The scale dependence of the statistical alignment tendencies of the eigenvectors of the strain-rate tensor ${\mathit{e}}_i$, with the vorticity vector $\mathbf{\omega }$, is examined in the self-preserving region of a planar turbulent mixing layer. Data from a direct numerical simulation are filtered at various length scales and the probability density functions of the magnitude of the alignment cosines between the two unit vectors $|{\mathit{e}}_i·\widehat{\mathbf{\omega }}|$ are examined. It is observed that the alignment tendencies are insensitive to the concurrent large-scale velocity fluctuations, but are quantitatively affected by the nature of the concurrent large-scale velocity-gradient fluctuations. It is confirmed that the small-scale (local) vorticity vector is preferentially aligned in parallel with the large-scale (background) extensive strain-rate eigenvector ${\mathit{e}}_1$, in contrast to the global tendency for $\mathbf{\omega }$ to be aligned in parallel with the intermediate strain-rate eigenvector [Hamlington et al., Phys. Fluids 20, 111703 (2008)]. When only data from regions of the flow that exhibit strong swirling are included, the so-called high-enstrophy worms, the alignment tendencies are exaggerated with respect to the global picture. These findings support the notion that the production of enstrophy, responsible for a net cascade of turbulent kinetic energy from large scales to small scales, is driven by vorticity stretching due to the preferential parallel alignment between $\mathbf{\omega }$ and nonlocal ${\mathit{e}}_1$ and that the strongly swirling worms are kinematically significant to this process.

Using a scaling analysis, we assess the impact of interfacial slip on the time required for the thin liquid film between two drops undergoing a head-on collision to drain to the critical thickness for rupture by van der Waals forces. Interfacial slip is included in our continuum development using a Navier slip boundary condition, with the slip coefficient modeled using previous theories [Helfand and Tagami, J. Chem. Phys. 57, 1812 (1972); Goveas and Fredrickson, Eur. Phys. J. B 2, 79 (1998)]. Slip decreases hydrodynamic resistance and speeds up film drainage. It renders the dependence of the drainage time on capillary number stronger in the spherical-film regime, but, interestingly, this dependence is altered only weakly in the dimpled-film regime. A subtle effect of slip is that it increases the range of capillary numbers in which the film remains predominantly spherical in shape during drainage (as opposed to being dimpled), leading to significantly faster drainage for these capillary numbers. Slip also leads to an increase in the critical capillary number beyond which coalescence is not possible in a head-collision.

The Interacting Particle Representation Model (IPRM) of homogeneous turbulence incorporates information about the morphology of turbulent structures within the confines of a one-point model. In the original formulation [Kassinos and Reynolds, Center for Turbulence Research: Annual Research Briefs, 31–51 (1996)], the IPRM was developed in a Lagrangian setting by evolving second moments of velocity conditional on a given gradient vector. In the present work, the IPRM is reformulated in an Eulerian framework, and evolution equations are developed for the marginal probability density functions (PDFs). Eulerian methods avoid the issues associated with statistical estimators used by Lagrangian approaches, such as slow convergence. A specific emphasis of this work is to use the IPRM to examine the long time evolution of homogeneous turbulence. We first describe the derivation of the marginal PDF in spherical coordinates, which reduces the number of independent variables and the cost associated with Eulerian simulations of PDF models. Next, a numerical method based on radial basis functions over a spherical domain is adapted to the IPRM. Finally, results obtained with the new Eulerian solution method are thoroughly analyzed. The sensitivity of the Eulerian simulations to parameters of the numerical scheme, such as the size of the time step and the shape parameter of the radial basis functions, is examined. A comparison between Eulerian and Lagrangian simulations is performed to discern the capabilities of each of the methods. Finally, a linear stability analysis based on the eigenvalues of the discrete differential operators is carried out for both the new Eulerian solution method and the original Lagrangian approach.

Liquid jets ultimately break up into droplets through an instability driven by surface tension. For highly viscous liquids, drops are connected by cylindrical liquid filaments whose radii linearly decrease with time, thus forming drops on a string structure. For a jet composed of two aqueous phases made in air by coaxial extrusion, we observe that, for moderate Weber and capillary numbers, drops slow down with different velocities, leading to drop coalescence. The origin of the traffic collision is linked to the spatial feature of the capillary instability where capillary and viscous forces acting on the drops evolve along the jet and ultimately amplify small velocity fluctuations. The emergence of such fluctuations is related to the unstable nature of the annular coflow of liquids having contrasting viscoelastic properties. From a practical point of view, flow and actuation conditions can be adjusted to inhibit drop collision and thus drop coalescence. These findings allow then the fabrication of monodisperse submillimeter core-shell objects based on the fragmentation of compound jets made of polymer solutions that find applications for three-dimensional cell culture.

