Liquid atomization processes generating sprays and aerosols of droplets are used in many delivery and coating systems involving pure solvents, solutions, and suspensions. In our recent experimental work, we introduced a novel liquid atomization process generating microsprays and aerosols of submicron-diameter droplets for pure solvents, solutions, and suspensions: gas jets disintegrate thin liquid films that are formed as bubbles approach a liquid surface. Here, we develop a theoretical description of droplet sizes and flow rates, using the first principles of conservation of mass and energy, and employing dimensional and scale analyses. We introduce atomization diagrams as a graphical tool to determine possible, impossible, and expected droplet diameters and specific flow rates in aerosols and sprays produced under various conditions. We find a reasonable agreement between the theory and experiments for five different liquids converted into aerosols of submicron-diameter droplets by an atomization process where gas jets disintegrate thin liquid films that are formed as bubbles approach a liquid surface, and also for five traditional pressure nozzles that produce sprays of droplets of hundreds of microns in diameter. Our study explores the overall range of mean droplet diameters between 0.1 and 100 μm and Ohnesorge numbers between 0.01 and 100, and the analysis and atomization diagrams contribute to understanding of liquid atomization and can serve as a theoretical framework for comparing different liquid atomization techniques.

We introduce a closure model for coarse-grained kinetic theories of polar active fluids. Based on a quasiequilibrium approximation of the particle distribution function, the model closely captures important analytical properties of the kinetic theory, including its linear stability and the balance of conformational entropy production and dissipation. Nonlinear simulations show the model reproduces the qualitative behavior and nonequilibrium statistics of the kinetic theory, unlike commonly used closure models. We use the closure model to simulate highly turbulent suspensions in both two and three dimensions in which we observe complex multiscale dynamics, including large concentration fluctuations and a proliferation of polar and nematic defects.

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.

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.

We study entrainment in dry thermals in neutrally and unstably stratified ambients, and moist thermals in dry-neutrally stratified ambients using direct numerical simulations. We find, in agreement with results of Lecoanet and Jeevanjee [J. Atmos. Sci. 76, 3785 (2019)], that turbulence plays a minor role in entrainment in dry thermals in a neutral ambient for Reynolds numbers $\text{Re}\lesssim {10}^4$. We then show that the net entrainment rate increases when the buoyancy of the thermals increases, either by condensation heating or because of an unstably stratified ambient. This is in contrast with the findings of Morrison et al. [J. Atmos. Sci. 78, 797 (2021)]. We also show that the role of turbulence is greater in these cases than in dry thermals and, significantly, that the combined action of condensation heating and turbulence creates intense small-scale vorticity, destroying the coherent vortex ring that is seen in dry and moist laminar thermals. These findings suggest that fully resolved simulations at Reynolds numbers significantly larger than the mixing transition Reynolds number $\text{Re}={10}^4$ are necessary to understand the role of turbulence in the entrainment in growing cumulus clouds, which consist of a series of thermals rising and decaying in succession.

Cilia and flagella are organelles that play central roles in unicellular locomotion, embryonic development, and fluid transport around tissues. In these examples, multiple cilia are often found in close proximity and exhibit coordinated motion. Inspired by the flagellar motion of biflagellate cells, we examine the synchrony exhibited by a filament pair surrounded by a viscous fluid and tethered to a rigid planar surface. A geometrically switching base moment drives filament motion, and we characterize how the stability of synchonized states depends on the base torque magnitude. In particular, we study the emergence of bistability that occurs when the antiphase, breast-stroke branch becomes unstable. Using a bisection algorithm, we find the unstable edge state that exists between the two basins of attraction when the system exhibits bistability. We establish a bifurcation diagram, study the nature of the bifurcation points, and find that the observed dynamical system can be captured by a modified version of Adler's equation. The bifurcation diagram and presence of bistability reveal a simple mechanism by which the antiphase breast stroke can be modulated, or switched entirely to in-phase undulations through the variation of a single bifurcation parameter.

The Peregrine soliton (PS) is widely regarded as a prototype nonlinear structure capturing properties of rogue waves that emerge in the nonlinear propagation of unidirectional wave trains. It has been recently demonstrated that the PS can emerge locally, as an asymptotic structure arising from the propagation of an arbitrary large decaying pulse, independently of its solitonic content. This mathematical discovery has changed the widely accepted paradigm of the solitonic nature of rogue waves by enabling the PS to emerge from partially radiative or even completely solitonless initial data. In this work, we realize this scenario in a water tank experiment with a particular aim to control the point of the PS occurrence in space-time by imposing an appropriately chosen initial chirp. By employing the inverse scattering transform for the synthesis of the initial data, we are able to engineer a localized wave packet with a prescribed solitonic and radiative content. This enables us to control the position of the emergence of the rogue wave by adjusting the inverse scattering spectrum. The proposed method of nonlinear spectral engineering is found to be robust to higher-order nonlinear effects, preceding the wave breaking dynamics, that are inevitable in realistic wave propagation conditions.

