Particle-resolved direct numerical simulations of monodisperse settling suspensions of cubes and spheres are performed for Galileo numbers $\text{Ga}=70$ and $\text{Ga}=160$, and solid volume fractions in the range $0.01⩽\varphi ⩽0.2$. The solid-to-fluid density ratio $m={\rho }_s/{\rho }_f$ is taken to be fixed at 2, representing liquid-solid suspensions. Strong columnar clustering is observed for $\text{Ga}=160$ and $\varphi =0.01$ in a sphere suspension, whereas similar vertical structures are not present as prominently in a cube suspension. We find that in all cases, cube suspensions tend to be more homogeneous compared to sphere suspensions, as indicated by both their microstructure and momentum transfer properties. The enhanced homogeneity is associated with the pronounced angular velocities of cubes and the resulting orientation- and rotation-induced lift forces, which promote transverse motions and the likelihood of escaping from clusters. Higher rotation rates of cubes thus play a major role in the transfer of momentum from the gravity to the transverse direction, demonstrated by the lower anisotropy of particle velocity fluctuations in cube suspensions. In more dilute cases, cubes induce significantly stronger pseudoturbulence in the flow, especially in the transverse direction. The drag of dynamic cube suspensions is found to be generally similar to static beds of cubes, the reason for which is speculated to be relevant to their motion freedom and the more homogeneous microstructure.

Air film stability underneath a drop is crucial for drop contact dynamics upon impact. An unstable film leads to the drop contacting the surface and subsequent spreading or splashing. Apart from previously reported film and kink contact modes, here we present the experimental evidence for a dimple failure mode of an air film, driven by a thin film instability when a drop impacts onto an atomically smooth surface. The dimple failure occurs beyond the inertial-capillary timescale and is initiated when the dimple inverts at the drop's central axis. For the same impact Weber number, the dimple failure observed in low-viscosity drops is absent at a higher viscosity, due to damping of capillary waves.

Flow and transport in coupled channel-matrix systems are ubiquitous to many environmental and engineering applications such as flows in fractured porous media over canopies and in membrane filtration units. The multiscale nature of such systems, where the horizontal length scale is often orders of magnitude larger than the vertical one, allows one to employ vertically averaged descriptions of the system. As a result, two-dimensional transport in the channel and the matrix can be upscaled to a coupled system of transient one-dimensional advection-dispersion equations, where matrix and channel properties can be analytically related to macroscopic transport observables. In this work, we first develop a semianalytical solution based on integral transforms that can be employed to predict macroscopic transport in channel-matrix shear flows in a computationally efficient manner. Then we demonstrate that under appropriate dynamic conditions, the coupled system at the macroscale can be further simplified to a single upscaled one-dimensional advection-dispersion equation, which admits an analytical closed-form solution, thus enabling real-time macroscale concentration estimates in relevant applications.

Dispersions of bubbles with a compound interface in liquids are ubiquitous in nature and various industrial processes, such as marine oil transport and froth flotation, hence understanding surface phenomena effect on bubble formation in liquids remains as a canonical topic in fundamental multiphase flows. Here, we experimentally investigate the formation of an oil-coated bubble at submerged coaxial orifices in quiescent liquids. The air bubble is initially injected inside a confined oil domain and then exits into the surrounding water under buoyancy, forming an oil-coated bubble. Compared with the bubble formation in a single-phase liquid, the bubble size is significantly modified due to the presence of the oil phase. We develop a force balance model to predict the oil-coated bubble size, considering the orifice geometry as well as the compound air/oil/water interface, which agrees well with the experimental results. We further discuss the dependencies of the bubble size on the Bond number, size ratio of the coaxial orifices, and the interfacial tension ratio of oil-water and oil-air interfaces. Our study could contribute to further understandings on the dynamics of bubble formation with a compound interface.

