We experimentally investigate a millimetric armored droplet of a water-isopropyl alcohol solution sedimenting through oil and approaching a water layer at the bottom of the container. Upon reaching the oil-water interface, the droplet is shown to rupture and coalesce with the water either for low droplet densities (floating rupture) or for low oil viscosities (sinking rupture). By contrast, for sufficiently large drop density or oil viscosity, the oil covering the armored drop pinches off in the underlying water, as the armored drop continues to sink. This leads to the double encapsulation of an aqueous solution in water, which can be utilized to transport desired ingredients within a wet environment. We show that a simplified quasistatic model of a rigid sphere successfully captures the limit of the floating rupture behavior. We also rationalize the transition from the sinking rupture to oil pinch-off, by comparing the timescales of the film drainage versus sinking. Our results demonstrate that an effective Bond number and an effective Ohnesorge number are the two key dimensionless parameters that characterize the pinch-off threshold in good agreement with the experiments.

Direct numerical simulation of polymer-laden turbulent flow is performed for the investigation of the two-way interaction. Lagrangian dynamic simulation is adopted for a finitely extensible nonlinear elastic (FENE-2) dumbbell model to observe polymer dynamics in turbulent flow. The impact of the polymers on fluid momentum is described using the elastic force between two beads. The elasticity of the polymer is characterized using the Weissenberg number, ${\text{We}}^{*}=\frac{{\tau }_p}{{\tau }_k}$, where ${\tau }_p$ and ${\tau }_k$ denote the elasticity timescale and the Kolmogorov timescale, respectively. We observe that for ${\text{We}}^{*}\le 1.0$ most of the polymers are in a coiled state and the hydrodynamic properties of fluid remain unchanged. The coil-stretch transition is observed at approximately ${\text{We}}^{*}=3.0$. The highly stretched polymers in turn contribute to significant turbulence modification for large values of the Weissenberg number. The effect of the Weissenberg number on various turbulent statistics is computed and analyzed. The highly stretched polymers tend to rotate around the vortical structures. The feedback force effectively suppresses the turbulence structures for large values of the elasticity parameter. The effect of ${\text{We}}^{*}$ on the alignment between the end-to-end distance vector, vorticity vector, and the eigenvector of the rate of strain tensor is presented. A better insight into the effect of polymers on turbulence is obtained through the direct force modeling in stationary turbulence although the effect itself has been known for a long time.

Viscous flow in the narrow gap between a rigid plate and a confined elastic solid has been observed to “choke” at high flow rates, due to the deforming solid making contact with the plate and sealing the gap. When the viscous flow is driven by injection of a gas bubble, the advancing meniscus is susceptible to the viscous-fingering instability. By comparing fingering experiments with axisymmetric numerical simulations, we demonstrate that, depending on the width of the fingers, the fingering instability can either promote or suppress choking, i.e., cause the system to choke when an axisymmetric system would not, or vice versa.

For partially wetting fluids, previous results suggest that the thickness and the dewetting velocity of gravity-driven films are uniquely determined by the triple line dynamics. In contrast, when flushing aqueous liquids through polymer tubes, our measurements show that the dewetting velocity and thickness can be selected. The control parameter is pressure, i.e., the macroscopic curvature of the meniscus. Our results demonstrate directly the major role played by the macroscopic geometry in the stability of a dynamic meniscus as predicted by Eggers, [Phys. Rev. Lett. 93, 094502 (2004)].

We present an experimental and theoretical investigation of steady jetting regimes in the electrohydrodynamic (EHD) jet printing process, wherein a liquid jet issuing from a needle is stretched by applying a high electric field between the needle and a collector substrate. While EHD jetting is well understood in the context of the electrospray process, we show that the jetting characteristics can differ significantly in the printing configuration in which the needle is kept close to the collector to prevent spraying. Through experimental visualization of EHD jets and current measurements, we show that steady EHD jetting can occur in three regimes, namely, the cone-jet, moderately stretched jet, and thick-jet regimes, depending on the flow rate, applied potential difference, and needle-to-collector gap. To elucidate the underlying physics of these experimentally observed regimes, we perform order-of-magnitude analysis for the current transfer region of the jet, where the conduction and surface convection currents are of comparable magnitude. Based on the relative size of the current transfer region and the jet diameter, we derive the criteria for observing the three steady EHD jetting regimes. For each of these regimes, we also describe the dependence of the jet diameter and the current carried by jet on flow rate, potential difference, and aspect ratio in the form of scaling relations. The theoretical criteria for various steady jetting regimes and the corresponding scaling relations for the jet diameter and current show good agreement with the experimental observations. These theoretical relations can be useful for the design, performance monitoring, and control of EHD jet printing.

