Soap bubbles are by essence fragile and ephemeral. Depending on their composition and environment, bubble bursting can be triggered by gravity-induced drainage and/or the evaporation of the liquid and/or the presence of nuclei. They can also shrink due to the diffusion of the inner gas in the outside atmosphere induced by Laplace overpressure. In this Letter, we design bubbles made of a composite liquid film able to neutralize all these effects and keep their integrity for more than 1 year in a standard atmosphere. The unique properties of this composite film are rationalized with a nonlinear model and used to design complex objects.

We derive self-similar continuum equations that govern the rupture of liquid threads at scales within the influence of interfacial dynamical effects. This regime and the obtained power-law solution for the evolution of the minimum neck radius, $h_{\min }=0.00107{(t_b-t)}^{2.34}$, fill a void in the literature in between the classical inertial-viscous regime and the stochastic formulation and reconcile flow features such as asymptotic slow boundary conditions far away from the singularity and symmetric profiles, respectively. Due to its inherent ties to the production of monosized droplets from jetting, this work can be utilized to approach, for example, the study of electrosprays or flow focusing at these critical scales for aerospace nano-thruster technology or single-biomolecule imaging with x-ray free-electron lasers.

The response of the endothelial glycocalyx (EG) to variations of the hemodynamic environment is of vital importance for the regulation of the blood vessel permeability and the balance of the blood components. Thus, it is necessary to quantify fundamental properties such as its apparent permeability, in addition to dynamic quantities like drag and torque on EG nanofibers, which are indicators of the glycocalyx mechanical integrity, and determine their dependence on the individual geometric features and mechanical properties of a single fiber. Because of the $O\left(100\mathrm{nm}\right)$ height of the fibers and the lack of relevant technology, these would be difficult to determine experimentally. In the present study, we model the flow of blood plasma over and past the EGL as a 3D dynamic viscous flow over and past an array of deformable fibers. We perform in silico start-up and pulsating shear experiments that typically appear in vessels of different sizes of the circulatory system in a representative volume of the fibrous glycocalyx layer. Numerical as well as analytical predictions for the tip displacement vector under steady-state conditions show that the horizontal and vertical components scale linearly and quadratically with the inverse blockage ratio, respectively. The dimensionless apparent permeability and the spatial-average velocity in the EG layer follow the same scalings as the vertical tip displacement. In the start-up shear flow, the fiber elasticity is found to contribute only to the transient phase, not to the steady value of the dimensionless apparent permeability, which is determined exclusively by the geometric ratios of the matrix. In the pulsatile flow only, backflow develops with the thickness of the order of the fiber radius and introduces asymmetries in the forward and the backward evolution of important quantities. Moreover, and for small ratios of the elastic to viscous forces, the time-average apparent EGL permeability is larger by at least an order of magnitude from the Darcy permeability for rigid EGL fibers. This finding gives an alternative perspective to the efficiency of paracellular and transcellular transport processes of biological molecules, plasma ions, and viruses.

We describe a crossover from the viscous fingering instability to a compact invasion regime during viscously unstable drainage of porous media, and we investigate the underlying mechanisms of this compact fluid displacement. The study is based on a series of drainage experiments in a radial porous Hele-Shaw cell where we systematically vary the viscosity of the defending (wetting) fluid and the overpressure of the invading (nonwetting) fluid to map out the resulting invasion structures as a function of viscosity ratio and injection pressure. We show that above a threshold of injection pressure and viscosity ratio a more stable and compact invasion structure emerges within the viscous fingering patterns, i.e., a roughly circular displacement with viscous fingers on the outside. The onset of the stable displacement is found to begin at a rather low viscosity ratio $M$ between the invading and defending fluids, i.e., when $M\ge {10}^{-3}$ for injection pressures of 3–5 kPa. We find that the ratio between the length of the outer fingers and the size of the compact invasion scales with the viscosity ratio and approaches a more or less constant value during growth, resulting in structures with proportionate growth and larger compact invasions for higher viscosity ratios. As opposed to the viscous fingering instability, we describe rich ganglion dynamics within the compact invasion structures and show that the pressure gradient is not screened by the outer fingers.

