When transported in confined geometries rigid fibers show interesting transport dynamics induced by friction with the top and bottom walls. Fiber flexibility causes an additional coupling between fiber deformation and transport and is expected to lead to more complex dynamics. A first crucial step for their understanding is the characterization of the deformed fiber shape. Here we characterize this shape for a fiber transported in a confined plug flow perpendicular to the flow direction using a combination of microfluidic experiments and numerical simulations. In the experiments, size, initial orientation, and mechanical properties of the fibers are controlled using microfabrication techniques and in situ characterization methods. The numerical simulations use modified Brinkman equations as well as full three-dimensional simulations. We show that the bending of a perpendicular fiber results from the force distribution acting on the elongated object and is proportional to the elasto-viscous number, which compares viscous to elastic forces. We quantitatively characterize the influence of the confinement on the fiber deformation. The precise understanding of the deformation of a flexible fiber in a confined geometry can also be used in future to understand the deformation and transport of more complex deformable particles in confined flows, such as vesicles or red blood cells.

Experiments were conducted with three-dimensional printed disks and rods to study the orientation dynamics of nonspherical particles under surface gravity waves. Trials were run with both neutrally buoyant and slightly negatively buoyant particles, which were large enough that inertia due to their finite size was important. Although the particles had a broad distribution of initial orientations, over time the waves were observed to focus these orientations toward a preferred angle that agreed with theory. Negatively buoyant particles additionally exhibited a tendency to adopt an orientation that maximized vertical drag. The overall orientation can be described as the result of a competition between the orientation favored by waves and the orientation favored by settling. The spread about the mean orientation was also observed to increase with wave strength. Finally, the stabilization of out-of-plane orientations of disk-shaped particles was observed due to their finite size.

We present an experimental analysis of the linear and nonlinear regimes of an attractor of inertial waves in a trapezoidal cavity under rotation. Varying the rotation rate and the forcing amplitude and wavelength, we identify the scaling laws followed by the attractor amplitude and wavelength in both regimes. In particular, we show that the nonlinear scaling laws can be well described by replacing the fluid viscosity in the linear model by a turbulent viscosity, a result that could help in extrapolating attractor theory to geophysically and astrophysically relevant situations. We further study the triadic resonance instability of the attractor which is at the origin of the turbulent viscosity. We show that the typical frequencies of the subharmonic waves produced by the instability behave very differently from previously reported numerical results and from the prediction of the theory of triadic resonance. This behavior might be related to the deviation from the horizontal invariance of the attractor in our experiment in relation to the presence of vertical walls of the cavity, an effect that should be at play in all practical situations.

To date, axisymmetric internal wave fields, which have relevance to atmospheric internal wave fields generated by storm cells and oceanic near-inertial wave fields produced by surface perturbations, have been experimentally realized using an oscillating sphere or torus as the source. Here we use a wave generator configuration capable of exciting axisymmetric internal wave fields of arbitrary radial form to generate axisymmetric internal wave modes. After establishing the theoretical background for axisymmetric mode propagation, taking into account lateral and vertical confinement, and also accounting for the effects of weak viscosity, we study modes of different order. We characterize the efficiency of the wave generator through careful measurement of the wave amplitude based upon group velocity arguments, and then consider the effect of vertical confinement to induce resonance, identifying a series of experimental resonant peaks that agree well with theoretical predictions. In the vicinity of resonance, the wave fields undergo a transition to nonlinear behavior that is initiated on the central axis of the domain and proceeds to erode the wave field throughout the domain.

The effects of trailing edge shape on the vortex dynamics and surface pressure distributions on pitching foils are examined using direct numerical simulation. Results are presented for a Reynolds number of $1\times {10}^4$ and a Strouhal number of 0.5, which corresponds to the Strouhal number for maximum efficiency as found by experiment [Van Buren et al., Phys. Rev. Fluids 2, 014702 (2017)]. For the trailing edge shapes studied here (square, convex, and concave), the maximum instantaneous thrust occurs at the moment when the vortex detaches from the trailing edge. At the same time, the surface pressure gradients across the panel surfaces increase, while viscous forces drop. The leading edge vortices are seen to merge with the side edge shear layers, and as they wrap around the trailing edge the thrust generation is depressed just prior to the instance of maximum thrust. This process, combined with momentum transfer associated with switching the direction of pitching, produces irregular variations in the thrust and side forces. Compared to the square panel, the wake of a concave trailing edge panel exhibits strong three-dimensional effects on its side edges leading to slower wake contraction, smoother vortex bending, and lower thrust. In contrast, the convex trailing edge panel allows detaching structures to grow longer prior to their detachment, resulting in bent structures formed closer to the trailing edge, which leads to faster wake contraction and higher thrust. Skeleton models of the wakes help explain their underlying structure.