To understand ultrasonic cavitation, it is imperative to analyze the effects of the vapor-liquid phase transitions on sound-wave propagation. Since current methods based on fluid dynamics offer limited information, it is imperative to carry out further research on this phenomenon. In this study, we investigated the effects of cavitation and near-critical fluid on sound waves using the molecular dynamics (MD) simulations of Lennard-Jones fluids. In the first-order liquid-to-vapor transition region (far from the critical point), the waveform does not continuously change with the temperature and source oscillation amplitude owing to the discontinuous change in the density due to the phase transition. Meanwhile, in the continuous transition region (crossing near the critical point), the waveform continuously varies with temperature regardless of the amplitudes because phase separation is not involved in this region. The density fluctuations increase as the amplitude increases; however, it does not affect the waveform. Thus, we clarified that the first-order and continuous transitions have different impacts on sound waves. Moreover, we determined the acoustic characteristics, such as attenuation and nonlinear parameters, by comparing the results of the numerical solution of Burgers' equation and MD simulation. Burgers' equation clearly describes the sound-wave phenomenon until phase separation or bubble formation occurs. In the continuous transition region, the attenuation parameters tend to diverge, reflecting a critical anomaly trend. We observed the bubbles move forward with the oscillation of their radii owing to their interaction with the sound waves. To the best of our knowledge, this is the first direct observation of the interaction using MD simulations.

While classic hydrodynamic models predict ordered formations for fish schools, observations show that schools are seemingly disordered. Our experiments on robotic swimmers may help to reconcile this discrepancy by showing that many different formations all emerge spontaneously and are stabilized due to flow interactions. Surprisingly, these locked states extend almost twice as far downstream for laterally displaced swimmers as for those in line. We also observe significant boosts in swimming speed—up to 60% faster than an isolated swimmer—for side-by-side formations. These findings demonstrate that benefits such as group cohesion and speed enhancement arise naturally via flow interactions and for the diverse relative arrangements seen in schools.

We apply a previously developed asymptotic model [J. Fluid Mech. 915, A133 (2021)] to study instabilities of free surface films of nanometric thickness on thermally conductive substrates in two and three spatial dimensions. While the specific focus is on metal films exposed to laser heating, the model itself applies to any setup involving films on the nanoscale whose material parameters are temperature-dependent. For the particular case of metal films heated from above, an important aspect is that the considered heating is volumetric, since the absorption length of the applied laser pulse is comparable to the film thickness. In such a setup, absorption of thermal energy and film evolution are closely correlated and must be considered self-consistently. The asymptotic model allows for a significant simplification, which is crucial from both modeling and computational points of view, since it allows for asymptotically correct averaging of the temperature over the film thickness. We find that the properties of the thermally conductive substrate—in particular, its thickness and rate of heat loss—play a critical role in controlling the film temperature and dynamics. The film evolution is simulated using efficient GPU-based simulations which, when combined with the developed asymptotic model, allow for fully nonlinear time-dependent simulations in large three-dimensional computational domains. In addition to uncovering the role of the substrate and its properties in determining the film evolution, one important finding is that, at least for the considered range of material parameters, strong in-plane thermal diffusion in the film results in negligible spatial variations of temperature, and the film evolution is predominantly influenced by temporal variation of film viscosity and surface tension (dictated by average film temperature), as well as thermal conductivity of the substrate.

Water-absorbing materials consisting of hydrogel particles are widely used for agricultural substrates, hygienic products, drug delivery systems, and microfluidic devices. Hydrogel particles absorb water with expansion, leading to dynamics involving complicated interactions of intergranular liquid flow and hydrogel deformation. It is thus difficult to predict the water absorption rate of these materials. Water flow in hydrogel-coated capillary tubes also occurs with the deformation of flow passages, so it can be analogous to capillary flow through porous structures made of hydrogels. Here we report a combined experimental and theoretical investigation of water flow through capillaries whose inner surface is covered with a hydrogel layer. We experimentally measured the flow rate of water through hydrogel-coated capillary tubes and the volume of water absorbed by the hydrogel layer. We developed a mathematical model for capillary flow including the effects of the water absorption and swelling of the hydrogel layer. Our model is in good agreement with the measurements of the water flow rate and elucidates how the absorption and swelling of hydrogel regulate capillary flow. This study provides a theoretical framework for understanding the dynamics of capillary flow through porous structures composed of hydrogels, leading to insights into the engineering applications of porous hydrogel materials.

Magnetic control is a feasible way to manipulate droplets in various applications. For actuating nonferromagnetic droplets, embedded magnetic particles or marbles that contact the droplet directly have been widely used; however, such strategies tend to result in departure, substrate contamination, and infection of biological samples. Herein we propose a portable and noncontact method for magnetic manipulation of water droplets on slippery liquid-infused porous surfaces by a single magnet. The migration velocity of the water droplet reaches 1 mm/s, which correlates positively with the droplet volume and negatively with the viscosity of the lubricating oils. The effects of droplet volume, viscosity of lubricating oil, and vertical spacing on the critical migration velocity of water droplet are investigated. Combined with experiments, numerical simulations, and theoretical analysis, the migration mechanism of the droplet is analyzed thoroughly. In addition, this method exhibits great potential for transporting low-surface-tension fluids, bubbles, and magnetic nanofluids. The present findings offer potential benefits for the design and application in droplet microfluidics.

