited on a flat solid substrate is studied numerically by means of the Finite Element Method in combination with an Arbitrary LagrangianEulerian technique. A good agreement is observed when our results are compared with predictions of linear stability analysis obtained by other authors. Moreover, we also analysed the influence of inertia for different contact angles and found that inertia strongly affects the growth rate of the instability when contact angles are large. By contrast, the wave number of the fastest growing mode does not show important variations with inertia. The numerical technique allows us to follow the evolution of the free surface instability until comparatively late stages, where the filament begins to break into droplets. The rupture pattern observed for several cases shows that the number of principal droplets agrees reasonably well with an estimation based on the fastest growing modes.

An extended Bretherton model for long Taylor bubbles at moderate capillary numbers
View Description Hide DescriptionWhen (long) bubbles are transported in tubes containing a fluid, the presence of a thin film of fluid along the tube walls causes the velocity of the bubble to be different from the average fluid velocity. Bretherton [“The motion of long bubbles in tubes,” J. Fluid Mech.10, 166 (1961)] derived a model to describe this phenomenon for pressure driven flows based on a lubrication approach coupled with surface deformation of the bubble. Bretherton found that the parameter governing the physics involved is the capillary number (Ca) which expresses the relationship between speed of the bubble, surface tension, and viscosity of the liquid. The results of Bretherton are here rederived and analyzed in a slightly more perspicuous manner. Incorporating the condition that the bubblefilm combination should fit inside the tube results in an expression very similar to the one found empirically by Aussillous and Quéré [“Quick deposition of a fluid on the wall of a tube,” Phys. Fluids12, 2367 (2000)] of the Taylor [“Deposition of a viscous fluid on the wall of a tube,” J. Fluid Mech.10, 161 (1961)] experimental data. Our expression is valid for Ca values up to Ca = 2.0, but approaches Bretherton's result for low values of Ca. The analysis is done in terms of the pressure buildup which originates from the interplay between surface tension and lubrication due to the thin layer of fluid near the tube wall.

Hydroelastic slamming response in the evolution of a flipthrough event during shallowliquid sloshing
View Description Hide DescriptionThe evolution of a flipthrough event [6] upon a vertical, deformable wall during shallowwater sloshing in a 2D tank is analyzed, with specific focus on the role of hydroelasticity. An aluminium plate, whose dimensions are Froudescaled in order to reproduce the first wet natural frequency associated with the typical structural panel of a Mark III containment system, is used. (Mark III Containment System is a membranetype tank used in the Liquefied Natural Gas (LNG) carrier to contain the LNG. A typical structural panel is composed by two metallic membranes and two independent thermal insulation layers. The first membrane contains the LNG, the second one ensures redundancy in case of leakage.) Such a system is clamped to a fully rigid vertical wall of the tank at the vertical ends while being kept free on its lateral sides. Hence, in a 2D flow approximation the system can be suitably modelled, as a doubleclamped Euler beam, with the Euler beam theory. The hydroelastic effects are assessed by crossanalyzing the experimental data based both on the images recorded by a fast camera, and on the strain measurements along the deformable panel and on the pressure measurements on the rigid wall below the elastic plate. The same experiments are also carried out by substituting the deformable plate with a fully stiff panel. The pressure transducers are mounted at the same positions of the strain gauges used for the deformable plate. The comparison between the results of rigid and elastic case allows to better define the role of hydroelasticity. The analysis has identified three different regimes characterizing the hydroelastic evolution: a quasistatic deformation of the beam (regime I) precedes a strongly hydroelastic behavior (regime II), for which the added mass effects are relevant; finally, the freevibration phase (regime III) occurs. A hybrid method, combining numerical modelling and experimental data from the tests with fully rigid plate is proposed to examine the hydroelastic effects. Within this approach, the measurements provide the experimental loads acting on the rigid plate, while the numerical solution enables a more detailed analysis, by giving additional information not available from the experimental tests. More in detail, an Euler beam equation is used to model numerically the plate with the addedmass contribution estimated in time. In this way the resulting hybrid method accounts for the variation of the added mass associated with the instantaneous wetted length of the beam, estimated from the experimental images. Moreover, the forcing hydrodynamic load is prescribed by using the experimental pressure distribution measured in the rigid case. The experimental data for the elastic beam are compared with the numerical results of the hybrid model and with those of the standard methods used at the design stage. The comparison against the experimental data shows an overall satisfactory prediction of the hybrid model. The maximum peak pressure predicted by the standard methods agrees with the result of the hybrid model only when the added mass effect is considered. However, the standard methods are not able to properly estimate the temporal evolution of the plate deformation.

Singular structures on liquid rims
View Description Hide DescriptionThis experimental note is concerned with a new effect we discovered in the course of studying water hammering phenomena. Namely, the ejecta originating from the solid plate impact on a water surface brings about a liquid rim at its edge with the fluid flowing towards the rim center and forming a singular structure resembling a “pancake.” Here, we present the experimental observations and a qualitative physical explanation for the effect, which proves to be fundamental to the situation when the size and speed of the impacting body are such that the capillary effects become important.
 Viscous and NonNewtonian Flows

Modelling capillary breakup of particulate suspensions
View Description Hide DescriptionWe have constructed a simple onedimensional model of capillary breakup to demonstrate the thinning behaviour of particulate suspensions previously observed in experiments. The presence of particles increases the bulk viscosity of a fluid and so is expected to retard thinning and consequently delay the time to breakup. However, experimental measurements suggest that once the filament thins to approximately five particle diameters, the thinning no longer follows the behaviour predicted by the bulk viscosity; instead thinning is “accelerated” due to the effects of finite particle size. Our model shows that accelerated thinning arises from variations in local particle density. As the filament thins, fluctuations in the local volume fraction are amplified, leading ultimately to particlefree sections in the filament. The local viscosity of the fluid is determined from the local particle density, which is found by tracking individual particles within the suspension. In regions of low particle density, the fluid is less viscous and can therefore thin more easily. Thus, we are able to model the accelerated thinning regime found in experiments. Furthermore, we observe a final thinning regime in which the thinning is no longer affected by particle dynamics but follows the behaviour of the solvent.

