We characterize the dynamical behavior of a clamped flexible fiber immersed in wall turbulence over a wide range of natural frequencies ($f_{\mathrm{nat}}$) by means of direct numerical simulations. Only two flapping states are possible: one where the fiber oscillates at the characteristic frequency of the largest turbulent eddies ($f_{\mathrm{turb}}$) and another where the natural structural response dominates. The former is obtained in the more flexible cases ($f_{\mathrm{nat}}<f_{\mathrm{turb}}$), while the latter in the more rigid ones ($f_{\mathrm{nat}}>f_{\mathrm{turb}}$). We observe that in the turbulence-dominated regime, the fiber always sways at a frequency proportional to the largest scale of the flow, regardless of its structural parameters. The hindrance of the clamp to the wall prevents the synchronization of the fiber with turbulent eddies of comparable size.

We present the observation of an expanding vortex ring below a fast-spreading ethanol-water film over a deep substrate of water. The radius of the vortex ring ($r_v$) is shown to scale with time as $t^{1/2}$. The outer radius of the disturbed region ($r_o$), which comprises the expanding film of length $r_f$ and the plume of length $l_p$ at its periphery, scales in the same way as $r_v$. Based on this observation, contrary to the earlier proposal of the origin of such vortex rings to be due to evaporative cooling, we hypothesize that such vortex rings occur due to the separation of the shear layer below the plumes. Based on this hypothesis, we obtain scaling laws for the radius of the vortex ring ($r_v$) and its radial expansion velocity ($U_v$). These scaling laws are shown to match our measurements, thereby validating the phenomenology of such vortex rings.

Prior to the impact of a horizontal disk onto a liquid surface, the air underneath flows radially outward across the liquid surface to escape from below the edge of the disk. Such airflow causes the surface to be elevated near the disk edge, creating a free-surface condition that influences the details of the subsequent impact dynamics. In this work, the nature of the surface elevation under an impacting disk is investigated by modulating the forcing of the free surface: The airflow below the disk is altered by imposing a radially symmetric wave structure of varying wavelength on the impacting disk surface. Subsequently, the liquid surface deformation before impact is measured experimentally using a total internal reflection technique. The experiments provide convincing evidence that supports the argument that the surface elevation is an instability of the Kelvin-Helmholtz type. In addition, the impact force exerted on the wave-structured disks is measured using a load cell. Due to the macroscopic wave structure on the disk, the maximum impact force is significantly reduced, and the results indicate that both the free-surface deformation before impact and the way in which the impacting surface is subsequently wetted influence the maximum impact force.

The thermal conductivity and self-diffusion coefficients for molecular nitrogen and oxygen are investigated with the direct molecular simulation (DMS) technique using high-fidelity, ab initio potential energy surfaces. The DMS results are compared to available experimental data, and remarkable agreement is observed in all cases. Such comparisons are restricted to relatively low temperature, typically below 2000 K. For temperatures up to 10 000 K, the DMS data are also in excellent agreement with the corresponding transport properties obtained using kinetic theory based on collision integrals evaluated with simplified, point-particle interatomic potentials. An analysis of the Eucken approximation shows that the Eucken correction factor is based upon reasonably accurate assumptions, but a significant improvement can be obtained by properly accounting for the ratio of mass to momentum diffusion. Finally, it is shown that the DMS transport data for mass, momentum, and energy are consistent with kinetic theory across a wide range of temperatures, thus offering convincing evidence for the reliability of the methodologies employed for their determination.

We develop neural-network active flow controllers using a deep learning partial differential equation augmentation method (DPM). The end-to-end sensitivities for optimization are computed using adjoints of the governing equations without restriction on the terms that may appear in the objective function. In one-dimensional Burgers' examples with analytic (manufactured) control functions, DPM-based control is comparably effective to standard supervised learning for in-sample solutions and more effective for out-of-sample solutions, i.e., with different analytic control functions. The influence of the optimization time interval and neutral-network width is analyzed, the results of which influence algorithm design and hyperparameter choice, balancing control efficacy with computational cost. We subsequently develop adjoint-based controllers for two flow scenarios. First, we compare the drag-reduction performance and optimization cost of adjoint-based controllers and deep reinforcement learning (DRL) -based controllers for two-dimensional, incompressible, confined flow over a cylinder at $\text{Re}=100$, with control achieved by synthetic body forces along the cylinder boundary. The required model complexity for the DRL-based controller is 4229 times that required for the DPM-based controller. In these tests, the DPM-based controller is 4.85 times more effective and 63.2 times less computationally intensive to train than the DRL-based controller. Second, we test DPM-based control for compressible, unconfined flow over a cylinder and extrapolate the controller to out-of-sample Reynolds numbers. We also train a simplified, steady, offline controller based on the DPM control law. Both online (DPM) and offline (steady) controllers stabilize the vortex shedding with a 99% drag reduction, demonstrating the robustness of the learning approach. For out-of-sample flows ($\text{Re}=\{50,200,300,400\}$), both the online and offline controllers successfully reduce drag and stabilize vortex shedding, indicating that the DPM-based approach results in a stable model. A key attractive feature is the flexibility of adjoint-based optimization, which permits optimization over arbitrarily defined control laws without the need to match a priori known functions.

