Most superhydrophobic surfaces undergo a wetting transition from the Cassie to the Wenzel state, either spontaneously or under the action of external perturbations. The reverse dewetting transition is hampered by a large energy barrier and in order to achieve it, external fields are usually applied. Here we perform experiments, theoretical analysis, and lattice Boltzmann simulations of droplet condensation on a patterned superhydrophobic surface and demonstrate that the dewetting energy barrier can be reduced by manipulating the adhesion forces. Moreover, the kinetics of dewetting is a result of a subtle interplay of wetting and adhesion and in certain geometries, such as cone-shaped texture, the dewetting transition from Wenzel to Cassie state becomes spontaneous.

Consider the dynamics of a thin film flowing down a heated substrate. The substrate heating generates a temperature distribution on the free surface, which in turn induces surface-tension gradients and corresponding thermocapillary stresses that affect the free surface and therefore the fluid flow. We study here the effect of finite substrate thermal diffusivity on the film dynamics. Linear stability analysis of the full Navier-Stokes and heat transport equations indicates if the substrate diffusivity is sufficiently small, the film becomes unstable at a finite wavelength and at a Reynolds number smaller than that predicted in the long-wavelength limit. This property is captured in a reduced-order system of equations derived using a weighted-residual integral-boundary-layer method. This reduced-order model is also used to compute the bifurcation diagrams of solution branches connecting the trivial flat film to traveling waves including solitary pulses. The effect of finite diffusivity is to separate a simultaneous Hopf-transcritical bifurcation into its individual component bifurcations. The appropriate Hopf bifurcation then connects only to the solution branch of negative-hump pulses, with wave speed less than the linear wave speed, while the branch of positive-single-hump pulses merges with the branch of positive-two-hump pulses at a supercritical Reynolds number. In the regime where finite-wavelength instability occurs, there exists a Hopf-bifurcation pair connected by a branch of periodic solutions, whose period cannot be increased indefinitely. Numerical simulation of the reduced-order system shows the development of a train of coherent structures, each of which resembles a stationary positive-hump pulse, and, in the regime of finite-wavelength instability, wavelength selection and saturation to periodic traveling waves.

We develop a continuous time random walk (CTRW) approach for the evolution of Lagrangian velocities in steady heterogeneous flows based on a stochastic relaxation process for the streamwise particle velocities. This approach describes the persistence of velocities over a characteristic spatial scale, unlike classical random walk methods, which model the persistence over a characteristic time scale. We first establish the relation between Eulerian and Lagrangian velocities for both equidistant and isochrone sampling along streamlines, under transient and stationary conditions. Based on this, we develop a space-continuous CTRW approach for the spatial and temporal dynamics of Lagrangian velocities. While classical CTRW formulations have nonstationary Lagrangian velocity statistics, the proposed approach quantifies the evolution of the Lagrangian velocity statistics under both stationary and nonstationary conditions. We provide explicit expressions for the Lagrangian velocity statistics and determine the behaviors of the mean particle velocity, velocity covariance, and particle dispersion. We find strong Lagrangian correlation and anomalous dispersion for velocity distributions that are tailed toward low velocities as well as marked differences depending on the initial conditions. The developed CTRW approach predicts the Lagrangian particle dynamics from an arbitrary initial condition based on the Eulerian velocity distribution and a characteristic correlation scale.

A combined numerical and experimental investigation of airfoil leading edge flow separation control with a nanosecond dielectric barrier discharge (DBD) plasma actuator is presented. Our study concentrates on describing dynamics of detailed flow actuation process and elucidating the nanosecond DBD actuation mechanism. A loose coupling methodology is employed to perform simulation, which consists of a self-similar plasma model for the description of pulsed discharge and two-dimensional Reynolds averaged Navier-Stokes (RANS) equations for the calculation of external airflow. A series of simulations of poststall flows around a NACA0015 airfoil is conducted with a Reynolds number range covering both low and high Re at $\text{Re}=(0.05,0.15,1.2)\times {10}^6$. Meanwhile, wind-tunnel experiment is performed for two low Re flows to measure aerodynamic force on airfoil model and transient flow field with time-resolved particle image velocimetry (PIV). The PIV measurement provides possibly the clearest view of flow reattachment process under the actuation of a nanosecond plasma actuator ever observed in experiments, which is highly comparable to that predicted by simulation. It is found from the detailed simulation that the discharge-induced residual heat rather than shock wave plays a dominant role in flow control. For any leading edge separations, the preliminary flow reattachment is realized by residual heat-induced spanwise vortices. After that, the nanosecond actuator functions by continuing exciting flow instability at poststall attack angles or acting as an active trip near stall angle. As a result, the controlled flow is characterized by a train of repetitive, downstream moving vortices over suction surface or an attached turbulent boundary layer, which depends on both angle of attack and Reynolds number. The advection of residual temperature with external flow offers a nanosecond plasma actuator a lot of flexibility to extend its influence region. Animations are provided for baseline flow and that subjected to plasma control at two typical Reynolds numbers.

