The dynamic frictional force between solid surfaces in relative motion differs from the static force needed to initiate motion, but this distinction is not usually thought to occur for liquid drops moving on a solid. Recent experiments [Gao et al., Nat. Phys. 14, 191 (2018)] have challenged this view and claim to observe an analog of solid-on-solid friction for sliding drops. We use molecular dynamics simulations to investigate the forces that moving liquids exert on solids in several situations. In contrast to the indirect techniques required in laboratory experiments, the forces involved in friction are directly accessible in these calculations. We find that, aside from possible inertial effects due to the abrupt initiation of motion and aging effects for unconfined drops, the frictional forces are constant in time.

In flows where the relaxation rate of molecular vibrational energy to equilibrium is comparable to the flow through timescales, the presence of turbulence can alter the mixing and equilibration processes. To understand the coupling between mixing and vibrational relaxation, a novel state-specific species model is solved in a background turbulent flow. The method is applied to mixing of two nitrogen streams at different static temperatures. The relaxation rates for each state are computed using quasiclassical trajectory analysis. The rates obtained from this study were used to first study relaxation to equilibrium in a constant volume bath. Results indicate that the thermal relaxation process is not linear over the range of conditions tested and exhibits quasisteady behavior with the higher energy levels relaxing first, followed by a slower relaxation of the lower energy levels. The state-specific model is then used to study the interaction of turbulent mixing and relaxation process in a turbulent mixing layer of two nitrogen streams at different static temperatures. The direct numerical simulation shows that gas compressibility effects impact the translational energy through flow acceleration and deceleration while the vibrational energy remains constant, triggering vibrational nonequilibrium. Also, the vibrational state populations are significantly affected by turbulence. In certain locations in the jet, the population from the direct calculation is several orders of magnitude different than that based on a Boltzmann distribution at the local vibrational temperature. These results show that considering details of the molecular populations in different vibrational states is important in a range of high enthalpy flows.

When a microfluidic crystal consisting of a concentrated emulsion flows in a convergent channel, the boundary conditions enforce a sequence of droplet rearrangements, also known as T1 events. At low flow rates, these T1 events are shown to be periodic both in space and in time, giving rise to a surprisingly ordered flow pattern. At high flow rates, however, the order is lost. To understand the transition from order to disorder, this paper examines the timescale and the spatial distribution of T1 events during the flow of a monolayer of monodisperse droplets within a concentrated emulsion confined in a convergent tapered microchannel. We show that the duration of a single T1 event consists of three distinct regimes with two transitions upon an increase in the applied flow rate. The first transition can be understood as a change in the forces that dominate during the T1 event, and the second transition can be associated with the emulsion transitioning from a solidlike state to a liquidlike state. Our results suggest that the loss of order in the flow of the concentrated emulsion, or the microfluidic crystal, is directly associated with the solidlike to liquidlike transition of the emulsion. Practically, our results are significant in understanding the relationship between the macroscopic property and the microscopic flow structures of the emulsion, as well as in guiding the design of flow control elements in microfluidic devices.

We present simulations of clean drops rising into a layer of dissolved surfactant. Immediately after entering the surfactant layer, the drop is seen to accelerate suddenly as surfactant adsorbs onto its surface. The drop subsequently slows down to reach a terminal velocity that is between that of a clean drop and that of a solid object. For drops of viscosity equal to that of the ambient fluid, the terminal drop velocity, transition length, and maximal speed are all quantified and plotted against the Biot number, the ratio of convective to desorption timescales, and the adsorption number, the ratio of desorption to adsorption timescales. We find that faster sorption generally results in greater acceleration on entering the surfactant layer, a faster transition to equilibrium, and a faster terminal velocity. Drops of two different Reynolds numbers are considered to investigate the influence of inertial effects.

Imbalance refers to the departure from the large-scale primarily vortical flows in the atmosphere and ocean whose motion is governed by a balance of Coriolis, pressure-gradient, and buoyancy forces and can be described approximately by quasigeostrophic theory or similar balance models. Imbalanced motions are manifest either as fully nonlinear turbulence or as internal gravity waves which can extract energy from these geophysical flows but which can also feed energy back into the flows. Capturing the physics underlying these mechanisms is essential to understanding how energy is transported from large geophysical scales ultimately to microscopic scales, where it is dissipated. In the atmosphere, it is also necessary for understanding momentum transport and its impact upon the mean wind and current speeds. During a February 2018 workshop at the Banff International Research Station (BIRS), atmospheric scientists, physical oceanographers, physicists, and mathematicians gathered to discuss recent progress in understanding these processes through interpretation of observations, numerical simulations, and mathematical modeling. The outcome of this meeting is reported upon here.