We provide comprehensive numerical insights into the displacement of droplets subject to soluble surfactant-driven flows. The effects of soluble surfactants on the dynamics of moving contact lines are introduced by the surfactant-dependent generalized Navier boundary condition. We show that surfactant transport significantly influences the displacement patterns of droplets on solid surfaces, affecting both the equilibrium state of the sliding motion and the critical conditions for detachment. In particular, a linear increase in the displacement velocity of a droplet with the dimensionless adsorption depth $K$ is observed. This rate of increase is more pronounced at higher elasticity numbers, as evidenced by a more significant increase in the advancing contact angle. The critical condition for droplet detachment depends on the surfactant's ability to swiftly adsorb from the bulk and replenish at interfaces, which is improved as the Biot number Bi or $K$ increases. Adsorption is enhanced by an increase in Bi, resulting in a decrease in the required time $t_d$ for droplet detachment. However, this enhancement effect becomes nonmonotonic at high Bi values. In contrast, consistently increasing the bulk Peclet number decreases $t_d$, eventually approaching the convection limit where the Marangoni-induced drag force ceases to increase. In addition, surfactant transfer near the moving contact line at a moderate Damköhler number restricts the motion of the advancing contact lines, promoting droplet detachment. For all detachment scenarios, we find that detachment necessitates a critical effective capillary number, and an increase in this number results in an exponential decline in $t_d$.

Small heavy particles in a fluid flow respond to the flow on a timescale proportional to their inertia or Stokes number $\text{St}$. Their behavior has been thought to be gradually modified as $\text{St}$ increases. We show, on the other hand, in the steady spatially periodic laminar Taylor-Green vortex flow, that particle dynamics, and their effective diffusivity, actually change in an irregular, nonmonotonic, and sometimes discontinuous manner with increasing $\text{St}$. At $\text{St}\sim 1$, we show chaotic particle motion, contrasting with earlier conclusions for heavy particles in the same flow [Wang et al., Phys. Fluids 4, 1789 (1992)]. Particles may display trapped orbits, or unbounded diffusive or ballistic dispersion, with the vortices behaving like scatterers in a soft Lorentz gas [Klages et al., Phys. Rev. Lett. 122, 064102 (2019)]. The dynamics is nonergodic.

An inertial gravity current released within a topographic depression may climb up the incline from a lower to an upper plateau if it is sufficiently energetic and then continue to flow unsteadily away from the step while simultaneously draining back into the depression. This density-driven motion is investigated theoretically using the shallow-water equations to simulate the flow up a smooth step from a lower to an upper horizontal plane and to compute the volume of fluid that escapes from the depression. It is shown that it is possible for all of the fluid to drain back down the step and that the volume of the escaped fluid diminishes with a power-law dependence on time. This phenomenon is explained by analyzing the unsteady flow of a gravity current along a semi-infinite horizontal plane along which the front advances but simultaneously fluid drains from the rear edge of the plane. The dynamics of this motion at early times is calculated both numerically and analytically. The latter exploits the hodograph transformation of the shallow water equation, a technique which allows rapid and precise evaluation of flow features such as reflections and the onset of bores. The flow at later times becomes self-similar, and the self-similarity is of the second kind. It features an anomalous exponent that provides the power-law dependence of the volume of fluid on time, and this exponent is a function of the imposed Froude number at the front of the current. In this way the diminishing volume of fluid that escapes from a topographic depression is explained quantitatively. Eventually the flow may transition to a regime in which drag becomes non-negligible; the model of simultaneous propagation and draining is extended to this regime to show that the escaped volume of fluid also decays temporally and ultimately vanishes.