In an effort to understand the locomotion dynamics of a simple vertebrate, the lamprey, both physical and computational models have been developed. A key feature of these models is the ability to vary the passive stiffness of portions of the swimmer, focusing on highly flexible models similar in material properties to lampreys and other anguilliform fishes. The physical model is a robotic lampreylike swimmer that is actuated along most of its length but has passively flexible tails of different stiffnesses. The computational model is a two-dimensional model that captures fluid-structure interactions using an immersed boundary framework. This simulated lamprey is passively flexible throughout its length and is also actuated along most of its length by the activation of muscle forces. Although the three-dimensional robot and the two-dimensional computational swimmer are such different constructs, we demonstrate that the wake structures generated by these models share many features and we examine how flexibility affects these features. Both models produce wakes with two or more same-sign vortices shed each time the tail changes direction (a “2P” or higher-order wake). In general, wakes become less coherent as tail flexibility increases. We examine the pressure distribution near the tail tip and the timing of vortex formation in both cases and find good agreement. Because we include flexibility, we are able to estimate resonant frequencies for several of the robotic and computational swimmers. We find that actuation at the resonant frequency dramatically increases the distance traveled per tail-beat cycle with only a small increase in the lost kinetic energy in the wake, suggesting that the resonant swimmers are more efficient.

We formulate and study computationally the low Mach number fluctuating hydrodynamic equations for electrolyte solutions. We are interested in studying transport in mixtures of charged species at the mesoscale, down to scales below the Debye length, where thermal fluctuations have a significant impact on the dynamics. Continuing our previous work on fluctuating hydrodynamics of multicomponent mixtures of incompressible isothermal miscible liquids [A. Donev et al., Phys. Fluids 27, 037103 (2015)], we now include the effect of charged species using a quasielectrostatic approximation. Localized charges create an electric field, which in turn provides additional forcing in the mass and momentum equations. Our low Mach number formulation eliminates sound waves from the fully compressible formulation and leads to a more computationally efficient quasi-incompressible formulation. We demonstrate our ability to model saltwater (NaCl) solutions in both equilibrium and nonequilibrium settings. We show that our algorithm is second order in the deterministic setting and for length scales much greater than the Debye length gives results consistent with an electroneutral approximation. In the stochastic setting, our model captures the predicted dynamics of equilibrium and nonequilibrium fluctuations. We also identify and model an instability that appears when diffusive mixing occurs in the presence of an applied electric field.

Laboratory experiments are performed to examine the sedimentation of particles that initially rise in a plume, then spread radially and settle in uniformly stratified fluid. Using light attenuation, the depth of the sediment bed is measured nonintrusively as a function of radius from the center of the plume. To gain some insight into these dynamics, an idealized model is developed by adapting well-established plume theory and a theory that accounts for sedimentation from surface gravity currents emanating from a plume impacting a rigid lid. We also account for recycling of falling particles that are re-entrained into the plume. With a suitable choice of parameters determining the intrusion height, entrainment during fountain collapse, and the radius at which settling from the intrusion begins, in most cases for which particles are predicted to be drawn back into the plume and recycled. The predictions for intrusion height, particle mound height, and spread agree within 20% of observations.