Gamma ($\gamma$) instability theory, originally proposed in 2003, continues to provide the most promising explanation of salt-fingering engendered thermohaline staircases that are ubiquitously present in both the global ocean and lakes. Our purpose herein is to extend $\gamma$ instability theory to salt-fingering systems in which the vertical gradients of temperature and salinity are not constant. Our goal is to explain why the characteristic “step size” in a salt-fingering staircase is larger in regions characterized by weak gradients. Through application of an appropriately modified linear stability analysis, we first demonstrate that the most quickly growing mode of instability is unaltered by the inhomogeneity of the background stratification in most cases. We then perform numerical simulations based upon the mean field equations to show that staircases tend to form and thereafter merge much more quickly in the low gradient regions than the high gradient regions. After explaining this difference of timescale within the framework of our model, we argue that the differences in background gradients of physical properties may arise naturally in a quasiequilibrium staircase environment. We further invoke observations from the Tyrrhenian Sea to support a quasiequilibrium staircase hypothesis.

A liquid hanging from a liquid-filled tube can spread spontaneously on rough hydrophilic surfaces while it cannot on smooth hydrophilic surfaces, a difference resulting from the competition between the capillary suction pressures provided by the tube and by the surface roughness. In order to pattern liquids on solid surfaces utilizing such wetting characteristics, we investigate the dynamics of a spontaneous liquid spreading from a tube onto a nanostructured superhydrophilic microlane surrounded by a superhydrophobic background. We find distinct regimes of liquid film propagation dynamics to arise depending on the lane width and the liquid column height in the tube. We theoretically analyze the spreading rates of films, which change power laws in the course of spreading, and corroborate the theory with experiments. The spontaneous liquid patterning process reported in this work can provide a viable venue for such applications as electronic circuit printing and biochip fabrication.

This work reports an experimental investigation of a liquid-solid fluidized bed involving inertial particles at a large Reynolds number. Owing to optical techniques and index matching, the statistics of the velocity fluctuations of both the particles and the liquid are measured for a wide range of the particle volume fraction ${\alpha }_p$. The dynamics of the fluctuations suggests that the flow possesses the following three properties: (1) The liquid volume involves a wake region in which vertical fluctuations are negative and an interstitial region where they are positive. (2) The statistics of the horizontal fluctuations are similar to vertical ones, except that they are symmetric. (3) Local instant particle fluctuations are proportional to liquid ones. Assuming these properties are true allows us to derive a model for the probability density functions (PDFs) of the two components of the velocity fluctuations of the two phases. This model involves a single reference PDF that is independent of ${\alpha }_p$ and one weighting parameter for each phase. The weighting parameter of the liquid phase is an affine function of ${\alpha }_p$, which characterizes the volume of the wakes relative to that of the interstices. That of the particle phase depends on the preferential concentration of the particles, which tend to avoid the wakes at low ${\alpha }_p$. This model accurately describes the experimental PDFs up to the third-order moment and reproduces all their peculiar features: the skewness of the vertical fluctuations which reverses at a given volume fraction, the presence of exponential tails corresponding to rare intense events, and the symmetry between low and large volume fractions.

The force experienced by an object moving in a granular medium is a necessary input to describe locomotion problems in such a context. Towards this objective, resistive force theory (RFT) has been developed for granular flows inspired by previous developments in the case of viscous flows. In viscous fluids, a reciprocal motion does not lead to a net propulsion due to the kinematics reversibility of viscous flows that is included in the RFT. We show that, in a granular medium, a reciprocal motion allows for propulsion. We investigate the specific mechanisms underlying this propulsion and discuss how they differ from that of viscous flows. Understanding these phenomena permit both the accurate description of locomotion in sand and the refinement of the RFT for granular materials. These achievements provide opportunities towards the development of robots that are able to progress inside granular media and are suitable for controlling industrial processes.

Small conical-shaped jets may emanate from a liquid bath a short while after a small drop has hit a liquid pool. Here we perform Particle Image Velocimetry (PIV) measurements of the liquid flow inside upward jets after drop impact and show that fluid elements inside the jets may decelerate up to 5–20 times the gravitational acceleration. The measurements show that both the shape of the jet and the velocity profile are self-similar. A theoretical model including surface tension, fluid inertia and gravity correctly predicts the self-similar velocity profile and shape of the jet, allowing us to provide the first quantitative explanation of the shape and dynamics of the emanating jets.