A three equation continuum model of drying is presented. The model explicitly considers the liquid phase as formed by a percolating liquid phase and a nonpercolating liquid phase. The model is tested against pore network simulations. A quite good agreement is obtained between the predictions of the continuum model and data obtained by volume averaging the pore network simulation results. Then, the model is extended to the case where a solute is present in the liquid phase. This leads to the consideration of a five equation continuum model as opposed to the classically considered two equation model. The model is tested when diffusion is the solute dominant transport mechanism. In agreement with the pore network simulations, the five equation continuum model predicts that the solute concentration in the percolating liquid phase is greater than in the nonpercolating liquid phase in the considered situation. The work illustrates the key role of the liquid fragmentation process occurring during drying on the solute dynamics. Counterintuitively, although diffusion is dominant, it is shown that the solution concentration varies over the liquid phase as the result of the liquid phase fragmentation process.

Jets with volumetric off-source heating have been studied extensively in the past few decades, especially since they mimic cumulus clouds, where diabatic heating of updrafts occurs due to condensation of droplets. In such systems, a pure jet, entering the flow domain via a round inlet in a neutrally buoyant environment, is heated within a specified “heat injection zone” (HIZ). The heating rate inside the HIZ is proportional to the concentration of tracer species, injected at the inlet. In this work, we construct one-dimensional Gaussian integral models for this system, in which we evolve the mean flow rates of volume, specific momentum, mean temperature, and mean tracer concentration, along the axial direction. We additionally evolve the mean flow rates of the squares of mean velocity, mean temperature, and mean tracer concentration, leading to an “energy consistent” closure for the entrainment rate coefficient and the integral flow variables. Unlike conventional integral models for jets and plumes, our formulation allows the widths for mean velocity, mean temperature, and mean tracer concentration profiles to evolve independently along the jet axis. We also perform large eddy simulations (LESs) of the system at different heating rates. A priori estimates of the source terms in the Gaussian integral equations, as well as a posteriori predictions from the one-dimensional integral model, compare reasonably well with LES statistics. Our results demonstrate the importance of evolving the dispersion ratios for velocity, temperature, and tracer concentration independently in integral models of such systems.

Bubbles bursting at the ocean surface are an important source of sea-spray aerosol. Indeed, a bubble bursting at the surface of a liquid produces a jet that then breaks up leading to several droplets. Here we simulate the bursting of a single bubble by numerical simulation of the axisymmetric two-phases air-water Navier-Stokes equations in the presence of small initial perturbations in the liquid phase. We describe the impact of this random noise on the size and velocity of the drops for a wide range of control parameters. We then demonstrate how the process of jet drop production is robust to perturbations in the initial conditions, which allows an accurate prediction of the size and speed of jet droplets over the entire parameter space. We propose a mechanism to explain why the existence of some droplets, called “primary droplets,” are robust to initial conditions and discuss why the generation of secondary droplets, much smaller than the primary ones, are sensitive to the same initial conditions. The production of these secondary droplets is sensitive to perturbations in the initial conditions through a mechanism of pinch-off escape. This can explain previously published experimental observations of bimodal distributions of jet drops.

Application of an electric field across the curved interface of two fluids of low but nonzero conductivities, or “leaky dielectrics,” can give rise to electric stresses that drive sustained fluid flow. In a uniform dc electric field of sufficiently weak magnitude, the electric and velocity fields around an isolated, neutrally buoyant leaky dielectric drop at zero Reynolds number are fore-aft and azimuthally symmetric about the applied field axis. Consequently, the drop remains stationary. The presence of a second drop breaks these symmetries, resulting in the relative motion of the drop pair. Recently, Sorgentone et al. derived an analytical expression for the relative velocity of a pair of widely separated drops of identical constitution, asymptotic in the inverse separation distance between the drop centroids [C. Sorgentone, J. I. Kach, A. S. Khair, L. M. Walker, and P. M. Vlahovska, Numerical and asymptotic analysis of the three-dimensional electrohydrodynamic interactions of drop pairs, J. Fluid Mech. 914, A24 (2021)]. In the present work, we generalize the theory of Sorgentone et al. to interactions of dissimilar drops (of different size or constitution), and the pairwise additive interactions of three or more drops. We perform experiments on silicone oil drops suspended in castor oil, and we compare to asymptotic predictions of the drop pair trajectories. Experimental trajectories of drops with their line of centers initially at an arbitrary angle to the field direction are shown to be qualitatively predicted by our theory. We show results of experiments of dissimilar drops and of three and four drops, again observing qualitative agreement with our theoretical predictions.