Water-repellent materials ideally operate at very different liquid scales: from centimeter-size for bugs living on ponds through millimeter-size for antirain functions to micrometer-size for antifogging solids. In the last situation, it was recently evidenced that microdrops condensing on a highly nonadhesive substrate can take advantage from coalescence to jump off the material, even if the dynamical characteristics of the jump were not established at such microscales. We demonstrate in this paper that the jumping speed of drops is nonmonotonic with the drop size, showing a maximum around $5\mu \mathrm{m}$ (a size commonly observed in dew), below and above which viscous and inertial effects, respectively, impede the takeoff. We quantitatively describe this optimum in antifogging. We also studied the ballistics of the jumping microdrops, from the height they reached to their behavior at landing; a situation where retakeoff is surprisingly found to be nearly unachievable despite the extreme nonwettability of the material.

Bacteriophage viruses, one of the most abundant entities in our planet, lack the ability to move independently. Instead, they crowd fluid environments in anticipation of a random encounter with a bacterium. Once they land on the cell body of their victim, they are able to eject their genetic material inside the host cell. Many phage species, however, first attach to the flagellar filaments of bacteria. Being immotile, these so-called flagellotropic phages still manage to reach the cell body for infection, and the process by which they move up the flagellar filament has intrigued the scientific community for decades. Berg and Anderson [Berg and Anderson, Nature (London) 245, 380 (1973)] proposed the nut-and-bolt mechanism in which, similarly to a rotated nut that is able to move along a bolt, the phage wraps itself around a flagellar filament possessing helical grooves (due to the helical rows of flagellin molecules) and exploits the rotation of the flagellar filament in order to passively travel along it. One of the main pieces of evidence for this mechanism is the fact that immotile mutants of bacterial species such as Escherichia coli and Salmonella typhimurium equipped with straight, but rotating, flagellar filaments with a preserved helical groove structure are still infected by their relative phages. Using two distinct approaches to address the short-range interactions between phages and flagellar filaments, we provide here a first-principles theoretical model for the nut-and-bolt mechanism applicable to mutants possessing straight flagellar filaments. Our model is fully analytical, is able to predict the speed of translocation of a bacteriophage along a flagellar filament as a function of the geometry of both phage and bacterium, the rotation rate of the flagellar filament, and the handedness of the helical grooves, and is consistent with past experimental observations.

Turbulent and other nonlinear flows are highly complex and time dependent, but are not fully random. To capture this spatiotemporal coherence, we introduce the idea of a linear neighborhood, defined as a region in an arbitrary flow field where the velocity gradient varies slowly in space over a finite time. Thus, by definition, the flow in a linear neighborhood can be approximated arbitrarily well by only a subset of the fluid-element trajectories inside it. This slow spatiotemporal variation also allows short-time prediction of the flow. We demonstrate that these linear neighborhoods are computable in real data using experimental measurements from a quasi-two-dimensional turbulent flow and find support for our theoretical arguments. We also show that our kinematically defined linear neighborhoods have an additional dynamical significance, in that the scale-to-scale spectral energy flux that is a hallmark of turbulent flows behaves differently inside the neighborhoods. Our results add additional support to the conjecture that turbulent flows locally tend to transport energy and momentum in space or in scale but not both simultaneously.

A random process and highly accurate pseudospectral method associated with compact finite differences are incorporated to evaluate effects of permeability heterogeneity to gravity-driven miscible porous media flows. Flows in heterogeneous permeability fields, based on multiple sets of random realizations with identical statistical characteristics, are simulated to elucidate the global trend of mean quantities and local variations. The presence of heterogeneity provokes more prominent fingering competition and greater variation of fingers' widths, hence the mean values of interested quantitative measures, i.e., breakthrough time, amount of fluid volumes transported, and normalized mixing effectiveness, are generally reduced. Resonant effects, whose influences on the flow fields are the most significant, are verified to occur in an intermediate correlation length, in which the widths of fingers are slightly less than the correspondent correlation length. Nevertheless, under the resonant conditions these measures are the most widely scattered between different random realizations associated with the same control parameters. The widest scatterings are mainly because of the enhancing sensitivity of flow path selections under such resonant conditions, especially in a few realizations whose high or low permeability regions align along with or transverse to the main flow direction. The significant scatterings of these quantitative measures, which had drawn little attention previously, suggest more cautious treatments for practical implementations in the regime of resonant effects.

The motion of a container filled with fluid perturbs the free surface and may result in spilling. In practice, most of the energy is localized in the modes of lowest frequencies (the gravest modes), and sloshing can be predicted once the dynamics of these modes is known. In this Rapid Communication, we investigate the nonlinear interactions between such grave modes in a cylindrical container. We first show that energy can be transferred from modes to modes with three-wave interactions: we derive the resonance conditions and characterize the early stage of this interaction. This result strongly contrasts with resonant interactions between surface gravity waves in extended domains such as the ocean, which involve at least four waves and are thus less efficient. An experiment is then performed to provide evidence of these nonlinear interactions.

