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We study the collapse of an axisymmetric liquid filament both analytically and by means of a numerical model. The liquid filament, also known as ligament, may either collapse stably into a single droplet or break up into multiple droplets. The dynamics of the filament are governed by the viscosity and the aspect ratio, and the initial perturbations of its surface. We find that the instability of long viscous filaments can be completely explained by the Rayleigh-Plateau instability, whereas a low viscous filament can also break up due to end pinching. We analytically derive the transition between stable collapse and breakup in the Ohnesorge number versus aspect ratio phase space. Our result is confirmed by numerical simulations based on the slender jet approximation and explains recent experimental findings by Castréjon-Pita et al. [Phys. Rev. Lett. 108, 074506 (2012)]10.1103/PhysRevLett.108.074506.

Surface and bulk nanobubbles are two types of nanoscopic gaseous domain that have recently been discovered in interfacial physics. Both are expected to be unstable to dissolution because of the high internal pressure driving diffusion and the surface tension which squeezes the gas out, but there is a rapidly growing body of experimental evidence that demonstrates both bubble types to be stable. However, the two types of bubbles also differ in many respects: surface nanobubble stability is most probably assisted by the nearby wall, which can repel the water (in the case of hydrophobicity), accept physisorbed gas molecules, and reduce the surface area through which outfluxing can occur; bulk nanobubbles, on the other hand, must stabilise themselves. This is perhaps through ionic shielding, perhaps through diffusive shielding, or perhaps through both. Herein, the features of both bubble types are described individually, their common and disparate features are discussed, and emerging applications are examined.

We report the results of the first systematic Lagrangian experimental investigation in a previously unexplored regime of very light (air bubbles in water) and large (D/¿ 1) particles in turbulence. Using a traversing camera setup and particle tracking, we study the Lagrangian acceleration statistics of ~3 mm diameter (D) bubbles in a water tunnel with nearly homogeneous and isotropic turbulence generated by an active grid. The Reynolds number (Re¿) is varied from 145 to 230, resulting in size ratios, D/¿, in the range of 7.3–12.5, where ¿ is the Kolmogorov length scale. The experiments reveal that gravity increases the acceleration variance and reduces the intermittency of the probability density function (PDF) in the vertical direction. Once the gravity offset has been subtracted, the variances of both the horizontal and vertical acceleration components are about 5 ± 2 times larger than those measured in the same flow for fluid tracers. Moreover, for these light particles, the experimental acceleration PDF shows a substantial reduction of intermittency at growing size ratios, in contrast with neutrally buoyant or heavy particles. All these results closely match numerical simulations of finite-sized bubbles with the Faxén corrections.

Targeted molecular imaging with ultrasound contrast agent microbubbles is achieved by incorporating targeting ligands on the bubble coating and allows for specific imaging of tissues affected by diseases. Improved understanding of the interplay between the acoustic forces acting on the bubbles during insonation with ultrasound and other forces (e.g. shear due to blood flow, binding of targeting ligands to receptors on cell membranes) can help improve the efficacy of this technique. This work focuses on the effects of the secondary acoustic radiation force, which causes bubbles to attract each other and may affect the adhesion of targeted bubbles. First, we examine the translational dynamics of ultrasound cont

Numerical results for kinetic and thermal energy dissipation rates in bubbly Rayleigh-Bénard convection are reported. Bubbles have a twofold effect on the flow: on the one hand, they absorb or release heat to the surrounding liquid phase, thus tending to decrease the temperature differences responsible for the convective motion; but on the other hand, the absorbed heat causes the bubbles to grow, thus increasing their buoyancy and enhancing turbulence (or, more properly, pseudoturbulence) by generating velocity fluctuations. This enhancement depends on the ratio of the sensible heat to the latent heat of the phase change, given by the Jakob number, which determines the dynamics of the bubble growth.