Liquid-infused surfaces display great advantages such as omniphobicity, anti-icing, antifouling, and self-cleaning. They can also reduce the drag of an object moving through an immiscible fluid since there is slip along the fluid-fluid interface. However, the trapped liquids are susceptible to the shear of the external flow, which will drain the lubricants from the surfaces and hinder their practical use. In this study, we investigate the shear-driven failure of liquid-infused surfaces under a broad range of ratios of the viscosity of the external fluid to that of the lubricant. The effect of viscosity ratio on the steady-state lubricant retention is characterized experimentally and analyzed analytically. The model offers a possible way to estimate the shear-driven failure of surfaces filled with different lubricants. In particular, it is shown that for a given external flow a lower lubricant viscosity results in more infused fluid being retained.

Molecular dynamics simulations are used to investigate the effective slip boundary condition for a simple fluid flowing over surfaces with one-dimensional sinusoidal roughness in the Wenzel state. The effective slip length is calculated as a function of the corrugation amplitude for flows along two principal orientations: transverse and longitudinal to the corrugation. Different atomic configurations, bent and stepped, are examined for strong and weak wall-fluid interactions and high and low wall densities. Molecular dynamics results for sparse bent surfaces quantitatively agree with continuum hydrodynamic predictions with a constant local slip length. Increasing the roughness amplitude reduces the effective slip length and the reduction is larger for transverse flow than longitudinal flow. Atomic effects become important for dense surfaces, because the local slip length varies with the local curvature and atomic spacing along the wall. These effects can be captured by applying a spatially varying boundary condition to the Navier-Stokes equations. Results for stepped surfaces are qualitatively different than continuum predictions, with the effect of corrugation rising linearly with corrugation amplitude rather than quadratically. There is an increased drag for transverse flow that is proportional to the density of step edges and lowers the slip length. Edges tend to increase the slip length for longitudinal flow because of order induced along the edges.

Transient growth of optimal disturbances with a turbulent mean velocity profile in a channel is investigated for Reynolds numbers, based on the wall-shear velocity and channel half height, of ${\mathrm{Re}}_{\tau }=180\sim 10000$. We consider optimal disturbances within near-wall regions ($0<y^{+}\le y_c^{+}$) by suppressing disturbances at $y^{+}>y_c^{+}$. The most amplified disturbances are streamwise velocity streaks induced by streamwise rolls. The wavelength and the growth time of these constrained optimal disturbances normalized in viscous wall units are nearly independent of ${\mathrm{Re}}_{\tau }$ but depend on the cutoff location $y_c^{+}$. The optimal disturbance corresponding to the cutoff location $y_c^{+}=40$, which is roughly the edge of the buffer layer, shows very similar characteristics to those of near-wall turbulence structures observed in turbulent channel flows, thus suggesting that the commonly observed turbulence structures are indeed the optimal disturbance within the buffer layer. The choice of this particular cutoff location, $y_c^{+}=40$, is justified from consideration of the shear rate parameter, $S^{*}=S{q}^2/\epsilon$, which is a measure of whether nonlinearity of turbulence can be neglected.

We study the origins of anomalous dispersion in heterogeneous porous media in terms of the medium and flow properties. To identify and quantify the heterogeneity controls, we focus on porous media which are organized in assemblies of equally sized conductive inclusions embedded in a constant conductivity matrix. We study the behavior of particle arrival times for different conductivity distributions and link the statistical medium characteristics to large-scale transport using a continuous time random walk (CTRW) approach. The CTRW models particle motion as a sequence of transitions in space and time. We derive an explicit map of the conductivity onto the transition time distribution. The derived CTRW model predicts solute transport based on the conductivity distribution and the characteristic heterogeneity length. In this way, heavy tails in solute arrival times and anomalous particle dispersion as measured by the centered mean square displacement are directly related to the medium properties. These findings shed light on the mechanisms of anomalous dispersion in heterogeneous porous media, and provide a basis for the predictive modeling of large-scale transport.