Smooth muscle-lined organs like the gut, the ureter, and the fallopian tubes transport matter by generating traveling contractile waves. Intestinal peristalsis is characterized by rhythmic trains of shallow, low-amplitude myogenic waves and high-amplitude, lumen-obliterating neurogenic waves. In this paper, we develop a simple analytical Poiseuille-flow model to predict the flow rates induced by these different contractions as a function of all relevant wave parameters, and compare them to a numerical fluid-solid finite element model. We rationalize experimentally observed bolus to-and-fro motion induced by shallow myogenic waves. We show that occluding waves induce considerable bolus mixing due to an upstream vortex. We then investigate the hydrodynamics induced by two waves propagating either in the same direction (colinear) or in opposite directions, as happens in the digestive tract. For colinear waves, we find that the bolus reflux is maximal at a distance between successive myogenic waves close to the one observed physiologically. Colliding waves create a high pressure region that gives rise to rapid fluid flow, high shear stress, and radial mixing upon annihilation. Our paper provides fundamental insight on the fluid dynamics (reflux, propulsion, and mixing) generated by different contraction patterns of the intestine.

While landing, birds often perform a perching maneuver, which involves pitching their wings upward while decelerating to a complete stop. This study is motivated by the observation that some birds fold their wings to create a wing sweep during such perching. The objective of this study is to find out whether such a wing sweep helps during a perching maneuver. We use two flat plates, one with a sweep and another without any sweep, and consider a deceleration maneuver where both of them decelerate to stop from Reynolds number $\text{Re}=13000$. We consider two cases: one, where the wings undergo only heaving, and two, where the wings perform both heaving and pitching. The latter maneuver was designed to mimic perching. By performing experiments and simulations, we compare the temporal evolution of the instantaneous forces and the vortex dynamics of both these plates. We show that during a major part of the deceleration, the instantaneous lift forces are higher in the case of the plate with sweep compared to the plate with no sweep during both kinematics. Our results indicate that the higher lift in the swept plate case was contributed by a stable leading-edge-vortex (LEV) which remains attached to the plate. This increase in stability was contributed by the spanwise vorticity convection caused by a distinct spanwise flow on the swept plate, as revealed by the numerical simulation. We also show that combined pitching and heaving resulted in higher force peaks, and the forces also decayed at a faster rate in this case compared to the heave-only case. Finally, by using an analytical model for unsteady flows, we prove that the higher lift characteristics of the swept plate were entirely due to higher circulatory forces.

The Childress-Soward model, consisting of a an electrically conducting Rayleigh-Bénard layer rotating about a vertical axis, is the conceptually simplest model configuration that captures all essentials of convectively driven dynamos. Here we study the effects of different boundary conditions on this type of dynamo. This closes a gap in the existing literature, which has primarily focused on simple, but geophysically not very realistic, cases. Furthermore, the extensive literature on boundary layers in nonrotating and rotating Rayleigh-Bénard convection makes the Childress-Soward model an ideal test bed for illuminating the fundamental effects that the boundary conditions have on convection-driven dynamos. In this study we systematically vary the thermal, mechanical, and electrical boundary conditions in direct numerical simulations, with a focus on flow regimes characterized by geostrophic turbulence. One key result applies to both dynamos and nonmagnetic, rotating convection. We show that for no-slip boundaries, the Nusselt number increases significantly when a fixed heat flux is imposed instead of a given temperature difference. This effect can be explained by an interplay of Ekman pumping and the internal structure of the thermal boundary layer, which is very sensitive to thermal boundary conditions. Dynamical changes are shown to exist only within the boundary layers, such that the bulk dynamics remains largely unaffected. In the dynamo case, we argue that care needs to be taken in order to ensure comparable energetics when changing from fixed-temperature to fixed-flux conditions. If done properly, no significant differences in the leading order features of the resulting dynamos are observed. In particular, the thermal boundary conditions have no noticeable influence on the horizontal flow scales, as might have been expected from studies in spherical geometry. In contrast, the mechanical boundary conditions largely control whether or not large-scale flows and fields can be generated. For no-slip boundaries, Ekman friction strongly suppresses upscale transport and eliminates the large-scale vortex dynamos that exist in the stress-free case. Finally, the magnetic boundary conditions are shown to strongly affect the topology of the generated magnetic fields. For an insulating exterior, the magnetic field is most intense in the central part of the fluid layer, whereas we observe a strong magnetic field buildup close to perfectly conducting boundaries. For large magnetic Reynolds numbers, we further observe thin layers of intense horizontal field attached to perfect conductors. The horizontal flow scales, however, remain largely unaffected in the investigated parameter regime.