Differently sized particles in sheared granular mixtures undergo size segregation and diffusive remixing, the relative magnitude of which controls the degree to which distinct particle layers form. The presence of viscous interstitial fluids affects individual particle dynamics, resulting in complex segregation and diffusion behaviors. In this study, the effects of different types of fluids (characterized by fluid density and viscosity) on these two processes are investigated, for various flow conditions and material parameters, via coupled numerical simulations of immersed granular shear flows. We observe that both the segregation velocity and the diffusion strength decrease with the fluid viscosity, but these effects occur only when the viscosity exceeds certain threshold values, indicating a transition from viscous to inertial regimes. In the low-viscosity limit where fluid and grain inertia dominate, both segregation and diffusion processes depend on flow conditions and material properties in a manner that is similar to those in dry inertial granular flows. On the other hand, decreasing the relative density between the particles and the fluid slows down segregation but does not significantly affect diffusion. Based on scaling analysis of the simulation data, empirical relationships for the segregation velocity and diffusion coefficient are developed as functions of a modified Stokes number, and are then used to extend an existing segregation-diffusion continuum equation for granular mixtures immersed in different types of fluids.

Obliquely impacting of droplet on horizontal solid surface is studied numerically. The impact velocity ($v_1$), both the magnitude and direction, is varied to analyze its effect on spreading area and droplet kinetics. The normal impact velocity ($v_1^{\mathrm{n}}$) is found to be the main factor that influences the temporal variation of spreading area in droplet obliquely impacting process. The influence of normal Weber number (${\mathrm{We}}_{\mathrm{n}}$) on the restitution coefficients (${\varepsilon }^{\mathrm{n}}\mathrm{and}{\varepsilon }^{\mathrm{t}}$) is also investigated. Within the same impact angle interval, the normal restitution coefficient (${\varepsilon }^{\mathrm{n}}$) grows with small ${\mathrm{We}}_{\mathrm{n}}$ and is with the general scaling relationship of ${\varepsilon }^{\mathrm{n}}\sim {{\mathrm{We}}_{\mathrm{n}}}^{-1/4}$ for moderate ${\mathrm{We}}_{\mathrm{n}}$, which is similar to that in the droplet normal impact process. The tangential restitution coefficient (${\varepsilon }^{\mathrm{t}}$) is found to vary around a constant value and this observation has been analyzed from the view of both droplet kinetics and dynamics. Moreover, we also study the influence of tangential velocity on viscous dissipation and find that large tangential velocity would induce higher viscous dissipation energy.

We present the extension of a modeling technique for Lagrangian tracer particles [B. Viggiano et al., J. Fluid Mech. 900, A27 (2020)] which accounts for the effects of particle inertia. Thereby, the particle velocity for several Stokes numbers is modeled directly by a multilayered Ornstein-Uhlenbeck process and a comparison of key statistical quantities (second-order velocity structure function, acceleration correlation function, and root-mean-square acceleration) to expressions derived from Batchelor's model as well as to direct numerical simulations (DNS) is performed. In both approaches, Stokes' drag is treated by an approximate “linear filter” which replaces the particle position entering the fluid velocity field by the corresponding ideal tracer position. Effects of preferential concentration of inertial particles are taken into account indirectly in terms of an effective Stokes number that is determined from the zero crossing of the acceleration correlation function from DNS. This approximation thus allows the modeling of inertial particle statistics through stochastic methods and models for the Lagrangian velocity; the particle velocity is effectively decoupled from the particle position. In contrast to the ordinary filtering technique [Cencini et al., J. Turbul. 7, N36 (2006)], our method reproduces the empirically observed sharp decrease of acceleration variance for increasing Stokes numbers. Furthermore, we discuss how our modeling approach could contribute to a better experimental characterization of inertial particle dynamics.