Contrary to incompressible flows, there has been an immense research gap in the flow transition control using velocity streaks for supersonic flows. The first direct numerical simulations (DNS) study in this direction was conducted at Mach 2.0 for an adiabatic wall condition and showed that effective control could be provided by employing streak modes having four to five times the fundamental wave number of the most amplified oblique disturbance waves. However, the application range of the method in terms of the control amplitude is studied roughly and only for adiabatic walls. The present study scrutinizes the controlling capability of these decaying streak modes under the influence of both adiabatic and weak wall heating/cooling by means of DNS. The stabilizing/destabilizing influence of the control streaks in combination with different thermal boundary conditions in a perturbed boundary layer is shown. The effective range of the streak amplitudes under the given flow conditions is presented both for adiabatic and isothermal wall conditions. No significant impact of the wall-boundary condition on the control-streak development is observed in the sustainable flow control range, but the useful control-streak amplitude range diminishes with wall heating.

Penetration of liquid with distinct volumes into a funnel-like pore structure is widely observed in nature and technical applications. However, when the droplet size is comparable with the pore size, the penetration criterion, i.e., under which condition the droplet can penetrate into the pore, remains an open question. In this work, we present theoretical models to address the penetration criteria in terms of the droplet size, the intrinsic wettability, and the opening angle of the funnel-shaped structure. The proposed theoretical models are well corroborated by phase-field simulations. Our findings demonstrate a critical contact angle below which a finite-volume droplet can penetrate into a hydrophobic pore. This critical contact angle is intimately related to the opening angle and the droplet size, which provides a complement to previous literature. Note that for a certain-sized droplet, the critical contact angle becomes invariant when the opening angle is greater than a certain threshold. Moreover, we find that for a constant opening angle, the critical contact angle decreases with the increase of the droplet size. As the droplet volume tends to be infinite, the opening angle has almost no influence on the penetration, and the critical contact angle asymptotically approaches ${90}^{\circ }$, being consistent with previous works. Our observations illuminate a special mechanism for a precise maneuver of droplets in pore structures with potential applications in filter systems and microfluidic platforms.

A theoretical and experimental study is presented of the one-dimensional compression of a networked suspension. Particular attention is given to relatively rapid compression where we extend previous works by including an elastoviscoplastic constitutive relation. Solutions of a one-dimensional model are presented, and asymptotic limits explored, for compressions controlling either displacement or load. The results are compared to complementary laboratory experiments using cellulose fiber suspensions, with the material functions appearing in the model calibrated by independent experiments. Measurements of load and local solid velocity as a function of displacement during compression and unloading gauge the importance of elastic effects. The comparison between experiment and theory is satisfying, demonstrating a dramatic improvement over existing inelastic constitutive models in reproducing the observed differential spatial compaction.

We experimentally study intrusion into fluid-saturated granular beds by a free-falling sphere, varying particle size and fluid viscosity. We test our results against Darcy-Reynolds theory, where the deceleration of the sphere is controlled by Reynolds dilatancy and the Darcy flow resistance. We find the observed intruder dynamics are consistent with Darcy-Reynolds theory for varied particle size. We also find that our experimental results for varied viscosity are consistent with Darcy-Reynolds theory, but only for a limited range of the viscosity. For large viscosities, observed forces begin to decrease with increasing viscosity, in contrast with the theoretical prediction. We suggest that a dynamic lubrication mechanism may be responsible for the observed discrepancy.

A hierarchical clustering method for volumetric vortical regions is proposed. Point clouds in vortical regions are extracted from an instantaneous flow field, using a series of parallel planes normal to a direction, and are grouped between consecutive planes. Cross-sectional distributions of points are then stacked in the direction. Each group of extracted points is identifiable as an individual entity that is referred to as a $p$ cluster, with the letter $p$ replaced by the terms proto, sub, super, and hyper, according to the level of clustering. The spatial distribution and temporal evolution of $p$ clusters are visualized and automatically tracked. The present method is applied to the late stage of the K-type natural transition of a boundary-layer flow. Our method clearly captures, with admitting a detailed analysis, pairs of vortex structures located in the viscous sublayers near the roots of hairpin vortices. Moreover, it allows the algorithmic identification of dominant mathematical terms in the enstrophy and helicity equations, and a categorization of the extracted points based on local dynamics characterized by sets of the dominant terms. Construction of ensemble-averaged quantities using the present method, an extension of the method to omnidirections, and comparison between the present method and conventional vortex analysis methods are also discussed.