Supercritical fluids (SCFs) are known to exhibit anomalous behavior in their thermophysical properties such as diverging compressibility and vanishing thermal diffusivity on approaching the critical point. This behavior leads to a strong thermomechanical coupling when SCFs are subjected to simultaneous thermal perturbation and mechanical vibration. The behavior of the thermal boundary layer leads to various interesting dynamics such as thermovibrational instabilities, which become particularly ostensive in the absence of gravity. In the present paper, two types of instabilities, Rayleigh-vibrational and parametric instabilities, have been numerically investigated under zero gravity in a two-dimensional configuration using a mathematical model wherein density is calculated directly from the continuity equation. A comparison of experimental observations with numerical simulations is also presented. The peculiarity of the model warrants the investigation of instabilities in a more stringent manner (in terms of higher quench percentage and closer proximity to the critical point), unlike the previous studies wherein the equation of state was linearized around the considered state for the calculation of density, resulting in a less precise analysis. In addition to providing an explanation of the physical causes of these instabilities, we analyze the effect of various parameters on the critical amplitude for the onset of these instabilities. Furthermore, various attributes such as wavelength of the instabilities, their behavior under various factors (quench percentage and acceleration), and the effect of cell size on the critical amplitude are also investigated. Finally, a three-dimensional stability plot is shown describing the type of instability (Rayleigh-vibrational or parametric or both) to be expected for the operating condition in terms of amplitude, frequency, and quench percentage for a given proximity to the critical point.

Motivated by the need to understand how external fields influence the stability of dynamic contact lines, the linear stability of gravity-driven spreading of a thin liquid film in the presence of electric and temperature fields is studied. The film is confined from below by a flat substrate and from above by an air gap and another flat substrate. An electrostatic potential difference or temperature difference can be applied between the two substrates and the liquid is taken to be a perfect dielectric whose surface tension decreases linearly with temperature. Traveling-wave solutions are found for the film profile, and both electric and temperature fields influence the height of the capillary ridge of liquid that forms near the advancing contact line. The linear stability analysis shows that electric fields destabilize the film front to transverse perturbations and that temperature fields can either stabilize or destabilize the front, depending on the direction of the temperature gradient. An energy analysis reveals that the electric field in the capillary ridge is most responsible for the enhancement of the perturbation growth. For the case of temperature fields, the perturbed temperature gradients are the dominant mechanism through which the perturbation in film height is affected.

The different flow regimes occurring for increasing Reynolds numbers (Re) in an arrow-shaped micro-mixer operated for liquid mixing are investigated by the synergic use of experimental flow visualizations and direct numerical simulations. The tilting angle of the arrow-mixer inlet channels with respect to those of the T-shaped mixer is $\alpha ={20}^{\circ }$. Consistent with previous studies in the literature, it is found that the onset of the engulfment regime, and consequently the sharp increase of the degree of mixing between the two flow streams, occurs at a lower Reynolds number than for a T-mixer operating in the same conditions. However, in contrast to what is observed for T-mixers, the degree of mixing does not increase monotonically with Re. In fact, at approximately $\text{Re}=150$, based on the inlet bulk velocity and the hydraulic diameter of the mixing channel, there is a drop of the mixing degree. This is due to a change in the topology of the vorticity field and, in particular, to the presence of a unique vortical structure in the mixing channel instead of two corotating ones typical of the engulfment regime. By further increasing the Reynolds number, the vortical structure in the mixing channel grows in size and eventually starts to oscillate, leading again to an increase of the degree of mixing, starting from $\text{Re}\simeq 170$. Additional simulations have been carried out in order to investigate the sensitivity to the tilting angle of the inlet channels, namely for $\alpha ={10}^{\circ },{15}^{\circ },{25}^{\circ }$. As expected, it is found that the value of Re at which the engulfment regime occurs decreases with increasing $\alpha$. Then, for $\alpha ={10}^{\circ }$ and ${15}^{\circ }$, the degree of mixing monotonically increases with the Reynolds numbers and the flow topology in the whole engulfment regime is practically the same as for T-mixers. Conversely, the configuration with $\alpha ={25}^{\circ }$ shows a behavior of mixing and of flow features with increasing Reynolds number very similar to those observed for $\alpha ={20}^{\circ }$.