Classic models of fish schools and flying formations of birds are built on the hypothesis that the preferred locations of an individual are determined by the flow left by its upstream neighbor. Lighthill posited that arrangements may in fact emerge passively from hydro- or aerodynamic interactions, drawing an analogy to the formation of crystals by intermolecular forces. Here, we carry out physical experiments aimed at testing the Lighthill conjecture and find that self-propelled flapping wings spontaneously assume one of multiple arrangements due to flow interactions. Wings in a tandem pair select the same forward speed, which tends to be faster than a single wing, while maintaining a separation distance that is an integer multiple of the wavelength traced out by each body. When perturbed, these locomotors robustly return to the same arrangement, and direct hydrodynamic force measurements reveal springlike restoring forces that maintain group cohesion. We also use these data to construct an interaction potential, showing how the observed positions of the follower correspond to stable wells in an energy landscape. Flow visualization and vortex-based theoretical models reveal coherent interactions in which the follower surfs on the periodic wake left by the leader. These results indicate that, for the high-Reynolds-number flows characteristic of schools and flocks, collective locomotion at enhanced speed and in orderly formations can emerge from flow interactions alone. If true for larger groups, then the view of collectives as ordered states of matter may prove to be a useful analogy.

Understanding the recovery of gas from reservoirs featuring pervasive nanopores is essential for effective shale gas extraction. Classical theories cannot accurately predict such gas recovery and many experimental observations are not well understood. Here we report molecular simulations of the recovery of gas from single nanopores, explicitly taking into account molecular gas-wall interactions. We show that, in very narrow pores, the strong gas-wall interactions are essential in determining the gas recovery behavior both quantitatively and qualitatively. These interactions cause the total diffusion coefficients of the gas molecules in nanopores to be smaller than those predicted by kinetic theories, hence slowing down the rate of gas recovery. These interactions also lead to significant adsorption of gas molecules on the pore walls. Because of the desorption of these gas molecules during gas recovery, the gas recovery from the nanopore does not exhibit the usual diffusive scaling law (i.e., the accumulative recovery scales as $R\sim t^{1/2}$) but follows a superdiffusive scaling law $R\sim t^n$ ($n>0.5$), which is similar to that observed in some field experiments. For the system studied here, the superdiffusive gas recovery scaling law can be captured well by continuum models in which the gas adsorption and desorption from pore walls are taken into account using the Langmuir model.

A largely unexplored type of hydrodynamic instability is examined: long-time algebraic growth. Such growth is possible when the dispersion relation extracted from classical stability analysis indicates neutral stability. A physically motivated class of partial differential equations that describes the response of a system to disturbances is examined. Specifically, the propagation characteristics of the response are examined in the context of spatiotemporal stability theory. Morphological differences are identified between system responses that exhibit algebraic growth and the more typical case of exponential growth. One key attribute of predicted algebraically growing solutions is the prevalence of transient growth in almost all of the response, with the long-time growth occurring asymptotically at precisely one wave speed.

The settling of heavy spherical particles in a column of quiescent fluid is investigated. The performed experiments cover a range of Galileo numbers $\left(110\le \text{Ga}\le 310\right)$ for a fixed density ratio of $\mathrm{\Gamma }={\rho }_p/{\rho }_f=2.5$. In this regime the particles are known to show a variety of motions [Jenny, Dušek, and Bouchet, Instabilities and transition of a sphere falling or ascending freely in a Newtonian fluid, J. Fluid Mech. 508, 201 (2004)]. It is known that the wake undergoes several transitions for increasing $\text{Ga}$ resulting in particle motions that are successively vertical, oblique, oblique oscillating, and finally chaotic. Not only does this change the trajectory of single, isolated, settling particles, but it also changes the dynamics of a swarm of particles as collective effects become important even for dilute suspensions with volume fraction up to ${\mathrm{\Phi }}_V=O\left({10}^{-3}\right)$, which are investigated in this work. Multicamera recordings of settling particles are recorded and tracked over time in three dimensions. A variety of analyses are performed and show a strong clustering behavior. The distribution of the cell areas of the Voronoï tessellation in the horizontal plane is compared to that of a random distribution of particles and shows clear clustering. Moreover, a negative correlation was found between the Voronoï area and the particle velocity; clustered particles fall faster. In addition, the angle between adjacent particles and the vertical is calculated and compared to a homogeneous distribution of particles, clear evidence of vertical alignment of particles is found. The experimental findings are compared to simulations.