We examine finite Reynolds number contributions to the inertial range solution of the third order structure functions $D_{3,0}$ and $D_{1,2}$ stemming from the unsteady and viscous terms. Under the assumption that the second order correlations $f$ and $g$ are self-similar under a coordinate change, we are able to rewrite the exact second order equations as a function of a normalized scale $\tilde{r}$ only. We close the resulting system of equations using a power law and an eddy-viscosity ansatz. If we further assume K41 scaling, we find the same Reynolds number dependence as previously in the literature. We proceed to extrapolate towards higher Reynolds numbers to examine the unsteady and viscous terms in more detail. We find that the intersection between the two terms, where their contribution to the solution of the structure function equations is relatively small, scales with the Taylor scale $\lambda$.

A mechanistic model, derived from kinetic theory, is developed to describe segregation in confined multicomponent suspensions such as blood. It incorporates the two key phenomena arising in these systems at low Reynolds number: hydrodynamic pair collisions and hydrodynamic migration. Two flow profiles are considered: simple shear flow (plane Couette flow) and plane Poiseuille flow. The theory begins by writing the evolution of the number density of each component in the suspension as a master equation with contributions from migration and collisions. By making judicious approximations for the collisions, this system of integrodifferential equations is reduced to a set of drift-diffusion equations. We focus attention on the case of a binary suspension with a deformable primary component that completely dominates the collision dynamics in the system and a trace component that has no effect on the primary. The model captures the phenomena of depletion layer formation and margination observed in confined multicomponent suspensions of deformable particles. The depletion layer thickness of the primary component is predicted to follow a master curve relating it in a specific way to confinement ratio and volume fraction. Results from various sources (experiments, detailed simulations, master equation solutions) with different parameters (flexibility of different components in the suspension, viscosity ratio, confinement, among others) collapse onto the same curve. For sufficiently dilute suspensions the analytical form predicted by the drift-diffusion theory for this curve is in excellent agreement with results from these other sources with only one adjustable parameter. In a binary suspension, several regimes of segregation arise, depending on the value of a “margination parameter” $\mathrm{M}$. Most importantly, in both Couette and Poiseuille flows there is a critical value of $\mathrm{M}$ below which a sharp “drainage transition” occurs: one component is completely depleted from the bulk flow to the vicinity of the walls. Direct simulations also exhibit this transition as the size or flexibility ratio of the components changes. Finally, some prior studies suggest a nonmonotonic dependence of margination propensity on volume fraction. We formulate a hypothesis regarding this observation. Theory predictions support the hypothesis, providing further insights into the mechanisms behind margination and segregation phenomena.

The interface between the fluid environment and the surface of the body in swimming fishes is critical for both physiological and hydrodynamic functions. The skin surface in most species of fishes is covered with bony scales or toothlike denticles (in sharks). Despite the apparent importance of fish surfaces for understanding aquatic locomotion and near-surface boundary layer flows, relatively little attention has been paid to either the nature of surface textures in fishes or possible hydrodynamic effects of variation in roughness around the body surface within an individual and among species. Fish surfaces are remarkably diverse and in many bony fishes scales can have an intricate surface texture with projections, ridges, and comblike extensions. Shark denticles (or scales) are toothlike and project out of the skin to form a complexly textured surface that interacts with free-stream flow. Manufacturing biomimetic foils with fishlike surfaces allows hydrodynamic testing and we emphasize here the importance of dynamic test conditions where the effect of surface textures is assessed under conditions of self-propulsion. We show that simple two-dimensional foils with patterned cuts do not perform as well as a smooth control surface, but that biomimetic shark skin foils can swim at higher self-propelled speeds than smooth controls. When the arrangement of denticles on the foil surface is altered, we find that a staggered-overlapped pattern outperforms other arrangements. Flexible foils made of real shark skin outperform sanded controls when foils are moved with a biologically realistic motion program. We suggest that focus on the mechanisms of drag reduction by fish surfaces has been too limiting and an additional role of fish surface textures may be to alter leading edge vortices and flow patterns on moving surfaces in a way that enhances thrust. Analysis of water flow over an artificial shark skin foil under both static and dynamic conditions shows that a shear layer develops over the denticle surface and we propose that there is limited flow under the expanded surfaces of shark denticles. The diversity of fish scale types and textures and the effect of these surfaces on boundary layer flows and fish locomotor energetics is a rich area for future investigation.

