For dissolving active oil droplets in an ambient liquid, it is generally assumed that the Marangoni effect results in repulsive interactions, while the buoyancy effects caused by the density difference between the droplets, diffusing product and the ambient fluid are usually neglected. However, it has been observed in recent experiments that active droplets can form clusters due to buoyancy-driven convection (Krüger et al. Eur. Phys. J. E, vol. 39, 2016, pp. 1-9). In this study, we numerically analyze the buoyancy effect, in addition to the propulsion caused by Marangoni flow (with its strength characterized by Péclet number Pe). The buoyancy effects have their origin in (i) the density difference between the droplet and the ambient liquid, which is characterized by Galileo number Ga, and (ii) the density difference between the diffusing product (i.e. filled micelles) and the ambient liquid, which can be quantified by a solutal Rayleigh number Ra. We analyze how the attracting and repulsing behaviour of neighbouring droplets depends on the control parameters Pe, Ga, and Ra. We find that while the Marangoni effect leads to the well-known repulsion between the interacting droplets, the buoyancy effect of the reaction product leads to buoyancy-driven attraction. At sufficiently large Ra, even collisions between the droplets can take place. Our study on the effect of Ga further shows that with increasing Ga, the collision becomes delayed. Moreover, we derive that the attracting velocity of the droplets, which is characterized by a Reynolds number Red, is proportional to Ra1/4/(â/R), where â/R is the distance between the neighbouring droplets normalized by the droplet radius. Finally, we numerically obtain the repulsive velocity of the droplets, characterized by a Reynolds number Rerep, which is proportional to PeRa-0.38. The balance of attractive and repulsive effect leads to Pe ~ Ra0.63, which agrees well with the transition curve between the regimes with and without collision.
Precise manipulation of droplets or bubbles hosts a broad range of applications for microfluidic devices, drug delivery, and soft robotics. Generally the existing approaches via passively designing structured surfaces or actively applying external stimuli, inherently confine their motions within the planar or curved geometry at a slow speed. Consequently the realization of 3D manipulation, such as of the underwater bubbles, remains challenging. Here, during the near-infrared-laser impacting on water, by simply introducing a thermally conductive interface, we unexpectedly observe a spontaneously bouncing bubble with hundreds-of-micrometer diameter at tens-of-Hertz frequency. The unique formation of temperature inversion layer in our system generates the depth-dependent thermal Marangoni force responsible for the bouncing behavior. Both the scaling analysis and numerical simulation agree with observations quantitatively. Furthermore, by controlling the navigation speed of the laser beam, the bubble not only shows excellent steerability with velocity up to 40 mm/s, but also exhibits distinctive behaviors from bouncing to dancing within water. We demonstrate the potential applications by steering the bubble within water to specifically interact with tiny objects, shedding light on the fabrication of bubble-based compositions in materials science and contamination removal in water treatment.
We numerically study turbulent Rayleigh-Bénard (RB) convection under spatial temperature modulation, where the bottom temperature varies sinusoidally around a mean value in space. Both two- and three-dimensional simulations are performed over the Rayleigh number range 10^{7}≤Ra≤10^{10} and the wave number range 1≤k≤120 at fixed Prandtl number Pr=0.7. It is demonstrated that spatial temperature modulation with small wave numbers can enhance the global heat transfer (characterized by the Nusselt number Nu) in the turbulent regime, while Nu is close to that in standard RB convection in the case of large wave numbers. Further, we propose two characteristic modulation length scales: one is the penetration depth δ_{k} above which spatial modulation is negligible, the other is the inversion depth δ_{k2} below which there exists a stable inverse temperature gradient. Based on the relative thickness of the thermal boundary layer (BL) δ_{th} compared with these two length scales, the underlying modulation mechanism is physically explained and three regimes are identified: (1) an unperturbed BL regime (δ_{k}<δ_{th}), in which the modulation effect does not penetrate through the thermal BL and Nu is nearly unchanged; (2) a partially modulated BL regime (δ_{k2}<δ_{th}<δ_{k}), in which hot spots trigger more plume emissions from the thermal BL, resulting in Nu enhancement; and (3) a fully modulated BL regime (δ_{th}<δ_{k2}), in which the stable temperature inversion over the cold phases begins to affect convective flows, which alters the trend of Nu enhancement.
