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.

We show that when a drop of water is maintained in its Leidenfrost regime, a sound in the form of periodic beats emits from the drop. The process of beat emission involves two distinct frequencies. One component is the frequency of beats itself, and the second is the frequency of sound in every beat which is emitted when one oscillation in the drop occurs. Experiments were performed by placing a drop of water over a concave metallic surface, and the beats of the drop were recorded by fixing a microphone above the drop. A video camera was also fixed above the drop to record its oscillations. Simple analytical techniques like Fourier and wavelet transforms of the audio signals and image processing of the videos of the drop were used to gain insight into the mechanism of the beat emission process. This analysis also helped us in studying the dependence of frequencies, if any, on the radius of the drop and the substrate temperature.

The influence of inertial migration of neutrally buoyant particles on inertial flow transitions in Taylor-Couette (TC) flow of a suspensions is studied; this work considers primarily transitions associated with the circular Couette flow (CCF) and Taylor vortex flow (TVF) regimes. A concentric cylinder Taylor-Couette device with a stationary outer cylinder and rotating inner cylinder is considered. The device has an inner to outer radius ratio of $\eta =d_i/d_o=0.877$, where $d_i$ and $d_o$ are the inner and outer diameters of the flow annulus. The ratio of the axial length to the radial gap of the annulus $\mathrm{\Gamma }=L/\delta =20.5$, where $\delta =(d_o-d_i)/2$. The ratio of radial gap $\delta$ and the particle diameter $d_p$ is $\alpha =\delta /d_p=30.4$ and the particle volume fraction considered in this work is $\varphi =0.10$. A flow structure (CCF or TVF) near the transition boundary with either uniform distribution across the annular region or fully migrated concentration profile is established. The Reynolds number (Re) is subjected to a rapid step change to study the effect of the concentration profile on the flow transition Re and resulting flow structure evolution; here the Reynolds number is $\text{Re}=\delta d_i{\omega }_i\rho /2{\mu }_s$, where ${\omega }_i$ is the rotation rate of the inner cylinder and $\rho$ and ${\mu }_s$ are the density and effective viscosity of the suspension. Our results show that, relative to uniform concentration, the particle distribution following inertial migration destabilizes the CCF state near the CCF-nonaxisymmetric flow transition boundary. In contrast to this destabilizing effect in CCF, migration of particles in the TVF regime has a stabilizing effect on the TVF-wavy Taylor vortex and TVF-nonaxisymmetric flow transition boundaries. The transition away from the TVF exhibits clear hysteresis associated with migration, as once initiated TVF could be sustained below and above the transition boundaries observed for suspension TC flow with uniform concentration.

The settling behavior of small inertial particles in turbulent convection is a fundamental problem across several disciplines, from geophysics to metallurgy. In a geophysical context, the settling of dense crystals controls the mode of solidification of magma chambers and planetary scale magma oceans, while rising of light bubbles of volatiles drives volcanic outgassing and the formation of primordial atmospheres. Motivated by these geophysical systems, we perform a systematic numerical study on the settling rate of particles in a rectangular two-dimensional Rayleigh-Bénard system with Rayleigh number up to ${10}^{12}$ and Prandtl number from 10 to 50. Under the idealized condition of spherically shaped particles with small Reynolds number, two limiting behaviors exist for the settling velocity. On the one hand, Stokes law applies to particles with small but finite response time, leading to a constant settling rate. On the other hand, particles with a vanishing response time are expected to settle at an exponential rate. Based on our simulations, we present a physical model that bridges the gap between the above limiting behaviors by describing the sedimentation of inertial particles as a random process with two key components: (i) the transport of particles from vigorously convecting regions into sluggish, low-velocity “piles” that naturally develop at the horizontal boundaries of the system, and (ii) the probability that particles escape such low-velocity regions without settling at their base. In addition, we identify four distinct settling regimes and analyze the horizontal distribution of sedimented particles. For two of these regimes settling is particularly slow and the distribution is strongly nonuniform, with dense particles being deposited preferentially below major clusters of upwellings. Finally, we apply our results to the crystallization of a magma ocean. Our prediction of the characteristic residence times is consistent with fractional crystallization, i.e., with the efficient separation of dense crystals from the residual lighter fluid. In absence of an efficient mechanism to reentrain settled particles, equilibrium crystallization appears possible only for particles with extremely small density contrasts.