Transverse velocity gradients can enhance the effective diffusion coefficient of a scalar in the primary flow direction, a phenomenon known colloquially as Taylor dispersion. In this work, we perform Taylor dispersion analysis on a canonical pressure-driven flow in a channel with a cross flow, using both perturbation theory and Brownian dynamics simulations. Moreover, we illustrate how mass transfer at the wall affects the evolution of the scalar. By writing a one-dimensional advection-diffusion-mass-transfer equation for the cross-sectionally averaged concentration, we elucidate how the effective diffusion coefficients, effective advective velocities, and effective mass-transfer rates depend on the strength of the cross flow and the wall transfer coefficient. We perform an asymptotic analysis to investigate the limit of strong cross flow and demonstrate that, in this limit, dispersion rapidly decreases with increasing cross-flow velocity $V$ as $V^{-4}$ and scales with the Brownian diffusivity $D$ as $D^3$. Additionally, we discuss the effect of the Schmidt number, the ratio of momentum to mass diffusion, which effectively controls the extent to which the cross flow affects the axial velocity profile. Finally, we describe how our results can be extended to include transverse velocities and diffusivities that are spatially nonuniform.

We study the contributions of acoustical and gravitational stresses to the dynamic and static wetting states of liquid atop a vertical substrate, which is in contact with a liquid reservoir, as a model for the acoustic-enhanced coating process. The propagation of MHz-frequency surface acoustic waves (SAWs) on the substrate and into a liquid reservoir gives rise to the continuous climb of a thin film of oil or to the finite climb of a water meniscus. Theory indicates that the local thickness of the climbing oil film balances the gravitational stress by supporting resonance-enhanced radiation pressure. Indeed, the measured rate of oil climb over the substrate appears to be independent of gravity and insensitive to the height of the liquid film above the reservoir. It is solely determined by a balance between acoustical and viscous stresses in the liquid. However, the partially wetting water meniscus is curved and does not support acoustical resonance and corresponding high values of radiation pressure. The meniscus climbs over the solid substrate to a finite height, which is determined from an interplay between acoustical, capillary, and gravitational stresses.

The present study numerically investigates the bubble-bursting phenomenon at the free surface under the influence of symmetric and asymmetric patterns of neighboring bubbles. To conduct the simulation, a static pierced bubble at the interface of liquid and gas has been used and neighboring unpierced bubbles are added, if necessary. In the presence of symmetric neighbors, fluidic stages of the bursting process are established as cavity collapse, jet formation, and consequential fragmentation of the jet into drops. A thorough comparison of bubble bursting with symmetric neighbors (BBSN) and similar bursting of a solitary bubble (BSB) has been shown. Bubble bursting under the influence of an asymmetric pattern is compared with BBSN. Bubble with absent neighbors (BWAN) placement turns into the formation of the bent jet which is lying in the plane of the angular bisector of the absent neighbors. Bending of the jet nullifies as time progresses and turns into a vertical one like the jet dynamics observed in BBSN. A simple pictorial understanding has been presented to describe the reason behind the jet bend in BWAN based on a study of velocity vectors and the gap between the collapsing waves. The effect of a number of absent neighbors is also addressed extensively. As the number of absent neighbors increases, eventually, the jet inclination angle first increases and then decreases to match with the observation of BBSN and BSB. Finally, physical insight behind the rich fluidic phenomenon of the bubble bursting under the influence of different surface tensions and bubble sizes in the same cluster is also addressed.

We show experimentally, and explain theoretically, what velocity is needed to break an elongated droplet entering a microfluidic T-junction. Our experiments on short droplets confirm previous experimental and theoretical work that shows that the critical velocity for breakup scales with the inverse of the length of the droplet raised to the fifth power. For long elongated droplets that have a length about thrice the channel width, we reveal a drastically different scaling. Taking into account that a long droplet remains squeezed between the channel walls when it enters a T-junction, such that the gutters in the corners of the channel are the main route for the continuous phase to flow around the droplet, we developed a model that explains that the critical velocity for breakup is inversely proportional to the droplet length. This model for the transition between breaking and nonbreaking droplets is in excellent agreement with our experiments.