Electrospray has the advantages of high efficiency and accurate thrust, which can meet the requirements of microsatellites on micropropulsion systems, and it is a new type of microthrust system with great potential. Due to the stable characteristics of the cone jet, most of the existing research focuses on the steady electric field, while the response of the Taylor cone shape to the pulse voltage has vital application significance in the attitude control of the microthruster and the active control of the electrospray switch. Therefore, this paper focuses on the research on the response mechanism of the Taylor cone shape to a single pulse voltage. Based on experimental research, a high-speed camera is used to capture the time-series images of the Taylor cone, and a trigger connection is used to synchronously collect the atomization current under a single pulse disturbance voltage to assist in exploring the oscillation mechanism. The research shows that the pulsation of a Taylor cone under the action of a single pulse voltage has a strong coupling relationship with the conductivity and permittivity of the dielectric in the fluid, that is, the oscillation time has a strong consistency with the polarization charge relaxation time of the dielectric in the fluid.

The Green function, or the wave motion due to a point source pulsating and advancing at constant forward speed along a semi-infinite ice sheet in finite water depth is investigated, based on the linear velocity potential theory for fluid flow and thin elastic plate model for the ice sheet. The result is highly relevant to the ship motions near marginal seas. The ice edge is assumed to be free, or zero bending moment and shear-force conditions are used, while other edge conditions can be similarly considered. The Green function $G$ is derived first through the Fourier transform along the direction of forward speed and then by the Wiener-Hopf technique along the transverse direction across both the free surface and ice sheet. The result shows that in the ice-covered domain, $G$ can be decomposed into three parts. The first one is that upper ocean surface is fully covered by an ice sheet, and the second and third ones are due to the free surface and ice edge. Similarly, in the free-surface domain, $G$ contains the component corresponding to that the upper water surface is fully free, while the second and third ones are due to the ice sheet and ice edge. In both domains, the latter two are due to the interactions of the free-surface wave and ice sheet deflection, which leads to the major complication. In-depth investigations are made for each part of $G$, and aim to shed some light on the nature of the wave motions induced by a ship advancing along a semi-infinite ice sheet at constant forward speed.

In an externally imposed electrolyte (salt) concentration gradient, charged colloids drift at speeds of order one micrometre per second. This phenomenon is known as diffusiophoresis. In systems with multiple salts and “crossed” salt gradients, a nonlocal component of the electric field associated with a circulating (solenoidal) ion current can arise. This is in addition to the conventional local component that depends only on the local salt gradients. Here we report experimental observations verifying the existence of this nonlocal contribution. To our knowledge this is the first observation of nonlocal diffusiophoresis. The current develops quasi-instantaneously on the timescale of salt diffusion. Therefore, in systems with multiple salts and crossed salt gradients, one can expect a nonlocal contribution to diffusiophoresis which is dependent on the geometry of the system as a whole and appears as a kind of instantaneous “action-at-a-distance” effect. The interpretation is aided by a magnetostatic analogy. Our experiments are facilitated by a judicious particle-dependent choice of salt (potassium acetate) for which the two local contributions to diffusiophoresis almost cancel, effectively eliminating conventional diffusiophoresis. This enables us to clearly identify the novel, nonlocal effect and may be useful in other contexts, for example, in sorting particle mixtures.

We conduct direct numerical simulations (DNS) by the full Eulerian finite difference method of a neutrally buoyant hyperelastic particle in Taylor–Green vortical flow. We investigate the case that the initial shape of the particle is spherical with a diameter comparable with the vortex radius. The particle orbit depends on the degree of its deformation due to the flow. When the particle is stiffer (i.e., the capillary number Ca is smaller than about 0.1), the particle is hardly deformed and slowly swept out from the vortex. In contrast, softer particles with $\text{Ca}\gtrsim 0.1$ are significantly deformed, in an initial period, and they are attracted towards the vortex; then, afterward, the deformation is relaxed so that they can stay around the vortex center. Such an attraction of anisotropic neutrally buoyant particles towards a vortex occurs, even if particles are rigid. We demonstrate this phenomenon by additional DNS of a rigid prolate spheroidal particle in the vortical flow. We also develop analytical arguments to show that the angle between the major axis of the particle and the pathline determines whether the vortex attracts or repulses the particle. This feature well explains the radial motion of neutrally buoyant elastic particles in vortical flow.

