In this study, a phase diagram is constructed for the impact of nanodroplets on nanopillared surfaces via molecular dynamics simulations. Four impact regimes, i.e., first nonbouncing (1NB), bouncing, second nonbouncing (2NB), and sticky, are discovered at various pillar heights and Weber numbers. The impact regimes are compared with those at the macroscale, and several significant differences are distinguished. The differences are attributed to the significantly enhanced viscous effect, the modified viscous dissipation mechanism, and the altered wetting transition mechanism. The impact regimes are found to strongly depend on the properties of surfaces. On monostable Wenzel surfaces (small pillar heights), the sticky regime is the only regime; on metastable coexisting Cassie–Wenzel surfaces (moderate pillar heights), the 1NB and sticky regimes successively take place with increasing Weber numbers; and on monostable Cassie surfaces (large pillar heights), the sticky regime disappears, but two new regimes, i.e., the bouncing and 2NB regimes, appear. The boundaries between the 1NB and sticky regimes, between the 1NB and 2NB regimes, and between the bouncing and 2NB regimes are all related to the formation of a partial wetting state, in which the central gaps beneath the nanodroplet are intruded and completely wetted. The wetting transition at the nanoscale does not follow the macroscale depinning mechanism. Therefore, a theoretical model is developed to understand the wetting transition mechanism at the nanoscale and thus predicting the critical Weber number for triggering the wetting transition, yielding $W{e}_{\mathrm{cr}}^{1/2}\sim -h^{*}cos{\theta }_i$, which well describes the boundaries mentioned above.

Inspired by the stenocara beetle, we study an ideal flat surface composed of a regular array of hydrophilic circular patches in a hydrophobic matrix on an incline of tilt $\alpha$ with respect to the horizontal. Based on an exact solution of the Laplace-Young equation at first order in the Bond number, the liquid storage capacity of the surface is maximized as a function of the patch radius, for suitable ranges of hydrophilic and hydrophobic contact angles, for tilt angles such as ${45}^{\circ }$ or ${90}^{\circ }$. It is found that the optimal radius equally prevents dewetting from the top of the patches and overflow at the bottom. These theoretical considerations are validated by several experiments for the glass/octadecyltrichlorosilane (OTS) system involving different patch sizes and different inclinations. In a simple dynamical model, taking into account the flux of fog onto the surface or condensation on a suitably cooled surface, we find that the conditions for maximum harvest agree with the ones of maximum static storage. The method could be developed for drop storage and drop transport applications such as water-harvesting systems.

This paper presents a study on wave cancellation in forced jets. Building on recent work on real-time control of forced turbulent jets by Maia et al. [Phys. Rev. Fluids 6, 123901 (2021)], we here assess the effect of jet upstream conditions and nonlinearity on wave-cancellation performance. The experiments are performed in jets with laminar and turbulent boundary layers inside the nozzle. An open-loop campaign is first conducted, in which the goal is to analyze the jet response to stochastic forcing with variable bandwidth. The upstream conditions of the jet are found to have a strong influence on the jet response. For narrow forcing bandwidths, both jets present a clear response regime. However, in the initially laminar jet, as bandwidth is increased, high growth rates and transition to turbulence in the initial region underpin the onset of nonlinear effects in jet response. In the initially turbulent jet, on the other hand, lower growth rates allow a linear response regime to be maintained for a broader range of forcing parameters. As the wave cancellation strategy is linear, reactive control is found to be more effective in the initially turbulent jet, consistent with the results of the open-loop analysis.

The interaction of an array of finite span synthetic jet actuators with a massively separated flow was explored experimentally over a cantilevered, swept, and tapered model having a deflected control surface. The synthetic jet actuators were placed slightly upstream of the control surface hinge-line of the wind tunnel model. The flow physics associated with the interaction of multiple jets and the separated crossflow over the control surface was investigated using stereoscopic particle image velocimetry. Experiments were conducted at two spanwise regions along the model, where separation severity varied. At the outboard region, the baseline flow field was characterized by a severe separation that was quasiuniform in the spanwise direction. At the inboard measurement domain, separation was milder but increased in severity in the outboard direction. When a single jet was activated, separation was reduced downstream and outboard of the jet orifice. In addition, spanwise velocity was augmented outboard of the jet's structures at the outboard measurement domain from an oblique vortex that was observed at the spanwise location where separation severity increased (as the flow approached the baseline state). In the inboard region, this vortex was not observed and the spanwise velocity decreased with a single jet active. When more jets were actuated along the span, the overall severity of separation decreased at both locations. Despite this, in the outboard region, the spanwise velocity near the surface was enhanced, and the strength of the jets’ vortical structures decreased as more jets were activated (i.e., they negatively impacted one another). On the contrary, at the inboard region, the jets beneficially affected each other. These differences were hypothesized to be related to the oblique vortices that were distinguishable outboard but not inboard with all jets active.