The economics, environmental impact, and mechanical properties of paper-based storage containers have been widely studied. However, knowledge of the physical processes relevant to the end-user experience is unavailable. This paper outlines the main effects associated with the closing and opening of telescoping boxes, which are used, for instance, to store and transport board games, footwear, mobile phones, and tablet computers. The sliding motion of the lid is controlled by the flow in a thin film of air in the gap separating the lid and the base of the box. Based on a broad comparison between theory and experiments on real and synthetic boxes, we find that the process is primarily controlled by the shape of the gap between the base and the lid. We derive a master equation for the lid motion and identify the origin of three distinct experimental regimes. Finally, an optimal design for a rapidly closing box is identified.

This paper presents a numerical method to study the pulsing behavior of soft corals. Evidence indicates that the pulsing behavior of soft corals in the family Xeniidae facilitates photosynthesis of their symbiotic algae. One way to investigate this complex behavior is through mathematical modeling and numerical simulations. The immersed boundary method is used to model the interaction of the tentacles with the surrounding fluid. The flow is then coupled with a photosynthesis model. The photosynthesis is modeled by advecting and diffusing oxygen, the byproduct of photosynthesis, where the coral tentacles act as a moving source of the oxygen. This study develops a methodology for solving a partial differential equation with boundary conditions on a moving immersed elastic boundary. In this study, the Reynolds and Péclet numbers are varied in the simulations to gain an understanding of how these parameters affect the mixing and photosynthesis. The mixing is quantified using both the fluid flow and oxygen concentration dynamics. The results show that for the biologically relevant Péclet number, the fluid dynamics significantly affect the photosynthesis and that the biologically relevant Reynolds number is advantageous for mixing and photosynthesis.

The Levitation of a droplet on a hot surface due to the rapid vaporization of the liquid at the proximity of the heat source is known as the Leidenfrost effect. This effect has been demonstrated when the surface is a solid or a liquid. Here, we explore the interaction between a liquid droplet and a hot granular material. The granular material is, by essence, a solid but adopts some behaviors similar to fluids. Surprisingly, we found that the droplet deeply penetrated the hot granular material. During the penetration process, the vapor production is so intense that the grains underneath the droplet are ejected. Consequently, the droplet moved downward under the action of gravity. A mechanism based on the Leidenfrost effect is proposed considering that the granular material can be modeled as a rough surface that can be eroded when the vapor speed is sufficient.

We present a deformation-dependent propulsion phenomenon for soft particles such as cells in microchannels. It is based on a broken time-reversal symmetry generated by a fast forward and a slow backward motion of a fluid which does not progress on average. In both sections, soft particles deform differently and thus progress relatively to the liquid. We demonstrate this by using Lattice-Boltzmann simulations of ubiquitous red blood cells in microchannels, as well as simulations for capsules and minimal-soft-tissue models in unbounded Poiseuille flows. The propulsion of the soft particles depends besides the oscillation asymmetry on their size, deformation type, and elasticity. This is also demonstrated by analytical calculations for a minimal model. Our findings may stimulate a rethinking of particle sorting methods. For example, healthy and malignant cells often differ in their elasticity. With the proposed method, several cell types with different deformabilities can be separated simultaneously without labeling or obstacles in a microfluidic device.

The role of streamwise length scales (${\lambda }_x$) in turbulent skin friction generation is investigated using a direct numerical simulation data set of an incompressible zero pressure gradient turbulent boundary layer and the spectral analysis based on the Fukagata-Iwamoto-Kasagi (FIK) identity by Fukagata et al. [K. Fukagata et al., Phys. Fluids 14, L73 (2002)]. The total skin friction generation associated with motions scaled with local boundary layer thickness $\delta$ of ${\lambda }_x<3\delta$ and ${\lambda }_x>3\delta$ is assessed. The FIK-identity-based spectral analysis is further extended to include the quadrant analysis of Reynolds shear stress. This allows one to relate the turbulent skin friction generation to the quadrant events of Reynolds shear stress, which plays a central role in the momentum transport in turbulent wall-bounded flows. The small-scale ejection and sweep events (${\lambda }_x<3\delta$) contribute to a significant portion of turbulent skin friction. However, it is found that the large-scale ejection and sweep events with streamwise length scales at ${\lambda }_x>3\delta$ are equally important. The turbulent skin friction reduction associated with the modification of large- and small-scale quadrant events is studied, using well-resolved simulation data sets of a large-eddy break-up (LEBU) device in a turbulent boundary layer. The results reveal that LEBUs modify both the large- and small-scale ejection and sweep events, yielding a substantial turbulent skin friction reduction.