Pore network modeling is an efficient and reliable approach for simulating the flow and transport of fluids in porous media. A key to this modeling approach is to extract pore networks that can accurately describe the actual pore space of porous media. To extract pore networks from the voxelized porous media, the Euclidean distance map, i.e., the distance of each void voxel to the nearest solid voxel, has been commonly employed so as to discern the hierarchy of the void voxels. However, for the porous media with pores of high aspect ratios, the void voxels can have the same Euclidean distance, and the hierarchy of the void voxels cannot be distinguished clearly by the Euclidean distance map. To address this issue, we propose a pore network extraction method based on the concept of the omnidirectional Euclidean distance, which is a set of Euclidean distances from a void voxel to all the accessible solid boundary voxels. We consider the situation in which two pore bodies are connected by more than one pore throat. Furthermore, a deterministic method is introduced to identify the pore body and the pore throat regions. The proposed pore network extraction method is validated by comparing the pore network modeling results, in terms of the single-phase flow and the quasistatic two-phase drainage, against the direct numerical simulation results and the experimental data. The proposed pore network extraction method not only preserves the topological and morphological properties of the void spaces in porous media, but it is also robust and insensitive to the image noise.

A new direct numerical simulation of a Poiseuille channel flow has been conducted for a friction Reynolds number of $10000$, using the pseudospectral code LISO. The mean streamwise velocity presents a long logarithmic layer, extending from 400 to 2500 wall units, longer than it was thought. The maximum of the intensity of the streamwise velocity increases with the Reynolds number, as expected. Also, the elusive second maximum of this intensity has not appeared yet. In case it exists, its location will be around $y^{+}\approx 120$, for a friction Reynolds number extrapolated to approximately 13 500. The small differences in the near-wall gradient of this intensity for several Reynolds numbers are related to the scaling failure of the dissipation, confirming this hypothesis. The scaling of the turbulent budgets in the center of the channel is almost perfect above 1000 wall units. Finally, the peak of the pressure intensity grows with the Reynolds number and does not scale in wall units. If the pressure at the wall is modeled as an inverse quadratic power of ${\text{Re}}_{\tau }$, then $p_{\infty }^{\prime +}\approx 4.7$ at the limit of infinite Reynolds number.

Using direct numerical simulations, we study rotating Rayleigh-Bénard convection in a cylindrical cell with aspect ratio $\mathrm{\Gamma }=1/2$, for Prandtl number 0.8, Ekman number ${10}^{-6}$, and Rayleigh numbers from the onset of wall modes to the geostrophic regime, an extremely important one in geophysical and astrophysical contexts. We connect linear wall-mode states that occur prior to the onset of bulk convection with the boundary zonal flow that coexists with turbulent bulk convection in the geostrophic regime through the continuity of length and timescales and of convective heat transport. We quantitatively collapse drift frequency, boundary length, and heat transport data from numerous sources over many orders of magnitude in Rayleigh and Ekman numbers. Elucidating the heat transport contributions of wall modes and of the boundary zonal flow are critical for characterizing the properties of the geostrophic regime of rotating convection in finite, physical containers and is crucial for connecting the geostrophic regime of laboratory convection with geophysical and astrophysical systems.

The dynamics of flow within a material transport network is dependent upon the dynamics of its power source. Responding to a change of these dynamics is critical for the fitness of living flow networks, e.g., the animal vasculature, which are subject to frequent and sudden shifts when the pump (the heart) transitions between different steady states. The combination of flow resistance, fluid inertia, and elasticity of the vessel walls causes the flow and pressure of the fluid throughout the network to respond to these transitions and adapt to the new power source operating profiles over a nonzero timescale. We find that this response time can exist in one of two possible regimes; one dominated by the decay rate of traveling wavefronts and independent of system size, and one dominated by the diffusive nature of the fluid mechanical energy over large length scales. These regimes are shown to exist for both single vessels and hierarchically structured networks with systems smaller than a critical size in the former and larger systems in the latter. Applying biologically relevant parameters to the model suggests that animal vascular networks may have evolved to occupy a state within the minimal response time regime but close to this critical system size.

Local-flux vectors of conserved quantities in the wavenumber space are proposed to investigate their directional properties in anisotropic turbulence. The proposed vectors are validated in statistically steady states of Charney-Hasegawa-Mima turbulence, which consists of anisotropic wave turbulence with zonal flow and isotropic vortex turbulence. The directions of the local-flux vectors are consistent with the energy-enstrophy double cascade in two-dimensional isotropic turbulence. The flux vectors of energy, furthermore, successfully show an anisotropic structure below the Rhines wavenumber, corresponding to the large-scale zonal flow, while those of enstrophy show almost isotropic structure. A couple of expressions of the critical balance are compared with the energy spectra and the flux vectors. The results confirm that the proposed method can quantitatively characterize the anisotropically directed flows of conserved quantities in the wavenumber space.