An investigation of the mechanical actions on a moving intruder into a granular medium subjected to a gravity field is provided using two-dimensional numerical simulation. The interactions between the grains are frictionless and modeled by Hertz's law with a viscous damping. The intruder has a cross-shaped geometry and was initially buried at a shallow depth. It has the ability to translate and rotate at constant velocities independently of each other, thus defining a translational Froude number $Fr$ and a rotational Froude number $\mathrm{\Gamma }$. We study the evolutions of the drag force $D_x$, the lift force $L_y$ and the torque $M_z$ exerted on the intruder. In the case of pure horizontal translation with a low Froude number, these quantities are constant and independent of $Fr$ with $M_z=0$. In the case of pure rotation leading to $D_x=0$, the torque is constant when $\mathrm{\Gamma }\to 0$ and increases with $\mathrm{\Gamma }$. For the combination of translation and rotation, we also determine the evolutions laws of the mechanical actions with $\mathrm{\Gamma }$: the rotation generates an increase of the torque on the intruder while the drag force decreases. We highlight the existence of a significant drop of the lift force favoring the anchoring of the intruder in the granular medium for a specific range of $\mathrm{\Gamma }$. By applying the granular resistive force theory, we determine theoretical expressions to describe the evolution of the drag force $D_x$ and the torque $M_z$. The theoretical results are in agreement with the simulation results.

We consider the flow of a Newtonian liquid film over an inclined hydrophobic wall textured with periodical microgrooves, the depth of which is much longer than their width, which is of the order of the capillary length of the liquid. Due to their structure, these grooves can be likened to slits. The flowing liquid fails to thoroughly wet the topography forming a second liquid-gas interface, with air encapsulated inside the topographical features. Under these conditions, two possible flow configurations may arise: (1) the inner interface will be pinned at the edges of the slit (ideal Cassie-Baxter state) and (2) the film may partially wet the sidewalls of the slits, forming two additional contact lines with the substrate. We investigate both the steady flow and the stability of a Newtonian liquid film flowing over various substrates with such flow configuration. We solve the 2D Navier-Stokes equations and develop a finite element model to accurately describe the exact shape of all liquid-gas interfaces at a steady state. We determine the linear stability of the steady-state solutions when subjected to perturbations in the streamwise direction and employ the Floquet-Bloch theory to account for disturbances of arbitrary wavelengths, i.e., not necessarily matching the periodicity of the substrate. Through numerical simulations, we highlight the effect of inertia, viscous and capillary forces, and the mobility of the contact line on the stability of the fluid flow. We examine the impact of substrate wettability and orientation with respect to gravity and geometric characteristics of the substrate. It is demonstrated that when the film partially wets the sidewalls of the trench, multiple steady states may arise, which are analyzed for their stability characteristics. It is also shown that the second air-liquid interface and the air pockets inside the grooves of a structured hydrophobic surface may considerably stabilize the flow mainly by the capillary forces, which act as a damper, preventing the disturbances of the outer free surface to grow.

The Levitation of a droplet on a hot surface due to the rapid vaporization of the liquid at the proximity of the heat source is known as the Leidenfrost effect. This effect has been demonstrated when the surface is a solid or a liquid. Here, we explore the interaction between a liquid droplet and a hot granular material. The granular material is, by essence, a solid but adopts some behaviors similar to fluids. Surprisingly, we found that the droplet deeply penetrated the hot granular material. During the penetration process, the vapor production is so intense that the grains underneath the droplet are ejected. Consequently, the droplet moved downward under the action of gravity. A mechanism based on the Leidenfrost effect is proposed considering that the granular material can be modeled as a rough surface that can be eroded when the vapor speed is sufficient.

The surface tension of living cells and tissues originates from the generation of nonequilibrium active stresses within the cell cytoskeleton. Here, using laser ablation, we generate gradients in the surface tension of cellular aggregates as models of simple tissues. These gradients of active surface stress drive large-scale and rapid toroidal motion. Subsequently, the motions spontaneously reverse as stresses reaccumulate and cells return to their original positions. Both forward and reverse motions resemble Marangoni flows in viscous fluids. However, the motions are faster than the timescales of viscoelastic relaxation and the surface tension gradient is proportional to mechanical strain at the surface. Further, due to active stress, both the surface tension gradient and surface strain are dependent upon the volume of the aggregate. These results indicate that surface tension can induce rapid and highly correlated elastic deformations in the maintenance of tissue shape and configuration.