We investigate the motion of multicellular magnetotactic bacteria (MMB) near a hard surface. Directing MMB towards a flat surface causes them to accumulate about the wall as an active gas. MMB are exponentially distributed about the surface with a penetration depth determined by the typical distance an MMB swims before it aligns with the ambient field. Increasing the magnetic field past a critical value, at which the penetration depth is of order the size of an MMB, causes the active gas to condense into a two-dimensional active fluid. Measurements of MMB motion in this phase reveal that contact with the surface enhances rotational diffusion by a factor of 8 and that velocity fluctuations are Laplace distributed. The fluid undergoes a percolation transition at a critical magnetic field. Supercritical active fluids exhibit dynamic voids, which limit the relaxation of density fluctuations. We describe the possible ecological significance of these results.

Effect of interfacial disturbances on instabilities of buoyant-thermocapillary convective flows in rectangular cavities is studied in a series of numerical experiments. The computations are carried out for several two-liquid two-layer systems taking into account properties of liquids used in previously published experiments. The relation between the interface deformations and the Boussinesq approximation is discussed. It is shown that in some systems, including the interface disturbances in the model can alter the critical temperature difference by approximately 10%, producing either a destabilizing or stabilizing effect. The interface oscillations appear as standing or traveling waves whose wavelength can vary from short wavelengths to a single wave occupying all the available space. Rough estimations show that in some liquid-liquid systems the interface oscillations’ amplitude can reach several tens of microns. Patterns of the most unstable disturbances are presented and discussed. It is argued that instabilities in some two-layer systems develop similarly to the Holmboe instabilities in stratified mixing layers.

A key question in the interaction of droplets with lubricated and liquid-infused surfaces is what determines the apparent contact angle of droplets. Previous work has determined this using measured values of the geometry of the “skirt”—the meniscus-like deformation that forms around the base of the deposited droplet. Here, we consider theoretically the equilibrium of a droplet on a smooth, impermeable lubricant-coated surface, and we argue that the small effect of gravity within the skirt and the size of the substrate are important for determining the final equilibrium. However, we also show that the evolution of the skirt toward this ultimate equilibrium is extremely slow (on the order of days for typical experimental parameter values). We therefore suggest that previous experiments on smooth lubricated surfaces may have observed only slowly-evolving transients, rather than “true” equilibria, potentially explaining why a wide range of skirt sizes have been reported.

Dispersing small particles in a liquid can produce surprising behaviors when the solids fraction becomes large: rapid shearing drives these systems out of equilibrium and can lead to dramatic increases in viscosity (shear thickening) or even solidification (shear jamming). These phenomena occur above a characteristic onset stress when particles are forced into frictional contact. Here we show via simulations how this can be understood within a framework that abstracts details of the forces acting at particle-particle contacts into general stress-activated constraints on relative particle movement. We find that focusing on just two constraints, affecting sliding and rolling at contact, can reproduce the experimentally observed shear thickening behavior quantitatively, despite widely different particle properties, surface chemistries, and suspending fluids. Within this framework parameters such as coefficients of sliding and rolling friction can each be viewed as proxy for one or more forces of different physical or chemical origin, while the parameter magnitudes indicate the relative importance of the associated constraint. In this way, a new link is established that connects features observable in macroscale rheological measurements to classes of constraints arising from micro- or nanoscale properties.

In the present study, we propose a spectral decomposition method to segregate the contributions of wall-attached/detached and self-similar/non-self-similar eddies by taking advantage of the proper orthogonal decomposition. It is applied to analyze the compressible and incompressible turbulent channel flows to verify the Reynolds number and compressibility effects on velocity fluctuations and investigate whether the temperature fluctuations share similar features. It is found that both the energetic wall-detached eddies and the small-scale wall-attached eddies (the so-called type C eddies) are self-similar, thereby supporting the methods of modeling them together. The medium-scale wall-attached eddies in the present study are equivalent to the original concept of attached eddies (type A eddies), whose features predicted by theories but not observed due to the interference of other types of eddies are fully revealed in the logarithmic region. Their growing hierarchy with the extension of the logarithmic region as the Reynolds number increases is reconfirmed to be responsible for the increment of inner peak of fluctuation variances. The large-scale wall-attached eddies representing the very-large-scale motions (type B eddies) manifest no inclination to have stronger superposition effects in the near-wall and logarithmic region, though intensified by the increasing Reynolds number. Compressibility, expectedly, only impacts the small-scale motions in the near-wall region. Regarding the temperature fluctuation, the large-scale type B eddies also show logarithmic decay in the logarithmic region. The type A eddies and the detached eddies are prominent, constituting a considerable portion of the spectra and variances.