An isolated wind turbine and a very large wind farm are introduced into large-eddy simulations of an atmospheric boundary layer. The atmospheric flow is forced with a constant geostrophic wind and a time-varying surface temperature extracted from a selected period of the CASES-99 field experiment. A control volume approach is used to directly compare the transfer of mean kinetic energy around a characteristic wind turbine throughout a diurnal cycle considering both scenarios. For the very large wind farm case, results illustrate that the recovery of mean kinetic energy around a wind turbine is dominated by the vertical flux, regardless of atmospheric stratification. Contrarily, for an isolated wind turbine, the recovery is dependent on the background atmospheric stratification and it is produced by a combination of advection, vertical flux, and pressure redistribution. The analysis also illustrates that during the unstable stratification periods vertical entrainment of mean kinetic energy dominates, whereas during the stable regime horizontal entrainment is predominant. Finally, it is observed that in both scenarios, the single wind turbine and the large wind farm cases, turbulent mixing is driven by the background convective stratification during the unstable period and by the effect of the wind turbine during the stable regime.

The near wake of wind turbines is characterized by the presence of the hub vortex, which is a coherent vorticity structure generated from the interaction between the root vortices and the boundary layer evolving over the turbine nacelle. By moving downstream, the hub vortex undergoes an instability with growth rate, azimuthal and axial wavenumbers determined by the characteristics of the incoming wind and turbine aerodynamics. Thus, a large variability of the hub vortex instability is expected for wind energy applications with consequent effects on wake downstream evolution, wake interactions within a wind farm, power production, and fatigue loads on turbines invested by wakes generated upstream. In order to predict characteristics of the hub vortex instability for different operating conditions, linear stability analysis is carried out by considering different statistics of the incoming wind turbulence, thrust coefficient, tip speed ratio, and blade lift distribution of a wind turbine. Axial and azimuthal wake velocity fields are modeled through Carton-McWilliams velocity profiles by mimicking the presence of the hub vortex, helicoidal tip vortices, and matching the wind turbine thrust coefficient predicted through the actuator disk model. The linear stability analysis shows that hub vortex instability is strongly affected by the wind turbine loading conditions, and specifically it is promoted by a larger thrust coefficient. A higher load of the wind turbines produces an enhanced axial velocity deficit and, in turn, higher shear in the radial direction of the streamwise velocity. The axial velocity shear within the turbine wake is also the main physical mechanism promoting the hub vortex instability when varying the lift distribution over the blade span for a specific loading condition. Cases with a larger velocity deficit in proximity of the wake center and less aerodynamic load towards the blade tip result to be more unstable. Moreover, wake swirl promotes hub vortex instability, and it can also affect the azimuthal wave number of the most unstable mode. Finally, higher Reynolds stresses and turbulent eddy viscosity decrease both growth rate and azimuthal wave number of the most unstable mode.

We analyze the effect of the Basset history force on the sedimentation of nearly neutrally buoyant particles, exemplified by marine snow, in a three-dimensional turbulent flow. Particles are characterized by Stokes numbers much smaller than unity, and still water settling velocities, measured in units of the Kolmogorov velocity, of order one. The presence of the history force in the Maxey-Riley equation leads to individual trajectories which differ strongly from the dynamics of both inertial particles without this force and ideal settling tracers. The main effect of the history force is an extraordinary slow, power-law type convergence to an asymptotic settling velocity of the center of mass, which is found numerically to be the settling velocity in still fluid. The spatial extension of the ensemble grows diffusively after an initial ballistic growth lasting up to circa one large eddy turnover time. We demonstrate that the settling of the center of mass for such light aggregates is best approximated by the settling dynamics in still fluid found with the history force, on top of which fluctuations appear which follow very closely those of the turbulent velocity field.

Observations are presented to show that in an adverse pressure gradient boundary layer, beneath free-stream turbulence, the interaction between Klebanoff streaks and naturally arising instability waves leads to helical disturbances which break down to form turbulent spots. This occurs under low to moderate levels, 1%–2%, of free-stream turbulence. At high levels of free-stream turbulence, conventional bypass mechanisms are seen. The helical structures are clearly identifiable in visualizations of isosurfaces of streamwise perturbation velocity. A direct numerical simulation also was performed in zero pressure gradient, with a time-periodic Tollmien-Schlichting wave eigenfunction at the inlet. Again, under a moderate level of free-stream turbulence, helices were observed, and found to trigger transition. Their wave speed is on the order of $\frac{1}{2}{U}_{\infty }$, so helical breakdown can be viewed as a type of inner mode, secondary instability.