Iceberg meltwater is a critical freshwater flux from the cryosphere to the oceans. Global climate simulations therefore require simple and accurate parametrizations of iceberg melting. Iceberg shape is an important but often neglected aspect of iceberg melting. Icebergs have an enormous range of shapes and sizes, and distinct processes dominate basal and side melting. We show how different iceberg aspect ratios and relative ambient water velocities affect melting using a combined experimental and numerical study. The experimental results show significant variations in melting between different iceberg faces, as well as within each iceberg face. These findings are reproduced and explained with multiphysics numerical simulations. At high relative ambient velocities melting is largest on the side facing the flow, and mixing during vortex generation causes local increases in basal melt rates of over 50%. Double-diffusive buoyancy effects become significant when the relative ambient velocity is low. Existing melting parametrizations do not reproduce our findings. We propose several corrections to capture the influence of aspect ratio on iceberg melting.

Red blood cells (RBCs)—erythrocytes—suspended in plasma tend to aggregate and form rouleaux. During aggregation the first stage consists in the formation of RBC doublets [S. M. Bertoluzzo, A. Bollini, M. Rasia, and A. Raynal, Blood Cells Mol. Dis. 25, 339 (1999)]. While aggregates are normally dissociated by moderate flow stresses, under some pathological conditions the aggregation becomes irreversible, which leads to high blood viscosity and vessel occlusion. We perform here two-dimensional (2D) simulations to study the doublet dynamics under shear flow in different conditions and its impact on rheology. A few illustrative results obtained here in 3D agree with 2D results. We sum up our results on the dynamics of doublet in a rich phase diagram in the parameter space (flow strength, adhesion energy) showing four different types of doublet configurations and dynamics. We find that membrane tank-treading plays an important role in doublet disaggregation, in agreement with experiments on RBCs. A remarkable feature found here is that when a single cell performs tumbling (by increasing vesicle internal viscosity) the doublet formed due to adhesion (even very weak) remains stable even under a very strong shear rate. It is seen in this regime that an increase of shear rate induces an adaptation of the doublet conformation allowing the aggregate to resist cell-cell detachment. We show that the normalized effective viscosity of doublet suspension increases significantly with the adhesion energy, a fact which should affect blood perfusion in microcirculation.

We study how the complex interplay between channel roughness, inertia, and diffusion controls tracer transport in rough channel flows. We first simulate flow and tracer transport over wide ranges of channel roughness, Reynolds number (Re), and Péclet number (Pe) observable in nature. Pe exerts a first-order control on first-passage time distributions, and the effect of roughness on the tracer transport becomes evident as Re increases. The interplay between the roughness and Re causes recirculating flows, which intensify or suppress anomalous transport depending on Pe. At infinite Pe, the late-time scaling follows a universal power-law scaling, which is explained by conducting a scaling analysis. With extensive numerical simulations and stochastic modeling, we show that the roughness, inertia, and diffusion effects are encoded in Lagrangian velocity statistics represented by velocity distribution and velocity correlation. We successfully reproduce anomalous transport using an upscaled stochastic model that honors the key Lagrangian velocity statistics.

Capillary bubbles burst at a free surface following a rapid sequence of events occurring at different length scales and timescales: hole nucleation, fast retraction of the micron-thick liquid film in a few microseconds preluding the much slower overall collapse of the millimeter-sized bubble in a matter of milliseconds. Each of these steps is associated with unsteady fluid forces and accelerations, and therefore with sound radiation. In this experimental study we focus on the airborne sound generated during bubble bursting. Investigating the physical mechanism at the root of sound emission with the help of synchronized fast imaging and sound recordings, we quantitatively link the film retraction dynamics with the frequency content of the acoustic signal. We demonstrate that, contrary to a Minnaert resonance scenario, the frequency here drifts and increases, consistent with a Helmholtz-type resonance of the cavity being more and more opened as the thin film retracts. We propose as an extension a simple model based on a collection of drifting Helmholtz resonators capturing the main features of the fizzing sound of an effervescing beverage.