The motion of an autophoretic spherical particle in a simple fluid is analyzed. This motion is powered by a chemical species which is absorbed or emitted by the particle and which diffuses and is advected in the surrounding fluid. The transition from the nonmotile to the motile state occurs if the Péclet number Pe (defined as the ratio of the solute emission rate over the solute diffusion rate) is sufficiently large. We first analyze the axisymmetric case (restricting the particle to a unique direction). In this case, we find that the motion of the particle transits from a motionless to a directed motion at a given critical Pe. Increasing Pe, we find a second critical value where the particle becomes stagnant in a symmetric flow. A further increase of Pe leads to a recovery of motile motion. When Pe is increased even further, the particle shows a periodic motion undergoing a subharmonic cascade before entering chaos. In this regime, the mean-square displacement behaves quadratically with time (a ballistic regime). When the axisymmetry constraint is relaxed, allowing the particle to freely move in three-dimensional space, we find that at a small Pe the particle moves in a straight manner. There exists a critical value where the particle exhibits an oscillatory motion with a meandering trajectory. Increasing Pe further leads to chaotic bursts for some time, before entering fully into chaos via the intermittency scenario at a critical Pe number. In this regime, the particle shows run-and-tumble–like dynamics: The trajectory is then characterized by a ballistic swimming nature at a short time and a diffusive nature at a long time.

Ultrasonic atomization is increasingly used in industry; however, the lack of corresponding theoretical studies on the atomization mechanism and performance effects has led to a lack of scientific application. In this study, multiple Faraday waves in ultrasonic atomization were simulated and a comparative study of Faraday instability theory was conducted in conjunction with experiments. For the inviscid case, the parametric curve equations explain the excitation and competition mechanisms of different frequency harmonics. The position of the parameter pair determines whether the perturbation of the Faraday wave is linear or not. The surface perturbation displacements of Faraday waves are plotted from theoretical, experimental, and simulation perspectives, respectively, and the three agree well. Different parameters correspond to different parameter curve positions and maximum perturbation growth rates, which determine the intensity of the Faraday instability and thus cause changes in the atomization characteristics. In the viscous case, the Faraday instability depends on the wave number and viscosity, and the intensity of the instability can be obtained from the instability threshold. All the theoretical predictions in this study are validated by experiments and simulations, which can provide scientific guidance for process optimization of practical ultrasonic atomization production.

We present a deformation-dependent propulsion phenomenon for soft particles such as cells in microchannels. It is based on a broken time-reversal symmetry generated by a fast forward and a slow backward motion of a fluid which does not progress on average. In both sections, soft particles deform differently and thus progress relatively to the liquid. We demonstrate this by using Lattice-Boltzmann simulations of ubiquitous red blood cells in microchannels, as well as simulations for capsules and minimal-soft-tissue models in unbounded Poiseuille flows. The propulsion of the soft particles depends besides the oscillation asymmetry on their size, deformation type, and elasticity. This is also demonstrated by analytical calculations for a minimal model. Our findings may stimulate a rethinking of particle sorting methods. For example, healthy and malignant cells often differ in their elasticity. With the proposed method, several cell types with different deformabilities can be separated simultaneously without labeling or obstacles in a microfluidic device.

Droplet oscillations of low-viscosity liquids spreading over textured surfaces arise from pinning of the three-phase contact line that is, in turn, related to hysteresis in the wetting behavior of real surfaces. A dynamic contact angle model proposed in the present work improves the existing models by including the pinning of contact line motion. Experiments are conducted on four substrates of distinct hydrophobicity. The initial Weber number of the drop is deliberately kept small (<0.34) so that surface characteristics dominantly influence spreading. Specifically, a superhydrophobic surface with small hysteresis is shown to display small oscillations, while a hydrophobic surface with large hysteresis has large persistent oscillations. Numerical simulations are subsequently performed with the proposed dynamic contact angle model and compared with experiments. The model is also validated against experiments reported in the literature at a higher Weber number of 31.67. The model successfully predicts the contact angle evolution on the chosen surfaces, including oscillations. Specific experimental trends such as spreading, retraction, pinning of the contact line and underdamped oscillations of the drop height emerge as part of the numerical solution. With the proposed contact angle model, propagation of surface waves at the gas-liquid interface from and toward the apex is revealed as a factor responsible for the observed behavior of drop spreading.