We present a tensorial theory for the microstructure and the stress in shear rate invariant particle suspensions that includes hydrodynamic and normal but not tangential hard sphere interaction forces. The theory predicts that hydrodynamic forces produce a negligible first normal stress difference, while contact forces produce a positive first normal stress difference. The theory thereby provides a rationale for seemingly contradicting experimental observations in the literature. In addition, the theory captures the experimentally observed time dependence of the shear stress after shear reversal.

The collision of a sphere with a wettable microtextured wall in a viscous fluid is investigated experimentally, focusing on the region close to the contact with the wall. High-frequency laser interferometry is used for measuring small displacements of the sphere in that region. The wall texture consists of an a array of square micropillars, whose geometrical parameters (height, width, and spacing of the pillars) are varied. The wall texture decreases the hydrodynamic resistance, and hence the drag on the sphere, compared to the case of a smooth wall. At small Reynolds and Stokes numbers, this drag reduction is quantified in terms of an equivalent plane boundary, shifted down from the top of the pillars. The shift length depends on the geometrical parameters of the pillars array and is compared to available predictions of effective slip length for a flow over arrays of micropillars in the Wenzel state. At finite Stokes number, below the bouncing transition, the wall texture influences the relative importance of sphere inertia and drag force in the near wall region. As a result, a great diversity of sphere dynamics are obtained by varying the texture geometrical parameters. These dynamics can be captured considering a shift-length-modified drag force in the equation of motion of the sphere.

Breaking of shoaling internal solitary waves (ISWs) is important for mixing and mass transport processes in oceans and lakes. For ISWs in a two-layer stratified fluid, previous studies identified four breaker types: surging, plunging, collapsing, and fission. The latest classification of these breaker types is based on the wave slope $S_w$ and the bottom slope $S$; however, this classification was found to be unsatisfactory in delineating collapsing and plunging breakers. The present study proposes a new classification for these two breaker types using extended data sets, consisting of published experimental data and the results of new numerical simulations. It was found that a single nondimensional index $B_{\mathrm{ISW}}=\left(S/S_w\right)\mathrm{R}{{\mathrm{e}}_{\mathrm{ISW}}}^2$ delineates collapsing and plunging breakers in the extended data, where $\mathrm{R}{\mathrm{e}}_{\mathrm{ISW}}$ is a new wave Reynolds number that accounts for nonlinear wave steepening.

We report a novel form of convection in suspensions of the bioluminescent marine bacterium Photobacterium phosphoreum. Suspensions of these bacteria placed in a chamber open to the air create persistent luminescent plumes most easily visible when observed in the dark. These flows are strikingly similar to the classical bioconvection pattern of aerotactic swimming bacteria, which create an unstable stratification by swimming upwards to an air-water interface, but they are a puzzle since the strain of P. phosphoreum used does not express flagella and therefore cannot swim. When microspheres were used instead of bacteria, similar flow patterns were observed, suggesting that the convective motion was not driven by bacteria but instead by the accumulation of salt at the air-water interface due to evaporation of the culture medium. Even at room temperature and humidity, and physiologically relevant salt concentrations, the water evaporation was found to be sufficient to drive convection patterns. To prove this hypothesis, experiments were complemented with a mathematical model that aimed to understand the mechanism of plume formation and the role of salt in triggering the instability. The simplified system of evaporating salty water was first studied using linear stability analysis, and then with finite element simulations. A comparison between these three approaches is presented. While evaporation-driven convection has not been discussed extensively in the context of biological systems, these results suggest that the phenomenon may be broadly relevant, particularly in those systems involving microorganisms of limited motility.

We investigate the effect of the capillary number $\mathrm{Ca}$ on the interfacial viscous fingering instability in radially tapered Hele-Shaw cells. By employing a perturbative weakly nonlinear approach, we manage to identify a fingering instability transition in the system at the onset of nonlinearities. We find that for low $\mathrm{Ca}$ the interface in tapered situations is stabilized (destabilized) in converging (diverging) cells, with respect to the equivalent behavior occurring in a parallel-plate (uniform) Hele-Shaw cell. However, for large $\mathrm{Ca}$, we observe that the relative stability behavior changes, so that converging cells destabilize the interface in comparison to uniform cells, while diverging cells lead to relatively more stable interfaces. Moreover, we verify that finger tip-splitting is favored for large $\mathrm{Ca}$, and restrained in the low-$\mathrm{Ca}$ regime. Our weakly nonlinear results are qualitatively consistent with recent intensive numerical simulations in the literature in which such an instability transition was examined at fully nonlinear stages of the flow.