Internal gravity waves propagating within homogeneous stratified turbulence are the subject of the present study. A spatiotemporal analysis is carried out on the results of direct numerical simulations including a forcing term, with the aim of showing the energy content of the simulations as a function of frequency, $\omega$, and wave-vector inclination to the horizontal, $\theta$. Clear signatures of the dispersion relation of internal gravity waves, $\omega =\pm Ncos\theta$, where $N$ is the Brunt-Väisälä frequency, are observed in all our simulations, which have low Froude number, ${\text{Fr}}_h\ll 1$, and increasing buoyancy Reynolds number up to ${\text{Re}}_b\approx 10$. Interestingly, we observe the presence of high-frequency waves with $\omega \sim N$ and a corresponding low-frequency vortex mode, both containing a non-negligible amount of energy. These waves are large-scale waves, their energy signature being found at scales larger than the forcing scales. We also observe the growth of energy in the shear modes, constituting a horizontal mean flow, and we show that their continuous growth is due to an upscale energy transfer, from the forcing scales to larger horizontal as well as vertical scales. These shear modes are found to be responsible for Doppler shifting the frequency of the large-scale waves. When considering the wave energy across the simulations at varying ${\text{Re}}_b$, such energy is seen to reduce as ${\text{Re}}_b$ is increased and the flow enters the strongly stratified turbulence regime. The classical wave-vortex decomposition, based on a purely spatial decomposition of instantaneous snapshots of the flow, is analyzed within the current framework and is seen to correspond relatively well to the “true” wave signal identified by the spatiotemporal analysis, at least for the large-scale waves with $\omega \sim N$. Distinct energy peaks in $\theta \text{−}\omega$ space highlight that the waves have preferential directions of propagation, specifically $\theta ={45}^{\circ }$ and $\theta \approx {55}^{\circ }$, similar to observations in studies of wave radiation from localized regions of turbulence. This suggests that the same wave-generation mechanisms may be relevant for homogeneous and inhomogeneous stratified turbulent flows.

Active navigation relies on effectively extracting information from the surrounding environment, and often features the tracking of gradients of a relevant signal—such as the concentration of molecules. Microfluidic networks of closed pathways pose the challenge of determining the shortest exit pathway, which involves the proper local decision-making at each bifurcating junction. Here, we focus on the basic decision faced at a T-junction by a microscopic particle, which orients among possible paths via its sensing of a diffusible substance's concentration. We study experimentally the navigation of colloidal particles following concentration gradients by diffusiophoresis. We treat the situation as a mean first passage time (MFPT) problem that unveils the important role of a separatrix in the concentration field to determine the statistics of path taking. Further, we use numerical experiments to study different strategies, including biomimetic ones such as run and tumble or Markovian chemotactic migration. The discontinuity in the MFPT at the junction makes it remarkably difficult for microscopic agents to follow the shortest path, irrespective of adopted navigation strategy. In contrast, increasing the size of the sensing agents improves the efficiency of short-path taking by harvesting information on a larger scale. It inspires the development of a run-and-whirl dynamics that takes advantage of the mathematical properties of harmonic functions to emulate particles beyond their own size.

Traditional models of electrokinetic transport in porous media are based on homogenized material properties, which neglect any macroscopic effects of microscopic fluctuations. This perspective is taken not only for convenience but also motivated by the expectation of irrotational electro-osmotic flow, proportional to the electric field, for uniformly charged surfaces (or constant $\zeta$ potential) in the limit of thin double layers. Here, we show that the inherent heterogeneity of porous media generally leads to macroscopic vortex patterns, which have important implications for convective transport and mixing. These vortical flows originate due to competition between pressure-driven and electro-osmotic flows, and their sizes are characterized by the correlation length of heterogeneity in permeability or surface charge. The appearance of vortices is controlled by a single dimensionless control parameter, defined as the ratio of a typical electro-osmotic velocity to the total mean velocity.

Speech is a potent route for viral transmission in the COVID-19 pandemic. Informed mitigation strategies are difficult to develop since no aerosolization mechanism has been visualized yet in the oral cavity. Here we show with high-speed imaging how phonation of common stop consonants, found in most of the world's spoken languages, form and extend salivary filaments in a few milliseconds as moist lips open or when the tongue separates from the teeth. Both saliva viscoelasticity and airflow associated with the plosion of stop consonants are essential for stabilizing and subsequently forming centimeter-scale thin filaments, tens of microns in diameter, that break into speech droplets. Moreover, these plosive consonants induce vortex rings that drive meter-long transport of exhaled air, tying this mechanism to transport associated with speech. We demonstrate that a similar mechanism of aerosolization occurs during the vibration of reeds in wind instruments and may occur during the flapping of the glottis folds. Finally, our research suggests a mitigation of droplet production during speech by using a lip balm.