Heavy or light particles introduced into a liquid trigger motion due to their buoyancy, with the potential to drive flow to a turbulent state. In the case of vapor bubbles present in a liquid near its boiling point, thermal coupling between the liquid and vapor can moderate this additional motion by reducing temperature gradients in the liquid. Whether the destabilizing mechanical feedback or stabilizing thermal feedback will dominate the system response depends on the number of bubbles present and the properties of the phase change. Here we study thermal convection with phase change in a cylindrical Rayleigh–Bénard cell to examine this competition. Using the Reynolds number of the flow as a signature of turbulence and the intensity of the flow, we show that in general the rising vapor bubbles destabilize the system and lead to higher velocities. The exception is a limited regime corresponding to phase change with a high latent heat of vaporization (corresponding to low Jakob number), where the vapor bubbles can eliminate the convective flow by smoothing temperature differences of the fluid.

Numerical and experimental data for the heat transfer as a function of the Rossby number Ro in turbulent rotating Rayleigh-Bénard convection are presented for the Prandtl number Pr=4.38 and the Rayleigh number Ra=2.91×108 up to Ra=4.52×109. The aspect ratio G=D/L, where L is the height and D the diameter of the cylindrical sample, is varied between G=0.5 and 2.0. Without rotation, where the aspect ratio influences the global large-scale circulation, we see a small-aspect-ratio dependence in the Nusselt number for Ra=2.91×108. However, for stronger rotation, i.e., 1/Ro»1/Roc, the heat transport becomes independent of the aspect ratio. We interpret this finding as follows: In the rotating regime the heat is mainly transported by vertically aligned vortices. Since the vertically aligned vortices are local, the aspect ratio has a negligible effect on the heat transport in the rotating regime. Indeed, a detailed analysis of vortex statistics shows that the fraction of the horizontal area that is covered by vortices is independent of the aspect ratio when 1/Ro»1/Roc. In agreement with the results of Weiss et al. [ Phys. Rev. Lett. 105 224501 (2010)], we find a vortex-depleted area close to the sidewall. Here we show that there is also an area with enhanced vortex concentration next to the vortex-depleted edge region and that the absolute widths of both regions are independent of the aspect ratio.

An air bubble driven by ultrasound can become shape-unstable through a parametric instability. We report time-resolved optical observations of shape oscillations (mode n=2 to 6) of micron-sized single air bubbles. The observed mode number n was found to be linearly related to the ambient radius of the bubble. Above the critical driving pressure threshold for shape oscillations, which is minimal at the resonance of the volumetric radial mode, the observed mode number n is independent of the forcing pressure amplitude. The microbubble shape oscillations were also analyzed numerically by introducing a small nonspherical linear perturbation to a Rayleigh-Plesset-type equation, capturing the experimental observations in detail.

In turbulent thermal convection in cylindrical samples with an aspect ratio G=D/L (D is the diameter and L the height), the Nusselt number Nu is enhanced when the sample is rotated about its vertical axis because of the formation of Ekman vortices that extract additional fluid out of thermal boundary layers at the top and bottom. We show from experiments and direct numerical simulations that the enhancement occurs only above a bifurcation point at a critical inverse Rossby number 1/Roc, with 1/Roc¿1/G. We present a Ginzburg-Landau–like model that explains the existence of a bifurcation at finite 1/Roc as a finite-size effect. The model yields the proportionality between 1/Roc and 1/G and is consistent with several other measured or computed system properties

The effect of rotation on the boundary layers (BLs) in a Rayleigh–Bénard system at a relatively low Rayleigh number, i.e., Ra = 4×107, is studied for different Pr by direct numerical simulations and the results are compared with laminar BL theory. In this regime, we find a smooth onset of the heat transfer enhancement as function of increasing rotation rate. We study this regime in detail and introduce a model based on the Grossmann–Lohse theory to describe the heat transfer enhancement as function of the rotation rate for this relatively low Ra number regime and weak background rotation Ro¿1. The smooth onset of heat transfer enhancement observed here is in contrast to the sharp onset observed at larger Ra¿108 by Stevens et al. [Phys. Rev. Lett. 103, 024503 (2009)] , although only a small shift in the Ra-Ro-Pr phase space is involved.