Steady viscous compressible gas flow through a microconduit is studied using the classical formulation of compressible Navier-Stokes equations with the no-slip condition. The mathematical theory of Klainerman and Majda for low Mach number flow is employed to derive asymptotic equations in the limit of small Mach number. The leading-order equations give rise to the Hagen-Poiseuille solution, and the equations at a higher order lead to a diffusive velocity field induced by self-diffusion of the gas. An explicit solution for the diffusive field is obtained under the no-slip condition and the overall flow exhibits a sliplike mass flow rate even though the velocity satisfies the no-slip condition. The results indicate that the classical formulation includes the self-diffusion effect and it embeds the extended Navier-Stokes equation (ENSE) theory without the need of introducing an additional constitutive hypothesis or assuming slip on the boundary. The predicted pressure profile agrees well with experiments. Contrary to reports in many ENSE publications, an extensive comparison with 35 experiments shows that in the slip-flow regime the predicted mass flow rate is still significantly below the measured mass flow rate, as the self-diffusion effect is too small to account for the observed mass flow-rate enhancement in this flow regime.

An experimental study of the wake of a model horizontal axis wind turbine with a three-bladed rotor and a turbine with a stationary disk is done within a wind turbine array in order to compare the structure of these wakes. Measurements of the flow field surrounding the center turbine in the fourth row of a $4\times 3$ array are made with stereo particle image velocimetry. Rotational effects of the blade are evident in the cross-stream mean velocity component in the rotor case and are absent in the disk case. The second and third invariants of the Reynolds stress anisotropy tensor have larger ranges in the wake of the rotor case than in the disk case, with the disk case displaying higher levels of anisotropy trailing the top tip, a key location relating to kinetic energy entrainment. Application of the proper orthogonal decomposition indicates a greater emphasis on intermediate scales in the near wake of the rotor case in comparison to the disk case, with such differences being mitigated in the far wake. The eigenfunction of the lowest rank mode, which contains the highest turbulence kinetic energy, displays coherence in both the near and far wakes in the rotor case while the disk wake lacks such apparent organization. Based on the discrepancies in the structure and scales of the wake of the rotor versus that of the disk, careful judgment is advised in order to apply stationary disk parametrizations in modeling applications.

We consider the large-scale structure of freely decaying incompressible homogeneous anisotropic helical turbulence, whose energy spectrum $E\left(k\right)$ is given by $E\left(k\right)=C{k}^2+o\left(k^2\right)$ at $k\to 0$. Here $k=\left|\mathit{k}\right|,\mathit{k}$ is the wave vector, and $C$ is a dynamical invariant. The helicity spectrum $H\left(k\right)$ is given by $H\left(k\right)=C_h{k}^3+o\left(k^3\right)$ at $k\to 0$, where $C_h$ is in general nonzero in helical turbulence. By generalizing Saffman's argument for nonhelical turbulence [Saffman, J. Fluid Mech. 27, 581 (1967)] to helical turbulence, it is shown that $C_h$ is another dynamical invariant. We present a theoretical analysis based on the time independence of the $O\left(k^0\right)$ term of the velocity correlation spectral tensor at $\mathit{k}\to \mathit{0}$ and a self-similarity assumption of flow evolution at large scales including the energy containing range scales. The analysis suggests that if the $O\left(k^0\right)$ term is reflection asymmetric at an initial instant, the turbulence does not relax to any reflection symmetric state at the large scales. A simple dimensional analysis yields the decay rates of the helicity and kinetic energy in the fully developed turbulence state. The theoretical results agree with results obtained by direct numerical simulation of incompressible helical turbulence in a periodic box.

Numerical simulations are used here to analyze the Rayleigh-Taylor instability in confined and isotropic porous media. The Rayleigh-Taylor instability phenomena arise when a layer of heavy fluid sits on top of a layer of a lighter fluid. Small fluctuations of the interface separating the two fluid layers produce larger structures that eventually drive the flow into a nonlinear convective stage. The flow is initially controlled by diffusion, but rather quickly the action of gravity produces efficient fluid mixing in the entire domain. The single parameter controlling the flow is the Rayleigh number, which is the dimensionless ratio of diffusive to convective timescales. The flow evolution is often parametrized by the mixing length (a suitably defined extension of the mixing region), which, according to Gopalakrishnan et al. [Phys. Rev. Fluids 2, 012501(R) (2017)], has a linear growth. From the analysis of a broad range of simulations spanning three orders of magnitude of the Rayleigh number, we could observe a superlinear asymptotic growth of the mixing length. The present results, which are in line with previous simulations, allow us to evaluate precisely the superlinear evolution coefficient. We further provide simple scaling arguments to justify the observed superlinear growth.