Electrosprays of highly conducting liquids operated in the cone-jet mode produce charged nanodroplets of controllable size and molecular ions. The study of this electrospraying regime is challenging due to the lack of experimental techniques for probing these nanometric systems, and the higher complexity of the physics associated with the onset of ion field emission and self-heating. Jet parameters in the breakup region such as its radius, velocity, potential, and electrification level are key for understanding the formation of droplets and emission of ions, and useful to validate numerical models of cone jets. In the case of micron-sized jets, these quantities can be determined with the values of the retarding potentials and mass-to-charge ratios of the droplets produced by the breakup. This article uses this technique to investigate the parameters of nanometric jets. Retarding potential and mass-to-charge distributions of the beam are measured with retarding potential and time-of-flight analyzers operated in tandem. This combination makes it possible to differentiate between droplets of similar mass-to-charge ratios which, unlike in the case of micrometric jets, are needed to apply the technique. Aside from the jet parameters, the experimental characterization also reveals with great detail the composition of the beam, which includes primary ions emitted from the jet breakup; ions resulting from the desolvation of primary ions; stable primary droplets produced at the breakup; smaller droplets resulting from the Coulomb explosion of unstable primary droplets; and small primary droplets that evaporate a significant fraction of their charge in flight. An analysis of the breakup, parametrized by dimensionless numbers, explains this complexity. Although the experimental characterization only studies the electrosprays of the ionic liquid 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl) imide, the analysis is general and can be used to understand the beams of other highly conducting liquids.

Every animal cell is filled with a cytoskeleton, a dynamic gel made of inextensible fibers, such as microtubules, actin fibers, and intermediate filaments, all suspended in a viscous fluid. Numerical simulation of this gel is challenging because the fiber aspect ratios can be as large as ${10}^4$. We describe a method for rapidly computing the dynamics of inextensible slender filaments in periodically sheared Stokes flow. The dynamics of the filaments is governed by a nonlocal slender body theory which we partially reformulate in terms of the Rotne-Prager-Yamakawa hydrodynamic tensor. To enforce inextensibility, we parametrize the space of inextensible fiber motions and strictly confine the dynamics to the manifold of inextensible configurations. To do this, we introduce a set of Lagrange multipliers for the tensile force densities on the filaments and impose the constraint of no virtual work in an $L^2$ weak sense. We augment this approach with a spectral discretization of the local and nonlocal slender body theory operators which is linear in the number of unknowns and gives improved spatial accuracy over approaches based on solving a line-tension equation. For dynamics, we develop a second-order semi-implicit temporal integrator which requires at most a few evaluations of nonlocal hydrodynamics and a few block-diagonal linear solves per time step. After demonstrating the improved accuracy and robustness of our approach through numerical examples, we apply our formulation to a permanently cross-linked actin mesh in a background oscillatory shear flow. We observe a characteristic frequency at which the network transitions from quasistatic, primarily elastic behavior to dynamic, primarily viscous behavior. We find that nonlocal hydrodynamics increases the viscous modulus by as much as 25%. Most of this increase, in contrast to the smaller (about 10%) increase in the elastic modulus, is due to short-ranged intrafiber interactions.

For two-dimensional (2D) Rayleigh-Bénard convection, classes of unstable, steady solutions were previously computed using numerical continuation [F. Waleffe et al., Phys. Fluids 27, 051702 (2015) and D. Sondak et al., J. Fluid Mech. 784, 565 (2015)]. The “primary” steady solution bifurcates from the conduction state at $\mathrm{Ra}\approx 1708$, and has a characteristic aspect ratio (length/height) of approximately 2. The primary solution corresponds to one pair of counterclockwise-clockwise convection rolls with a temperature updraft in between and an adjacent downdraft on the sides. By adjusting the horizontal length of the domain, Waleffe et al. and Sondak et al. also found steady, maximal heat transport solutions, with a characteristic aspect ratio less than 2 and decreasing with increasing $\mathrm{Ra}$. Compared to the primary solutions, optimal heat transport solutions have modifications to boundary layer thickness, the horizontal length scale of the plume, and the structure of the downdrafts. The current study establishes a direct link between these (unstable) steady solutions and transition to turbulence for $\mathrm{Pr}=7$ and $\mathrm{Pr}=100$. For transitional values of $\mathrm{Ra}$, the primary and optimal-heat-transport solutions both appear prominently in appropriately sized subfields of the time-evolving temperature fields. For $\mathrm{Ra}$ beyond transitional, our data analysis shows persistence of the primary solution for $\mathrm{Pr}=7$, while the optimal heat transport solutions are more easily detectable for $\mathrm{Pr}=100$. In both cases, $\mathrm{Pr}=7$ and $\mathrm{Pr}=100$, the relative prevalence of primary and optimal solutions is consistent with the $\mathrm{Nu}$ vs $\mathrm{Ra}$ scalings for the numerical data and the steady solutions.