Numerical data for the heat transfer as a function of the Prandtl (Pr) and Rossby (Ro) numbers in turbulent rotating Rayleigh–Bénard convection are presented for Rayleigh number Ra=108. When Ro is fixed, the heat transfer enhancement with respect to the non-rotating value shows a maximum as a function of Pr. This maximum is due to the reduced effect of Ekman pumping when Pr becomes too small or too large. When Pr becomes small, i.e. for large thermal diffusivity, the heat that is carried by the vertical vortices spreads out in the middle of the cell and Ekman pumping thus becomes less effective. For higher Pr the thermal boundary layers (BLs) are thinner than the kinetic BLs and therefore the Ekman vortices do not reach the thermal BL. This means that the fluid that is sucked into the vertical vortices is colder than that for lower Pr, which limits the upwards heat transfer

Weakly rotating turbulent Rayleigh-Bénard convection was studied experimentally and numerically. With increasing rotation and large enough Rayleigh number a supercritical bifurcation from a turbulent state with nearly rotation-independent heat transport to another with enhanced heat transfer is observed at a critical inverse Rossby number 1/Roc 0.4. The strength of the large-scale convection roll is either enhanced or essentially unmodified depending on parameters for 1/Ro

Experimental and numerical data for the heat transfer as a function of the Rayleigh-, Prandtl-, and Rossby numbers in turbulent rotating Rayleigh-Bénard convection are presented. For relatively small Ra=10^8 and large Pr modest rotation can enhance the heat transfer by up to 30%. At larger Ra there is less heat-transfer enhancement, and at small Pr=0.7 there is no heat-transfer enhancement at all. We suggest that the small-Pr behavior is due to the breakdown of the heat-transfer-enhancing Ekman pumping because of larger thermal diffusion.

We present an investigation of the statistics of velocity gradient related quantities, in particular energy dissipation rate and enstrophy, along the trajectories of fluid tracers and of heavy/light particles advected by a homogeneous and isotropic turbulent flow. The refined similarity hypothesis (RSH) proposed by Kolmogorov and Oboukhov in 1962 is rephrased in the Lagrangian context and then tested along the particle trajectories. The study is performed on state-of-the-art numerical data resulting from numerical simulations up to Re¿~400 with 20483 collocation points. When particles have small inertia, we show that the Lagrangian formulation of the RSH is well verified for time lags larger than the typical response time tp of the particle. In contrast, in the large inertia limit when the particle response time approaches the integral time scale of the flow, particles behave nearly ballistic, and the Eulerian formulation of RSH holds in the inertial range.

Single-point hot-wire measurements in the bulk of a turbulent channel have been performed in order to detect and quantify the phenomenon of preferential bubble accumulation. We show that statistical analysis of the bubble-probe colliding-time series can give a robust method for investigation of clustering in the bulk regions of a turbulent flow where, due to the opacity of the flow, no imaging technique can be employed. We demonstrate that microbubbles (R0 ¿ 100 µm) in a developed turbulent flow, where the Kolmogorov-length scale is ¿ ¿ R0, display preferential concentration in small scale structures with a typical statistical signature ranging from the dissipative range, O(¿), up to the low inertial range O(100¿). A comparison to Eulerian–Lagrangian numerical simulations is also presented to further support our proposed way to characterize clustering from temporal time series at a fixed position.

The fluid dynamic interaction of cavitation bubbles with adherent cells on a substrate is experimentally investigated. We find that the nonspherical collapse of bubbles near to the boundary is responsible for cell detachment. High-speed photography reveals that a wall bounded flow leads to the detachment of cells. Cel

Air bubbles entrapped in the ink channel are a major problem in piezo-driven inkjet printing. They grow by rectified diffusion and eventually counteract the pressure buildup at the nozzle, leading to a breakdown of the jetting process. Experimental results on the droplet velocity udrop as a function of the equilibrium radius R0 of the entrained bubble are presented. Surprisingly, udrop(R0) shows a pronounced maximum around R0 = 17 µm before it sharply drops to zero around R0 = 19 µm. A simple one-dimensional model is introduced to describe this counterintuitive behavior which turns out to be a resonance effect of the entrained bubble.

Air bubbles can cause nozzle failures in piezo-driven inkjet printheads [1]. The time development of the entrapped air bubbles has experimentally been studied [2]. It was found that the air bubble has a radius of 5µm just after the entrapment. The bubble then grows by rectified diffusion due to the applied pressure field, used for jetting droplets. Bjerknes forces drive the displacement of the air bubble. First, the bubble is pushed into the channel. After reaching the resonance size, given by the characteristic printhead frequency, the Bjerknes force reverses sign, pushing the air bubble towards the nozzle. At this time the air bubble has grown so large that it is not possible to jet it out, resulting in a nozzle failure.