The role of streamwise length scales (${\lambda }_x$) in turbulent skin friction generation is investigated using a direct numerical simulation data set of an incompressible zero pressure gradient turbulent boundary layer and the spectral analysis based on the Fukagata-Iwamoto-Kasagi (FIK) identity by Fukagata et al. [K. Fukagata et al., Phys. Fluids 14, L73 (2002)]. The total skin friction generation associated with motions scaled with local boundary layer thickness $\delta$ of ${\lambda }_x<3\delta$ and ${\lambda }_x>3\delta$ is assessed. The FIK-identity-based spectral analysis is further extended to include the quadrant analysis of Reynolds shear stress. This allows one to relate the turbulent skin friction generation to the quadrant events of Reynolds shear stress, which plays a central role in the momentum transport in turbulent wall-bounded flows. The small-scale ejection and sweep events (${\lambda }_x<3\delta$) contribute to a significant portion of turbulent skin friction. However, it is found that the large-scale ejection and sweep events with streamwise length scales at ${\lambda }_x>3\delta$ are equally important. The turbulent skin friction reduction associated with the modification of large- and small-scale quadrant events is studied, using well-resolved simulation data sets of a large-eddy break-up (LEBU) device in a turbulent boundary layer. The results reveal that LEBUs modify both the large- and small-scale ejection and sweep events, yielding a substantial turbulent skin friction reduction.

Turbulence in driven stratified active matter is considered. The relevant parameters characterizing the problem are the Reynolds number $\mathrm{Re}=\overline{u}L/\nu$ and an active matter Rayleigh number, $R=\left|\zeta \right|S^{2}L/D\overline{u}$. Here $\overline{u}$ is the mean velocity of flow, $L$ is the system size, $\nu$ is the kinematic viscosity, $\zeta$ is the activity coefficient, $S$ is the concentration gradient, and $D$ is the active matter diffusion coefficient. In the mixing limit, $\mathrm{Re}\gg 1,R\ll 1$, we show that the standard Kolmogorov energy spectrum law, $E\left(k\right)\propto k^{-5/3}$, is realized. On the other hand, in the stratified limit, $\mathrm{Re}\gg 1,R\ll 1$, there is a new turbulence universality class with $E\left(k\right)\propto k^{-7/5}$. The crossover from one regime to the other is discussed in detail. Experimental predictions and probes are also discussed.

Research in the last decades has shown a strong interaction between near-wall turbulence and outer-layer large-scale motions in turbulent wall-bounded flows. In this paper, we propose a spatiotemporal multivariate approach based on state-of-the art methods of signal processing and a significantly enlarged data base to provide insight into the inner-outer interaction via superposition, bursts, and amplitude modulation. Spatially resolved, two-dimensional velocity fields within the viscous sublayer and the log layer are used to study spatial interactions. The temporal information provides insight into the temporal evolution of these features. In contrast to traditional studies, a noise-assisted multivariate empirical mode decomposition is applied to determine the involved scales. In this method, all velocity components of one time instant are simultaneously decomposed, which preserves intercomponent relations in the modal representations. In addition, the noise assistance ensures a temporal coherence of the resulting modes. Intermode comparisons, and thus the inner-outer interaction analysis, significantly benefit from this mode alignment by more precise findings, which is verified by comparisons with the univariate empirical mode decomposition results. The analysis reveals a considerable time-dependent behavior of the interaction phenomena with respect to the inner-outer correlation and the associated inclination angle. Regarding the superposition and the sweeps, the temporal variations are strongly linked to the rates of high-speed large scales to total large-scale fluctuations. The comparison to findings from purely temporal signals demonstrates distinct differences.

Kinetic helicity in most geodynamo simulations has a distinct distribution above and below the equator—it is negative in the north and positive in the south. Using direct numerical simulations of rotating convection, with the rotation axis perpendicular to gravity, we investigate the role of Ekman pumping as a possible mechanism behind this helicity segregation. For a fixed Rayleigh number $\mathrm{Ra}={10}^5$ and Prandtl number $\mathrm{Pr}=1$, we consider two values of Taylor number, $\mathrm{Ta}={10}^5$ and ${10}^6$, and two different boundary conditions, no-slip and fixed stress at the walls normal to the rotation axis. We observe cyclonic flow in the bulk and helical flow driven by Ekman pumping near the boundaries normal to the rotation axis. This leads to helicity being negative (positive) near the wall with outward normal parallel (antiparallel) to the rotation vector. The peak in helicity (averaged in the plane normal to the rotation axis) occurs inside the Ekman layer in all simulations. The helicity magnitude is smaller for the fixed stress boundary condition as compared to no-slip. We also observe that the buoyancy causes the large helicity regions inside the Ekman boundary layer to migrate away from the rotation axis. We also present the helicity budget analysis, with the contribution of Coriolis force, pressure vorticity, buoyancy force, and viscosity in the helicity segregation. We find that both pressure vorticity and Coriolis force contribute significantly to the helicity segregation. Moreover, from modal energy analysis we find that the mode (2, 2), which represents the secondary flows, is important for the helicity segregation.