Evaporationdriven low Reynolds number vortices in a cavity
View Description Hide DescriptionThis paper describes low Reynolds number vortices that can occur during the evaporation of a polymer solution inside a cavity. Confocal microscopy combined with image processing, micro particle image velocimetry, and micro laser induced fluorescence are used to measure the unsteady evaporationdriven velocity field and the concentration field in a shallow liquid film inside a microliter cavity near a wall. In addition to evaporationdriven flow and Marangoni flow, the velocity field also reveals single and multiple vortices generated by the creeping flow induced by evaporation. Similar to other low Reynolds number vortices, it is seen that the geometry strongly affects the presence, endurance and size of these vortices during the evaporation process. The bulk shear stress of the solution affects the vortex behavior, and no recirculation is observed at high viscosity.

Mechanical energy dissipation induced by sloshing and wave breaking in a fully coupled angular motion system. I. Theoretical formulation and numerical investigation
View Description Hide DescriptionA dynamical system involving a driven pendulum filled with liquid is analyzed in the present paper series. The study of such a system is conducted in order to understand energy dissipation resulting from the shallow water sloshing and induced wave breaking. This analysis is relevant for the design of Tuned Liquid Damper devices. The complexity and violence of the flow generated by the roll motion results in the impossibility of using an analytical approach, requiring in turn the use of a suitable numerical solver. In this paper, the coupled dynamical system is thoroughly described, revealing its nonlinear features associated with the large amplitude of the forcing, both in terms of mechanical and fluid dynamical aspects. A smoothed particle hydrodynamics model, largely validated in literature, is used to calculate the frequency behavior of the whole system. For small rotation angles, a semianalytical model of the energy dissipated by the fluid, based on a hydraulic jump solution, is developed; the energy transfer is numerically calculated in order to extend the analysis to large oscillation angles. The experimental part of the investigation is carried out in Paper II [B. Bouscasse, A. Colagrossi, A. SoutoIglesias, and J. L. C. Pita, “Mechanical energy dissipation induced by sloshing and wave breaking in a fully coupled angular motion system. II. Experimental investigation,” Phys. Fluids 26, 033104 (2014)] of this work.

Mechanical energy dissipation induced by sloshing and wave breaking in a fully coupled angular motion system. II. Experimental investigation
View Description Hide DescriptionIn Paper I of this series [B. Bouscasse, A. Colagrossi, A. SoutoIglesias, and J. L. C. Pita, “Mechanical energy dissipation induced by sloshing and wave breaking in a fully coupled angular motion system. I. Theoretical formulation and numerical investigation,” Phys. Fluids26, 033103 (2014)], a theoretical and numerical model for a driven pendulum filled with liquid was developed. The system was analyzed in the framework of tuned liquid dampers and hybrid mass liquid dampers (HMLD) theory. In this paper, in order to measure the energy dissipation resulting from shallow water sloshing, an experimental investigation is conducted. Accurate evaluations of energy transfers are obtained through the recorded kinematics of the system. A set of experiments is conducted with three different liquids: water, sunflower oil, and glycerine. Coherently with the results of Paper I, the energy dissipation obtained when the tank is filled with water can mainly be explained by the breaking waves. For all three liquids, the effects of varying the external excitation amplitude are discussed.

Thermocapillar instability of a twodimensional viscoelastic planar liquid sheet in surrounding gas
View Description Hide DescriptionA twodimensional viscoelastic planar liquid sheet subjected to a considerable temperature gradient perpendicular to the surfaces, moving in a gas medium, was investigated in a linear scope. The sheet instability was explored by solving the dispersion relation in the sinuous mode. Results suggested that the viscoelastic liquid sheet could behave with greater stability than its Newtonian counterpart when the temperature difference was sufficiently large. Thermal effects improved sheet instability, while the liquid elasticity had a dual effect when considering the temperature difference. It should be noted that thermal effects could retard the breakup process of viscoelastic planar liquid sheets at a large liquid Weber number. Deformation retardation time was a destabilizing factor when there were great temperature differences, which was polar to the case without thermal effects. However, the effects of liquid viscosity, liquid velocity, gastoliquid density ratio, and surface tension were analogous, whether or not there existed a difference in temperature. Finally, the competition between thermocapillar and aerodynamic instabilities on sheet instability was examined.

Instability of a polymeric thread
View Description Hide DescriptionWhen a liquid containing a dilute solution of long, flexible polymers breaks up under the action of surface tension, it forms long threads of nearly uniform thickness. However, at a thickness in the order of microns, the thread becomes unstable to the formation of a nonuniform “blistering” pattern: tiny drops separated by threads of highly concentrated polymer solution. We show that standard models for the coupling between stress and polymer concentration lead to a linear instability, which exhibits very strong transient growth of the free surface perturbation. A high concentration of polymer remains in the thread part of the structure.