We consider phoretic self-propulsion of a chemically active colloid where solute is produced on the colloid surface (with a spatially varying rate) and consumed in the bulk solution (or vice versa). Assuming first-order kinetics, the dimensionless transport problem is governed by the surface Damköhler number $\mathcal{S}$ and the bulk Damköhler number $\mathcal{B}$. The dimensionless colloid velocity $U$, normalized by a self-phoretic scale, is a nonlinear function of these two parameters. In the limit of small $\mathcal{S}$, the solute flux is effectively prescribed by the surface activity distribution, resulting in an explicit expression for $U$ that is proportional to $\mathcal{S}$. In the limit of large $\mathcal{B}$, the deviations of solute concentration from the equilibrium value are restricted to a narrow layer about the active portion of the colloid boundary. The associated boundary-layer analysis yields another explicit expression for $U$. Both asymptotic predictions are corroborated by an eigenfunction expansion solution of the exact problem for the cases when all physical parameters are held fixed except for a varying colloid size (resulting in $\mathcal{S}\propto {\mathcal{B}}^{1/2}$) or a varying solute diffusivity (resulting in $\mathcal{S}\propto \mathcal{B}$). The boundary-layer structure breaks down near the transition between the active and inactive portions of the boundary. The local solution in the transition region partially resembles the classical Sommerfeld solution of wave diffraction from an edge.

In this study we explore the effect of an offset between the velocity and density interfaces on the dynamics and mixing of the Kelvin-Helmholtz (KH) instability in stratified shear flows. Most prior studies have assumed a coincident interface-symmetric KH instability. To investigate the asymmetric KH instability that emerges in the presence of offset interfaces, we conduct a linear stability analysis and direct numerical simulations, comparing results with the well-known symmetric KH instability. We find that the asymmetric KH instability is a hybrid mode of symmetric KH and Holmboe instabilities, with features of both overturning and scouring flows and a nonzero propagation speed. In contrast to the symmetric KH instability, the asymmetric KH instability does not generate a large-scale overturning of the central isopycnal but scours fluid of intermediate density from the upper portions of the interface, resulting in a significant interface deepening and sharpening of the density interface during mixing events. We observe that the dynamics and amount of mixing are strongly influenced by the degree of asymmetry (i.e., the offset distance between density and velocity interfaces) in the flow. With a larger asymmetry, the kinetic energy of the instability is larger but the cumulative mixing and mixing efficiency increase to a maximum then decrease. We find a similar transition of the gradient Richardson number distribution after the instabilities become turbulent, which has important implications for interpreting oceanographic data. Our study suggests that asymmetry should be taken into account in future studies of the KH instability.

This work investigates the wetting dynamics of cryogenic fluids in inertia-dominated conditions. We experimentally characterize an oscillating gas-liquid interface of liquid nitrogen in a partially filled U-shaped quartz tube. The experiments were carried out in controlled cryogenic conditions, with interface oscillations produced by releasing the liquid column from an unbalanced position and having nitrogen vapor as the only ullage gas. During the experiments, the interface shape was tracked via image processing and used to fit a model from which the contact angle could be accurately determined. The results show that the dynamic contact angle evolution in advancing conditions is linearly linked to the capillary number, with a slope depending on whether the interface moves over a dry or a prewet surface. However, the contact angle remains close to the one at equilibrium in receding conditions. To analyze the relation between contact angle and interface dynamics, we define an equivalent contact angle as the one that would make a spherical interface produce the same capillary pressure drop as the actual interface shape. The evolution of this equivalent contact angle proved to be independent of the evolution of the actual one, suggesting that the interface shape is not influenced by it. Finally, a theoretical analysis of the interface motion using a simplified model shows that viscous forces dominate the damping of the interface for small tube sizes, while gravity and inertial forces dominate the oscillating dynamics of the liquid column for larger tubes.

We study the time-dependent flow behavior of gravity-driven free surface granular flows using the discrete element method and continuum modeling. Discrete element method (DEM) simulations of slightly polydisperse disks flowing over a periodic chute with a bumpy base are performed. A simple numerical solution based on a continuum approach with the inertial-number-based $\mu \text{−}I$ rheology has been proposed to predict the flow dynamics. The results of the continuum model are compared with the DEM simulation results for a wide range of chute inclinations. Solutions for the constitutive model described by the popular Jop-Forterre-Pouliquen (JFP) model as well as the recently proposed modified rheological model using a nonmonotonic variation of $\mu \text{−}I$ are obtained. Our results demonstrate that the popular JFP model reliably predicts the flow at low to moderate inclination angles (i.e., for $I\lesssim 0.5$). However, it fails to predict the flow properties at high inclinations. The modified rheological model, on the other hand, is very well able to predict the time-averaged flow properties for all the inclination angles considered in this study. Accounting for the presence of the slip velocity, layer dilation, and stress anisotropy is found to be crucial for accurate predictions of transient flows at high inertial numbers (i.e., for $I\gtrsim 1$).