We derive a model entirely from first principles to explain the Leidenfrost self-propulsion phenomenon in a quantitative way, where the deformable nature of the liquid has been taken into account. Experiments show a good agreement with our model, suggesting this model supersedes the limited scaling analysis previously given in the literature. Our annular ring design enables liquid droplets to reach high terminal velocities, up to $0.42\pm 0.04$ m/s, which is potentially beneficial to energy harvesting and flow chemistry applications.

We experimentally investigated the rising dynamics of oil-coated compound bubbles at various oil fractions in a quiescent water medium. Three-dimensional particle tracking velocimetry was used to characterize the trajectories of the bubbles, and particle image velocimetry was used for complementary flow characterization. Results show that the oil-coated bubbles undergo a zigzagging path with a steady oscillation pattern at comparatively low oil fractions. In contrast, damped oscillations occur at high oil fractions, which do not happen in clean gas bubbles. The oil coating changes the rising dynamics of the bubble mainly by adjusting the bubble surface boundary condition and effective density. A lightly coated bubble experiences a smaller shape deformation, similar drag coefficient, a larger frequency, and smaller amplitude in the path oscillation compared to a clean gas bubble. In addition, the increase of oil fraction results in reduced shape deformation and drag coefficient with a lower frequency and amplitude of the path oscillation. Estimation of the forces using a Frenet reference frame shows that the wake-induced lift and drag decreased with oil fraction, and became negligible for bubbles with damped oscillations. Overall, our work contributes to the fundamental understanding of the rising dynamics of oil-coated bubbles with various oil fractions and viscosities.

We observe the emergence of strong vertical drafts in direct numerical simulations of the Boussinesq equations in a range of parameters of geophysical interest. These structures, which appear intermittently in space and time, generate turbulence and enhance kinetic and potential energy dissipation, providing a possible explanation for the observed variability of the local energy dissipation in the bulk of oceanic flows and the modulation of its probability distribution function. We show how, due to the extreme drafts, in runs with Froude numbers observable in geophysical scenarios, roughly $10\%$ of the domain flow can account for up to $50\%$ of the global volume dissipation, reminiscent of estimates based on oceanic models.

Geological storage of ${\mathrm{CO}}_2$ in deep saline aquifers is a promising measure to mitigate global warming by reducing the concentration of this greenhouse gas in the atmosphere. When ${\mathrm{CO}}_2$ is injected in the geological formation, it dissolves partially in the interstitial brine, thus rendering it denser than the ${\mathrm{CO}}_2$-devoid brine below, which creates a convective instability. The resulting convection accelerates the rate of the perennial trapping of ${\mathrm{CO}}_2$ by dissolution in the brine. The instability and resulting convection have been intensively discussed with numerical and theoretical approaches at the Darcy scale, but few experimental studies have characterized them quantitatively. By using both refractive index matching and planar-laser-induced fluorescence, we measure the onset characteristics of the convective dissolution instability in a three-dimensional porous medium located below a gas compartment. Our results highlight that the dimensional growth rate of the instability remains constant when the ${\mathrm{CO}}_2$ partial pressure in the compartment is varied, in clear discrepancy with the theoretical predictions. Furthermore, within the ${\mathrm{CO}}_2$ partial pressure range studied, the measured growth rate is one to three orders of magnitude larger than the predicted value. The Fourier spectrum of the front is very broad, highlighting the multiscale nature of the flow. Depending on the measurement method and ${\mathrm{CO}}_2$ partial pressure, the mean wavelength is one to three times smaller than the predicted value. Using a theoretical model developed recently by Tilton [J. Fluid Mech. 838, 129 (2018)], we demonstrate that these experimental results are consistent with a forcing of convection by porosity fluctuations. Finally, we discuss the possible effects of this forcing by the porous medium's pore structure on the ${\mathrm{CO}}_2$ flux across the interface, measured in these experiments about one order of magnitude higher than expected. These results obtained in model laboratory experiments show that accounting for sub-Darcy-scale flow heterogeneities may be necessary to correctly predict convective dissolution during ${\mathrm{CO}}_2$ subsurface sequestration.