Recent experiments have shown that liquid Leidenfrost drops levitated by their vapor above a flat hot surface can exhibit symmetry-breaking spontaneous dynamics [A. Bouillant et al., Nat. Phys. 14, 1188 (2018)]. Motivated by these observations, we theoretically investigate the translational and rotational dynamics of Leidenfrost drops on the basis of a simplified two-dimensional model, focusing on near-circular drops small relative to the capillary length. The model couples the equations of motion of the drop, which flows as a rigid wheel, and thin-film equations governing the vapor flow, the profile of the deformable vapor-liquid interface, and thus the hydrodynamic forces and torques on the drop. In contrast to previous analytical models of Leidenfrost drops levitating above a flat surface which predict only symmetric solutions, we find that the symmetric Leidenfrost state is unstable above a critical drop radius: $R_1$ for a free drop and $R_2>R_1$ for an immobilized drop. In these respective cases, symmetry breaking is manifested in supercritical pitchfork bifurcations into steady states of pure rolling and constant angular velocity. In further qualitative agreement with the experiments, when a symmetry-broken immobilized drop is suddenly released it initially moves at an acceleration $\alpha g$, where $\alpha$ is an angle characterizing the slope of the liquid-vapor profile and $g$ is the gravitational acceleration; moreover, $\alpha$ exhibits a maximum with respect to the drop radius at a radius increasing with the temperature difference between the surface and the drop.

We study the effect of inhomogeneous environments on the swimming direction of the microalgae Chlamydomonas reinhardtii (CR) in the presence of a light stimulus. Positive or negative phototaxis describe the ability of microorganisms to bias their swimming toward or away from a light source. Here we consider microswimmers with negative phototaxis in a microfluidic device with a microfabricated square lattice of pillars as obstacles. We measured a mean deflection of microswimmers that shows an interesting nonlinear dependence on the direction of the guiding light beam with respect to the symmetry axes of the pillar lattice. By simulating a model swimmer in a pillar lattice and analyzing its scattering behavior, we identified the width of the reorientation distribution of swimmers to be also crucial for the nonlinear behavior of the swimmer deflection. On the basis of these results we suggest in addition an analytical model for microswimmers, where the pillar lattice is replaced by an anisotropic scattering medium, that depends only on a scattering rate and the width of the reorientation distribution of swimmers. This flexible and handy model fits the experimental results as well. The presented analysis of the deflection of light guided swimmers through pillar lattice may be used for separating swimmers having different reorientation distributions.

We study the retraction of a viscous liquid sheet of finite length with negligible effect of the ambient medium. Using the long-wavelength model we derive the scaling laws and similarity solution for the interface profile of the retracting sheet. Far from the tip, the similarity solution for the interface profiles converges to an asymptotic value of 1/4. Direct numerical simulations are performed to compare the theoretical results with the simulations. When the inertia is negligible, the interface profiles remain flat during the retraction process which is in agreement with the self-similar solution. Using this similarity solution we derive the expression for the temporal variation of the tip speed for finite liquid sheets. We demonstrate that unlike an infinite sheet where the sheet retracts with a steady speed (known as Taylor-Culick speed), the tip speed decreases as a function of time for a finite liquid sheet. This is true when the viscous effects are larger than or of the same order with the inertia effects. Otherwise, the sheet retracts with the formation of a bulbous tip whose speed reaches a value closer to the Taylor-Culick speed.

We present a new mesoscale model for ionic liquids based on a low Mach number fluctuating hydrodynamics formulation for multicomponent charged species. The low Mach number approach eliminates sound waves from the fully compressible equations leading to a computationally efficient incompressible formulation. The model uses a Gibbs free-energy functional that includes enthalpy of mixing, interfacial energy, and electrostatic contributions. These lead to a new fourth-order term in the mass equations and a reversible stress in the momentum equations. We calibrate our model using parameters for [$\mathrm{DMPI}+$][F6P-], an extensively studied room temperature ionic liquid (RTIL), and numerically demonstrate the formation of mesoscopic structuring at equilibrium in two and three dimensions. In simulations with electrode boundaries the measured double-layer capacitance decreases with voltage, in agreement with theoretical predictions and experimental measurements for RTILs. Finally, we present a shear electroosmosis example to demonstrate that the methodology can be used to model electrokinetic flows.