Cablelike bodies play a key role in many interdisciplinary systems but are hard to simulate. Asymptotic theories, called slender-body theories, are effective but apply in specific regimes and can be hard to extend beyond leading order. In this paper we develop an exact slender-body-like theory for the surface traction of cablelike bodies in viscous flow. This theory expresses the traction as a series of solutions to a well-behaved one-dimensional Fredholm integral equation of the second kind. This process can be simply generalized to other systems.

The wake behind a bluff body in the presence of a density gradient is characterized by competing effects of buoyancy, momentum, and ultimately viscosity as the flow decays. Consequently, there are a number of distinct flow regimes into which the wakes can be placed, and there is some interest in whether any given wake can be traced back to its source through interrogation of selected fluid mechanical properties in the wake. Here we use dynamic mode decomposition (DMD) to find modes that can be used to characterize and automate such a process. A custom-designed algorithm is proposed that can sort and classify stratified wakes based on a selection of the most energetic DMD modes. The approach is very, or partially successful, depending on the quality and dimension of the input data. The success of these first steps may be used to develop similar methods for more challenging and fully turbulent wakes, and also can serve as a guide for data-driven methods that require no prior knowledge of the flow structure.

Ciliates are ubiquitous in the marine environment and important consumers of phytoplankton and flagellates. The feeding on suspended food particles in ciliates is complex and relies typically on coordinated motion in bands of transversal rows of cilia known as membranelles. Many ciliates are upstream collectors that use a single membranelle band to generate feeding flow, retain food particles, and transport them to the mouth region. To explore a representative upstream collector, we consider the ciliate Euplotes vannus. We determine the clearance rate using particle tracking and estimate the flow-generating force by fitting a point force model to the observed flow. To obtain a mechanistic understanding of feeding flow and particle retention, we use high-speed video microscopy. The cilia move parallel to the membranelle band towards the mouth region in the power strokes, and a metachronal wave propagates away from the mouth region parallel to the band and outwards along the membranelles. A gap, therefore, opens between neighboring membranelles from the inner side of the band where the mouth region is located, and while food particles are retained, water is drawn in and pushed outwards across the membranelle band as the gap closes from the inner side. We suggest a model that rationalizes our observations and quantifies the mechanism by which the membranelle band can both generate feeding flow and retain food particles. The model compares favorably with our observations and suggests a trade-off between the clearance rate and the membranelle gap that determines the lower cutoff in the prey size spectrum. We quantify the trade-off and discuss the ecological significance of our findings.

Recently the dynamics of flows beneath ice cover has garnered much interest in the environmental fluid dynamics community. Of particular importance is understanding how heat introduced via solar radiation is transported within a body of cold fresh water (characteristic temperatures are below the temperature of maximum density), and how a subsurface current affects this process. In this study we present high-resolution numerical simulations of the interaction between cold water convection and a parallel shear flow. The results of this paper show that for a sufficiently strong shear current, the growth phase of instabilities generated by volumetric thermal forcing (which represents solar radiation) is nearly two-dimensional and that the transition to more vigorous three-dimensional motion is initialized by baroclinic production of vorticity by convective instabilities followed by a rapid increase in streamwise vorticity generated by vortex tilting and stretching. We describe how this process is modified by differences in shear strength and thermal forcing attenuation length.

Although liquid behaviors in micrometric scales can be observed optically and those below nanometric scales can be probed with atomic force microscopy, those in the ranges from tens to hundreds of nanometers have seldom been visualized due to limits in optical and electron microscopy. Here we report direct visualization of condensation and wicking of water on arrays of solid walls with gaps ranging from tens to hundreds of nanometers, by reducing electron-beam-induced heating in the environmental scanning electron microscopy. We find that the water condensing and wicking on hydrophilic nanopatterns exhibits little difference from what has been observed on micropatterns. However, the condensation behavior of water on hydrophobic nanopatterns is found not to follow the conventional capillary condensation theory. The hydrophobic grooves of 40–80 nm widths are observed to be completely wetted by condensing water vapor, but do not allow externally approaching liquid water to invade themselves. We expect our experiments to trigger further experimental attempts to observe nanoscale liquid menisci in various situations. In addition, those peculiar nanoscale behaviors of water reported here will broaden our knowledge of nanoscale wetting and feed empirical inputs for theoretical models.