Direct numerical simulations are carried out for thermally stratified turbulent channel flow laden with finite-size particles using an immersed boundary method that was developed for use in nonuniform grids. We consider the stratification effect at friction Richardson numbers ${\text{Ri}}_{\tau }=0$ and 20 with a friction Reynolds number ${\text{Re}}_{\tau }=180$. The particle diameter is chosen as $0.21\delta$ and the global volume fraction of the particles ranges between 0 and $8\%$, where $\delta$ is the channel half gap. Particles are neutrally buoyant or slightly heavier than fluids. We find that neutrally buoyant particles make the internal gravity waves stronger. The vertical motion of the particles is limited to each half of the channel due to the gravity wave, which acts as a wall at the center of the channel. If the particles are slightly heavier than the fluid, the turbulence structures are greatly modified by the particles. The particle movements in the near-wall and core regions are statistically analyzed using particle velocities or residence times, and individual particle movements are presented. The particles stay in the high-speed streak region for a relatively long time and disappear rapidly in the near-wall region when encountering the ejection event of the turbulent flow. Analysis of the vortex structure with the heat flux shows that the particles play a role in suppressing the vertical heat transport. Additional budget analysis of heat flux is performed for a detailed investigation.

We show that the spectrum of a flow field can be extracted within a local region by straightforward filtering in physical space. We find that for a flow with a certain level of regularity, the filtering kernel must have a sufficient number of vanishing moments for the “filtering spectrum” to be meaningful. Our derivation follows a similar analysis by V. Perrier et al. [J. Math. Phys. 36, 1506 (1995)] for the wavelet spectrum, where we show that the filtering kernel has to have at least $p$ vanishing moments to correctly extract a spectrum $k^{-\alpha }$ with $\alpha <p+2$. For example, any flow with a spectrum shallower than $k^{-3}$ can be extracted by a straightforward average on grid-cells of a stencil. We construct two new “simple stencil” kernels, ${\mathcal{M}}^I$ and ${\mathcal{M}}^{II}$, with only two and three fixed stencil weight coefficients, respectively, and that have sufficient vanishing moments to allow for extracting spectra steeper than $k^{-3}$. We demonstrate our results using synthetic fields, 2D turbulence from a direct numerical simulation, and 3D turbulence from the JHU Database. Our method guarantees energy conservation and can extract spectra of nonquadratic quantities self-consistently, such as kinetic energy in variable density flows, which the wavelet spectrum cannot. The method can be useful in both simulations and experiments when a straightforward Fourier analysis is not justified, such as within coherent flow structures covering nonrectangular regions, in multiphase flows, or in geophysical flows on Earth's curved surface.

Metallic fluids may contain rather rich unconventional surface wave behaviors when subjected to specific forcing conditions. Here we introduce a high-surface-tension liquid metal–solution bilayer to the Faraday system and investigate its wave evolution under cylindrical confinement. Beyond the Faraday threshold, we observe the formation of highly symmetric wave patterns when the acceleration remains below an upper threshold value ${\mathrm{\Gamma }}_{\mathrm{D}}$, exceeding which gives rise to disordered wave patterns. By varying the driving frequency from 20 to 80 Hz, diverse wave patterns with fold symmetry from 2 to 10 are excited. We further show that noncoalescent droplets of the same liquid metal can be sustained on the structured wave patterns. Distant droplets can be confined at the antinodes of the wavy surface and self-assemble the corresponding wave structures. Besides outlining some major differences between the current system and conventional ones, we also demonstrate a simple yet fast method to switch the surface waves between different states by electrically altering the liquid metal surface tension.

We systematically investigate the dynamic behavior of two neighboring nanobubbles for various gas-liquid-solid interactions by molecular dynamics simulations. The weaker the interaction between gas and liquid, the larger are the bulk nanobubbles formed. The dynamic behavior of bulk nanobubbles depends not only on the ratio of gas-gas to liquid-gas interaction strengths, but also on that of solid-gas to liquid-gas interaction strengths. A very small bulk nanobubble remains stable in bulk liquid, as long as the ratio of solid-gas to liquid-gas interaction strengths is sufficiently large. Under the condition that the three-phase contact line is not pinned, different dynamic behaviors of two neighboring surface nanobubbles are observed. For a higher ratio of solid-gas to solid-liquid interaction strengths, the two neighboring surface nanobubbles can merge directly owing to the existence of a film layer of gas molecules between them. This film layer allows transfer of gas molecules from one surface nanobubble to the other along the solid substrate. This result is consistent with other theoretical results. If the interaction between solid and gas is sufficiently strong, two neighboring unsaturated surface nanobubbles can form a gas-rich layer on the solid surface. The formation of such a layer is very important for effective weakening of the solid-liquid interaction, leading to a greater reduction in drag. The effect of the ratio of solid-gas to solid-liquid interaction strengths on the shape of the gas-rich layer is also discussed in detail.