The freezing of a sessile droplet unveils fascinating physics, characterized by the emergence of a frost halo on the underlying substrate, the progression of the liquid-ice interface, and the formation of a cusplike morphology at the tip of the droplet. We investigate the freezing of a volatile sessile droplet, focusing on the frost halo formation, which has not been theoretically explored. The formation of the frost halo is associated with the inherent evaporation process in the early freezing stages. We observe a negative evaporation flux enveloping the droplet in the initial stages, which indicates that vapor produced during freezing condenses on the substrate close to the contact line, forming a frost halo. The condensate accumulation triggers reevaporation, resulting in a temporal shift of the frost halo region away from the contact line. Eventually, it disappears due to the diffusive nature of the water vapor far away from the droplet. We found that increasing the relative humidity increases the lifetime of the frost halo due to a substantial reduction in evaporation that prolonged the presence of net condensate on the substrate. Increasing liquid volatility increases the evaporation flux and condensation occurs closer to the droplet, as a higher amount of vapor is in the periphery of the droplet. We also found that decreasing the thermal conductivity of the substrate increases the total freezing time. The slower freezing process is accompanied by increased vaporized liquid, resulting in condensation with its concentration reaching supersaturation.

Buckling induced by viscous flow changes the shape of sheetlike nanomaterial particles suspended in liquids. This instability at the particle scale affects collective behavior of suspension flows and has many technological and biological implications. Here, we investigated the effect of viscous hydrodynamic interactions on the morphology of flexible sheets. By analyzing a model experiment using thin sheets suspended in a shear cell, we found that a pair of sheets can bend for a shear rate ten times lower than the buckling threshold defined for a single sheet. This effect is caused by a lateral hydrodynamic force that arises from the disturbance flow field induced by the neighboring sheet. The lateral hydrodynamic force removes the buckling instability but massively enhances the bending deformation. For small separations between sheets, lubrication forces prevail and prevent deformation. Those two opposing effects result in a nonmonotonic relation between distances and shear rate for bending. Our study suggests that the morphology of sheetlike particles in suspensions is not purely a material property but also depends on particle concentration and microstructure.

A majority of numerical experiments of the Navier-Stokes equations, lacking physical boundaries, have been conducted under periodic boundary conditions so far. In this paper, in order to access the effect of periodicity imposed upon the flow properties, we take up specifically two-dimensional incompressible flows and carry out numerical simulations on the whole plane to compare with those under periodic boundaries, with or without adjusting the Reynolds number. We solve the Navier-Stokes equations on a square domain using a finite-difference scheme to simulate flows on ${\mathbb{R}}^2$. After checking the time evolution of the Oseen vortex with the exact solution, we simulate merging of like-signed vortices to compare it with that under periodic boundaries. Generally speaking, we find that flows decay in norms faster on ${\mathbb{T}}^2$ than on ${\mathbb{R}}^2$, even when the Reynolds number is adjusted. We also simulate merging of three localized vortices that generates finer spatial structure in order to study the decay law of the total enstrophy and spatial patterns in vorticity. In this case, norms on ${\mathbb{T}}^2$ decay in a manner very close to how those on ${\mathbb{R}}^2$ do, but still marginally faster than those on ${\mathbb{R}}^2$. We also study the power law of the energy spectrum on ${\mathbb{R}}^2$, comparing it with the predictions of, for example, Gilbert's spiral model including $E\left(k\right)\sim k^{-11/3}$, which sits at the Sulem-Frisch borderline.

Assessing the compliance of a white-box turbulence model with known turbulent knowledge is straightforward. It enables users to screen conventional turbulence models and identify apparent inadequacies, thereby allowing for a more focused and fruitful validation and verification. However, comparing a black-box machine-learning model to known empirical scalings is not straightforward. Unless one implements and tests the model, it would not be clear if a machine-learning model, trained at finite Reynolds numbers preserves the known high Reynolds number limit. This is inconvenient, particularly because model implementation involves retraining and reinterfacing. This work attempts to address this issue, allowing fast a priori screening of machine-learning models that are based on feed-forward neural networks (FNN). The method leverages the mathematical theorems we present in the paper. These theorems offer estimates of a network's limits even when the exact weights and biases are unknown. For demonstration purposes, we screen existing machine-learning wall models and RANS models for their compliance with the log layer physics and the viscous layer physics in an a priori manner. In addition, the theorems serve as essential guidelines for future machine-learning models.