A closed-form solution is presented for the collective Marangoni-induced motion of a two-dimensional periodic array, or “flotilla,” of Marangoni boats on deep water at zero Reynolds, capillary, and surface Péclet numbers. The physical setup is identical to the model of Marangoni propulsion proposed by Lauga and Davis [J. Fluid Mech. 705, 120 (2012)], but now accounts for interaction effects between boats and is in a simpler two-dimensional setting. The boats are modeled as identical thin floating strips, each self-actuated by a trailing edge surfactant source that lowers the surface tension there according to a linear equation of state. The collective Marangoni propulsion speed of a flotilla of boats is found to be ${\left(2\pi \mu \delta \right)}^{-1}\mathrm{\Delta }\sigma lnsec(\pi \delta /2)$, where $\delta$ is the meniscus coverage fraction, $\mu$ is the subphase fluid viscosity, and $\mathrm{\Delta }\sigma$ is the surfactant-induced surface tension disparity across each boat. The theoretical result exemplifies the mechanism for collective rectilinear motion due to Marangoni convection caused by the diffusion of the insoluble surfactant.

Fluid-structure simulations of slender inextensible filaments in a viscous fluid are often plagued by numerical stiffness. Recent coarse-graining studies have reduced the computational requirements of simulating such systems, though they have thus far been limited to the motion of planar filaments. In this paper we extend such frameworks to filament motion in three dimensions, identifying and circumventing coordinate-system singularities introduced by filament parametrization via repeated changes of basis. The resulting methodology enables efficient and rapid study of the motion of flexible filaments in three dimensions, and is readily extensible to a wide range of problems, including filament motion in confined geometries, large-scale active matter simulations, and the motility of mammalian spermatozoa.

Dispensing, transporting, and manipulating minute liquid volumes is important to a wide range of scientific and application areas, spanning from biology and medicine to chemistry and materials. Although digital microfluidics are emerging as a popular methodology in the lab-on-a-chip field, important obstacles to its broad adoption, such as those related to reusability, reconfigurability, and susceptibility to fouling, persist. In addition, as liquid volumes decrease in size, their sustenance in an open atmosphere becomes practically impossible due to high volatility, leading rapidly to complete evaporation. Here we introduce and demonstrate a microfluidic platform based on the coalescence-induced self-propulsion of sessile microdroplets on unpatterned substrates. We employ controlled dropwise liquid ejection by electrohydrodynamic printing to create, actively sustain (despite high volatility), and freely translate femtoliter-sized droplets (∼2–5 μm radius) under open-atmosphere conditions. The omnidirectional planar movement of the droplets is achieved by a precisely controlled, on-demand sequence of coalescence events, where the directed motion of an already deposited droplet is dictated by the positioning of the subsequent droplet printed adjacent to it. We studied the transport mechanism experimentally and theoretically and found that, for short time scales (relative to the substrate translation and droplet evaporation), the radial growth of the new smaller droplet being printed can greatly exceed the retraction of the neighboring, already deposited droplet. This rapid growth is exploited to create a liquid meniscus bridging the so generated droplet doublet, and merging it into a single droplet by the action of capillary pressure differences. Evaporative losses ensure that the moving droplets are kept at a constant size after merging, in each coalescence cycle. We observe this coalescence whenever the interspacing between two sequentially printed droplets is below a critical value, and show that we can control this with the underlying substrate velocity. Armed with this transport mechanism, we then demonstrate the utility of this approach by tasking the coalescing self-propelled droplet doublet to perform microfluidic operations such as collecting, transporting, and merging solid residues on a surface, in an on-demand, Pac-Man type motion, exemplifying capabilities for digital microfluidic applications.

It is now recognized that aerosol transport contributes to the transmission of the SARS-CoV-2 virus. Here, we improve existing social distancing guidelines for airborne pathogens, which are typically given in terms of distance with vague statements about contact times. Also, estimates of inhalation of virus in a contaminated space usually assume a well-mixed environment, which is realistic for some, but not all, situations. In particular, we consider a local casual interaction of an infected individual and a susceptible individual, both maskless, account for the air flow and aerosol transport characteristics of speaking and breathing in a poorly ventilated space, and propose social distancing guidelines that involve both space and contact time, based on a conservative model of fluid dynamics of the interactions.