Plasmonic bubbles are of great relevance in numerous applications, including catalytic reactions, micro/nanomanipulation of molecules or particles dispersed in liquids, and cancer therapeutics. So far, studies have been focused on bubble nucleation in pure liquids. Here we investigate plasmonic bubble nucleation in ternary liquids consisting of ethanol, water, and trans-anethole oil, which can show the so-called ouzo effect. We find that oil (trans-anethole) droplet plumes are produced around the growing plasmonic bubbles. The nucleation of the microdroplets and their organization in droplet plumes is due to the symmetry breaking of the ethanol concentration field during the selective evaporation of ethanol from the surrounding ternary liquids into the growing plasmonic bubbles. Numerical simulations show the existence of a critical Marangoni number Ma (the ratio between solutal advection rate and the diffusion rate), above which the symmetry breaking of the ethanol concentration field occurs, leading to the emission of the droplet plumes. The numerical results agree with the experimental observation that more plumes are emitted with increasing ethanol-water relative weight ratios and hence Ma. Our findings on the droplet plume formation reveal the rich phenomena of plasmonic bubble nucleation in multicomponent liquids and help to pave the way to achieve enhanced mixing in multicomponent liquids in chemical, pharmaceutical, and cosmetic industries.
When a fluid system is subject to strong rotation, centrifugal fluid motion is expected, i.e., denser (lighter) fluid moves outward (inward) from (toward) the axis of rotation. Here we demonstrate, both experimentally and numerically, the existence of an unexpected outward motion of warm and lighter vortices in rotating thermal convection. This anomalous vortex motion occurs under rapid rotations when the centrifugal buoyancy is sufficiently strong to induce a symmetry-breaking in the vorticity field, i.e., the vorticity of the cold anticyclones overrides that of the warm cyclones. We show that through hydrodynamic interactions the densely distributed vortices can self-aggregate into coherent clusters and exhibit collective motion in this flow regime. Interestingly, the correlation of the vortex velocity fluctuations within a cluster is scale-free, with the correlation length being proportional ( ≈ 30%) to the cluster length. Such long-range correlation leads to the counterintuitive collective outward motion of warm vortices. Our study brings insights into the vortex dynamics that are widely present in nature.
The physicochemical hydrodynamics of bubbles and droplets out of equilibrium, in particular with phase transitions, display surprisingly rich and often counterintuitive phenomena. Here we experimentally and theoretically study the nucleation and early evolution of plasmonic bubbles in a binary liquid consisting of water and ethanol. Remarkably, the submillimeter plasmonic bubble is found to be periodically attracted to and repelled from the nanoparticle-decorated substrate, with frequencies of around a few kilohertz. We identify the competition between solutal and thermal Marangoni forces as the origin of the periodic bouncing. The former arises due to the selective vaporization of ethanol at the substrate's side of the bubble, leading to a solutal Marangoni flow toward the hot substrate, which pushes the bubble away. The latter arises due to the temperature gradient across the bubble, leading to a thermal Marangoni flow away from the substrate, which sucks the bubble toward it. We study the dependence of the frequency of the bouncing phenomenon from the control parameters of the system, namely the ethanol fraction and the laser power for the plasmonic heating. Our findings can be generalized to boiling and electrolytically or catalytically generated bubbles in multicomponent liquids.
To quantify the fate of respiratory droplets under different ambient relative humidities, direct numerical simulations of a typical respiratory event are performed. We found that, because small droplets (with initial diameter of 10 µm) are swept by turbulent eddies in the expelled humid puff, their lifetime gets extended by a factor of more than 30 times as compared to what is suggested by the classical picture by Wells, for 50% relative humidity. With increasing ambient relative humidity the extension of the lifetimes of the small droplets further increases and goes up to around 150 times for 90% relative humidity, implying more than 2 m advection range of the respiratory droplets within 1 sec. Employing Lagrangian statistics, we demonstrate that the turbulent humid respiratory puff engulfs the small droplets, leading to many orders of magnitude increase in their lifetimes, implying that they can be transported much further during the respiratory events than the large ones. Our findings provide the starting points for larger parameter studies and may be instructive for developing strategies on optimizing ventilation and indoor humidity control. Such strategies are key in mitigating the COVID-19 pandemic in the present autumn and upcoming winter.