We carry out direct numerical simulation together with an adhesive discrete element method calculation (DNS-DEM) to investigate agglomeration of particles in homogeneous isotropic turbulence (HIT). We report an exponential-form scaling for the size distribution of early-stage agglomerates, which is valid across a wide range of particle inertia and interparticle adhesion values. Such scaling allows one to quantify the state of agglomeration using a single scale parameter. An agglomeration kernel is then constructed containing the information of agglomerate structures and the sticking probability. An explicit relationship between the sticking probability and microscale particle properties is also proposed based on the scaling analysis of the equation for head-on collisions. Our results extend Smoluchowski's theory to the condition of noncoalescing solid adhesive particles and can reproduce DNS-DEM results with a simple one-dimensional simulation.

In this paper, we report an experimental study to examine the lift generation and friction reduction using soft porous media. The study is inspired by the frictionless motion of a red blood cell gliding over the highly porous endothelial glycocalyx layer that covers the inner surface of our blood vessels. The experimental setup consists of a running conveyer belt coated with a soft porous sheet and an upper fully instrumented planar board, i.e., a planing surface. Both the lubrication pressure and the sliding friction are measured. The results clearly demonstrate a huge potential for using highly compressible porous media for a new generation of soft bearings with tremendously increased pore pressure and infinite life.

Wet active matter in the presence of an imposed temperature gradient, or chemical potential gradient, is considered. It is shown that there is a type of convective instability that is caused by a (negative) activity parameter. Physically this corresponds to active fluids with contractual stress. In this nonequilibrium steady state the singular generic long-ranged correlations are computed and compared and contrasted with the analogous results in a passive fluid. In addition, the singular nonequilibrium Casimir pressure or force is determined. The fluid motion above the instability is determined by generalizing the Lorenz equations for the Rayleigh-Benard problem in a passive fluid to Lorenz-like equations to describe this instability.

Pouring a liquid into a container filled with a denser miscible liquid creates a downward jet. The penetration of this jet into the tank is opposed by buoyancy, thus a return flow toward the upper surface occurs and forms a fountain. In such a condition, due to entrainment, a mixed layer of the two liquids is created in the upper part of the tank, while the lower section is only filled with the original denser liquid. In this experimental study, we characterize the behavior of fountains in a bounded container, i.e., a filling box, based on the Reynolds $\mathrm{Re}$ and Froude $\mathrm{Fr}$ numbers of the initial state. Unlike a conventional turbulent fountain, we focus on the regime at lower Reynolds numbers, $\mathrm{Re}<500$, where $\mathrm{Re}$ is defined based on the jet radius, average speed, and the kinematic viscosity of the environment. Furthermore, we measure the fountain volume entrainment coefficient $B$ by modeling the mixing in this configuration as a filling-box problem. We then show that $B$ is a function of both $\mathrm{Re}$ and $\mathrm{Fr}$, in contrast to the turbulent regime where $B$ remains approximately constant. Similarly, the fountain volume entrainment flux ratio (the ratio of the fountain volume entrainment flux $Q_E$ to the injected volume flux $Q_0)$ is also a function of $\mathrm{Re}$ and $\mathrm{Fr}$ for low Reynolds numbers. For a given $\mathrm{Fr}$, the fountain volume entrainment flux ratio at the initial stage of the injection reaches a local peak at an intermediate Reynolds number $\mathrm{Re}\approx 200$. We reason that this local peak of entrainment occurs due to the enhanced penetration of the downward jet and the moderate fountain volume entrainment coefficient at intermediate Reynolds numbers. Consequently, the total volume of the mixture, which is controlled by the injection depth of the fountain and the fountain volume entrainment flux ratio, reaches a maximum value at a similar intermediate Reynolds number, $\mathrm{Re}\approx 200$. Results of this study provide guidelines to achieve effective jet-driven mixing of two miscible liquids in a container.