The effect of a single, vertical edge on a draining liquid film was studied recently [Phys. Rev. Lett. 125, 064502 (2020)]. In this experimental study, we characterize the structure of a liquid film, draining due to gravity, on a vertical, narrow substrate. We show that surface tension affects the draining film at the two vertical edges. The edge effects propagate into the film to eventually influence the shape over the entire width. Interferometry is performed to measure the film thickness profile. A motorized stage is used to vertically translate the thin film and the substrate, which extends the range of the measurements. Our experiments show that the thickness of the liquid film scales with the well-known Jeffreys' solution, which is the thickness of a draining film on a vertical substrate of infinite width. However, due to the existence of the two vertical edges, near the top contact line, the film thickness changes sharply near the edges and is flat near the middle of the substrate. In contrast, away from the top contact line, the edge effects propagate towards the middle, and the overall horizontal film shape eventually becomes approximately quartic. Further, we identify characteristic length scales in the vertical direction, which combine the effects of the surface tension, viscosity, and gravitational drainage. These length scales, respectively, highlight the effects from the vertical edges and the top contact line, and the experimental results are in agreement with the scaling arguments.

This work aims to estimate time-resolved velocity field that is directly associated with pressure fluctuations in a subsonic round jet. To achieve this goal, synchronous measurements of the velocity field and in-flow pressure fluctuations were performed at Mach number 0.3. Two different experiment campaigns were conducted: the first experimental campaign aims to explore the time-resolved dynamics of the axisymmetric velocity components, and the second experiment focuses on the time-resolved, two-dimensional velocity estimates on a streamwise plane. Two different methods were utilized to estimate the input-output relation between velocity and in-flow pressure measurements. A hybrid approach based on the spectral linear stochastic estimation and the proper orthogonal decomposition was applied to set up the model in a linear manner, and a wavelet-based filter was implemented to attenuate the noise level in the cross-correlation functions. In addition, the pressure-velocity relationship was also described by neural network architectures based on the multilayer perceptron (MLP) and bidirectional long-short-term memory (LSTM). In both experimental sets, pressure fluctuations inside the flow are found to be connected to the streamwise convection of large-scale coherent structures in the flow. A unique advantage of the bidirectional LSTM method was found among all estimation schemes and is also reported in this work. The estimation result represents the space-time dynamics of the turbulent structures that are linked to the pressure wave packets in the flow, and it is of great importance to understand the noise generation mechanism.

We study, by direct numerical simulations in two and three dimensions, the instability caused by the settling and evaporation of water droplets out of a cloudy layer saturated with vapor into a dry subcloud ambient under conditions where mammatus clouds were shown to form but with the addition of background shear. We show that shear changes the type of cloud formation qualitatively from mammatus-like to a newly identified cloud type called asperitas. Intermediate levels of shear are shown to be needed. Shear suppresses the growth of small-scale perturbations, giving rise to smooth, long-lasting structures and smaller rates of mixing. Three-dimensionality is shown to make a qualitative difference, unlike in mammatus clouds. We also show that under non-cloud-like conditions, the instability can be very different.

To gain insight into the microscopic processes leading to the observed collective settling of particles from the base of a particle-bearing fresh water layer overlying salt water, we perform numerical simulations of the settling of weakly inertial particles through uniform density, uniformly stratified and nonuniformly stratified fluids. Intuition is gained first through simulations of a descending horizontal row and planar arrays of particles. These show that stratification acts to reduce cluster sizes and to slow the relative descent speed of clusters as a result of upward flows that develop around the clusters. This occurs even for a descending vertical planar array: in unstratified fluid, the ambient fluid rises laterally around the particles with the flow in the plane of the particles being predominantly downward; in stratified fluid, upward as well as downward motion is evident in the plane of particles. For a random three-dimensional particle array with concentration by volume between 0.1% and 1%, upflows in the ambient fluid likewise retard cluster formation and descent speeds. The mean horizontal displacement of the particles is reduced, resulting in more small clusters with more closely packed particles. The particles become more vertically aligned in lower diffusivity (higher Schmidt number) fluid, although such clustering takes longer to develop. The results suggest that both stratification and relative diffusivity play a crucial role in the collective settling behavior observed in laboratory experiments.