Body Fluids/chemistry , Body Fluids/virology , COVID-19/transmission , Models, Biological , Aerosols/chemistry , Air Microbiology , Air Movements , COVID-19/virology , Computer Simulation , Disease Transmission, Infectious , Exhalation , Humans , Pandemics , SARS-CoV-2/chemistry , SARS-CoV-2/isolation & purification
Many natural and industrial turbulent flows are subjected to time-dependent boundary conditions. Despite being ubiquitous, the influence of temporal modulations (with frequency f) on global transport properties has hardly been studied. Here, we perform numerical simulations of Rayleigh-Bénard convection with time periodic modulation in the temperature boundary condition and report how this modulation can lead to a significant heat flux (Nusselt number Nu) enhancement. Using the concept of Stokes thermal boundary layer, we can explain the onset frequency of the Nu enhancement and the optimal frequency at which Nu is maximal, and how they depend on the Rayleigh number Ra and Prandtl number Pr. From this, we construct a phase diagram in the 3D parameter space (f, Ra, Pr) and identify the following: (i) a regime where the modulation is too fast to affect Nu; (ii) a moderate modulation regime, where Nu increases with decreasing f, and (iii) slow modulation regime, where Nu decreases with further decreasing f. Our findings provide a framework to study other types of turbulent flows with time-dependent forcing.
Brownian motion of particles in fluid is the most common form of collective behavior in physical and biological systems. Here, we demonstrate through both experiment and numerical simulation that the movement of vortices in a rotating turbulent convective flow resembles that of inertial Brownian particles, i.e., they initially move ballistically and then diffusively after certain critical time. Moreover, the transition from ballistic to diffusive behaviors is direct, as predicted by Langevin, without first going through the hydrodynamic memory regime. The transitional timescale and the diffusivity of the vortices can be collapsed excellently onto a master curve for all explored parameters. In the spatial domain, however, the vortices exhibit organized structures, as if they are performing tethered random motion. Our results imply that the convective vortices have inertia-induced memory such that their short-term movement can be predicted and their motion can be well described in the framework of Brownian motions.
Droplets can self-propel when immersed in another liquid in which a concentration gradient is present. Here we report the experimental and numerical study of a self-propelling oil droplet in a vertically stratified ethanol-water mixture: At first, the droplet sinks slowly due to gravity, but then, before having reached its density matched position, jumps up suddenly. More remarkably, the droplet bounces repeatedly with an ever increasing jumping distance, until all of a sudden it stops after about 30 min. We identify the Marangoni stress at the droplet-liquid interface as responsible for the jumping: its strength grows exponentially because it pulls down ethanol-rich liquid, which in turn increases its strength even more. The jumping process can repeat because gravity restores the system. Finally, the sudden death of the jumping droplet is also explained. Our findings have demonstrated a type of prominent droplet bouncing inside a continuous medium with no wall or sharp interface.
Many natural and engineering systems are simultaneously subjected to a driving force and a stabilizing force. The interplay between the two forces, especially for highly nonlinear systems such as fluid flow, often results in surprising features. Here we reveal such features in three different types of Rayleigh-Bénard (RB) convection, i.e., buoyancy-driven flow with the fluid density being affected by a scalar field. In the three cases different stabilizing forces are considered, namely (i) horizontal confinement, (ii) rotation around a vertical axis, and (iii) a second stabilizing scalar field. Despite the very different nature of the stabilizing forces and the corresponding equations of motion, at moderate strength we counterintuitively but consistently observe an enhancement in the flux, even though the flow motion is weaker than the original RB flow. The flux enhancement occurs in an intermediate regime in which the stabilizing force is strong enough to alter the flow structures in the bulk to a more organized morphology, yet not too strong to severely suppress the flow motions. Near the optimal transport enhancements all three systems exhibit a transition from a state in which the thermal boundary layer (BL) is nested inside the momentum BL to the one with the thermal BL being thicker than the momentum BL. The observed optimal transport enhancement is explained through an optimal coupling between the suction of hot or fresh fluid and the corresponding scalar fluctuations.
Coherent structures are ubiquitous in turbulent flows and play a key role in transport. The most important coherent structures in thermal turbulence are plumes. Despite being the primary heat carriers, the potential of manipulating thermal plumes to transport more heat has been overlooked so far. Unlike some other forms of energy transport, such as electromagnetic or sound waves, heat flow in fluids is generally difficult to manipulate, as it is associated with the random motion of molecules and atoms. Here we report how a simple geometrical confinement can lead to the condensation of elementary plumes. The result is the formation of highly coherent system-sized plumes and the emergence of a new regime of convective thermal turbulence characterized by universal temperature profiles and significantly enhanced heat transfer. It is also found that the universality of the temperature profiles and heat transport originate from the geometrical properties of the coherent structures, i.e., the thermal plumes. Therefore, in contrast to the classical regime, boundary layers in this plume-controlled regime are being controlled, rather than controlling.