We report on an intriguing phenomenon taking place in a liquid rotating around a fixed horizontal axis. Under suitable conditions, bubbles and particles are observed to drift along the axis of rotation maintaining a constant distance from it and a constant angle of elevation above the horizontal. Absence of fore-aft symmetry of the bubble or particle shape is a prerequisite for this phenomenon. For bubbles, this requires a volume sufficiently large for surface-tension effects to be small and large deformations to be possible. Particle image velocimetry and flow visualization suggest that the wake does not play a role. The dependence on bubble radius, particle shape, liquid viscosity, and speed of rotation is investigated.

The Ra and Pr number scaling of the Nusselt number Nu, the Reynolds number Re, the temperature fluctuations, and the kinetic and thermal dissipation rates is studied for (numerical) homogeneous Rayleigh–Bénard turbulence, i.e., Rayleigh–Bénard turbulence with periodic boundary conditions in all directions and a volume forcing of the temperature field by a mean gradient. This system serves as model system for the bulk of Rayleigh–Bénard flow and therefore as model for the so-called "ultimate regime of thermal convection." With respect to the Ra dependence of Nu and Re we confirm our earlier results [D. Lohse and F. Toschi, "The ultimate state of thermal convection," Phys. Rev. Lett. 90, 034502 (2003)] which are consistent with the Kraichnan theory [R. H. Kraichnan, "Turbulent thermal convection at arbitrary Prandtl number," Phys. Fluids 5, 1374 (1962)] and the Grossmann–Lohse (GL) theory [S. Grossmann and D. Lohse, "Scaling in thermal convection: A unifying view," J. Fluid Mech. 407, 27 (2000); "Thermal convection for large Prandtl number," Phys. Rev. Lett. 86, 3316 (2001); "Prandtl and Rayleigh number dependence of the Reynolds number in turbulent thermal convection," Phys. Rev. E 66, 016305 (2002); "Fluctuations in turbulent Rayleigh–Bénard convection: The role of plumes," Phys. Fluids 16, 4462 (2004)], which both predict Nu~Ra1/2 and Re~Ra1/2. However the Pr dependence within these two theories is different. Here we show that the numerical data are consistent with the GL theory Nu~Pr1/2, Re~Pr–1/2. For the thermal and kinetic dissipation rates we find /(2L–2)~(Re Pr)0.87 and u/(3L–4)~Re2.77, both near (but not fully consistent) the bulk dominated behavior, whereas the temperature fluctuations do not depend on Ra and Pr. Finally, the dynamics of the heat transport is studied and put into the context of a recent theoretical finding by Doering et al. ["Comment on ultimate state of thermal convection" (private communication)].

The motion and the action of microbubbles in homogeneous and isotropic turbulence are investigated through (three-dimensional) direct numerical simulations of the Navier–Stokes equations and applying the Lagrangian approach to track the bubble trajectories. The forces acting on the bubbles are added mass, drag, lift, and gravity. The bubbles are found to accumulate in vortices, preferably on the side with downward velocity. This effect, mainly caused by the lift force, leads to a reduced average bubble rise velocity. Once the reaction of the bubbles on the carrier flow is embodied using a point-force approximation, an attenuation of the turbulence on large scales and an extra forcing on small scales is found.

The ultimate regime of thermal convection, the so-called Kraichnan regime [R.¿H. Kraichnan, Phys. Fluids 5, 1374 (1962)], hitherto has been elusive. Here numerical evidence for that regime is presented by performing simulations of the bulk of turbulence only, eliminating the thermal and kinetic boundary layers and replacing them with periodic boundary conditions.

Decaying and periodically kicked turbulence are analyzed within the Gledzer–Ohkitani–Yamada shell model, to allow for sufficiently large scaling regimes. Energy is transferred towards the small scales in intermittent bursts. Nevertheless, mean field arguments are sufficient to account for the ensemble averaged energy decay E(t)~t–2 or the parameter dependencies for the ensemble averaged total energy in the kicked case. Within numerical precision, the inertial subrange intermittency remains the same, whether the system is forced or decaying.