The response of a soap film to the continuous deformation of its wire boundary is considered, with particular attention to the topological transitions that can occur at critical stages of the deformation process. Two well-known examples that have been studied by both theory and experiment are the catenoid suspended between circular wires in parallel planes, and the Möbius-strip soap film spanning a wire that is twisted and folded back on itself. In this latter case, we have shown in previous publications that, when the wire is unfolded, the soap film undergoes a topological transition through a boundary singularity to a two-sided film, with a corresponding jump in the linking number between the axis of the wire and the Plateau boundary on its surface. Here, we review this particular aspect of the problem, and propose a simplified model experiment through which the slipping adjustment of a Plateau border on a solid surface may be investigated.

A classic result due to Taylor is that a weakly conducting drop bearing zero net charge placed in a uniform electric field adopts a prolate or oblate spheroidal shape, the flow and shape being axisymmetrically aligned with the applied field. Here I overview some intriguing symmetry-breaking instabilities occurring in strong applied dc fields: Quincke rotation resulting in drop steady tilt or tumbling, and pattern formation on the surface of a particle-coated drop.

Understanding the flows in planetary cores, i.e., the large liquid iron oceans hidden in the central part of terrestrial planets, is a tremendous interdisciplinary challenge, at the frontier of fundamental fluid dynamics and planetary sciences. Beyond buoyancy driven flows that constitute the standard model for core fluid dynamics, an increasing amount of research has focused on the rotational dynamics of these spinning systems, periodically perturbed by tides, precession, and libration. Although of small amplitude, those harmonic forcings are capable of exciting resonant instabilities in planetary cores, providing alternative routes towards turbulence and magnetic field generation. In this paper I provide an overview of some recent works on this field, focusing on the mechanisms of tide and libration driven elliptical instabilities. Combined laboratory experiments and pioneering numerical simulations have allowed a full description of the stability and linear state of these flows, as well as the investigation of some convincing planetary applications. Open questions now remain regarding the nonlinear saturation of the excited flows as well as their dynamo capability. These will undoubtedly be the focus of future research, in the context of intense activity in planetary exploration of our solar system and others, which highlights the need to go beyond the standard convective models.

In this paper we exploit some analogies between flows near capillary interfaces and near elastic interfaces. We first consider the elastohydrodynamics of a ball bearing and the motion of a gas bubble inside a thin channel. It is shown that there is a strong analogy between these two lubrication problems, and the respective scaling laws are derived side by side. Subsequently, the paper focuses on the limit where the involved elastic interfaces become extremely soft. It is shown that soft gels and elastomers, like liquids, can be shaped by their surface tension. We highlight some recent advances on this class of elastocapillary phenomena.

Accurate long-term forecasts of the path and intensity of severe hurricanes are imperative to protect property and save lives. Extensive real-time measurements within hurricanes, especially near their core, are essential for supplementing the limited relevant information accessible by satellites in order to improve such forecasts. Current operational methods for obtaining in situ information, such as dropsondes and repeated manned and unmanned aircraft flights over and within hurricanes, are both expensive and limited in duration. In the present work it is demonstrated by numerical experiments how a swarm of robust, inexpensive, buoyancy-controlled, sensor-laden balloons might be deployed and controlled in an energetically efficient, coordinated fashion, for days at a time, to continuously monitor relevant properties (pressure, humidity, temperature, and wind speed) of a hurricane as it develops. Rather than fighting its gale-force winds, the strong and predictable stratification of these winds is leveraged to efficiently disperse the balloons into a favorable time-evolving distribution. An iterative bootstrap approach is envisioned in which (a) sensor balloons are used to help improve the available computational estimate of the uncertain and underresolved flow field of the hurricane and (b) this (imprecise) estimate of the hurricane flow field is leveraged to improve the distribution of the sensor balloons, which then better facilitates (a), etc. The control approach envisioned in this ambitious effort is a combination of (centrally computed) model predictive control for coordination at the largest scales, which is the focus of the present paper, coupled with a feedback control strategy (decentrally computed, on the balloons themselves), for smaller-scale corrections. Our work indicates that, following such an approach, certain target orbits of interest within the hurricane can be continuously sampled by some balloons, while others make repeated sweeps between the eye and the spiral rain bands.

Diffusive processes exhibit a strong dependence on history effects. For a gas bubble at rest in a liquid, such effects arise when the concentration of dissolved gas at the bubble surface, dictated by Henry's law, depends on time. In this paper we consider several such situations. An oscillating ambient pressure field causes the occurrence of rectified diffusion of gas into or out of the bubble. Unlike previous investigators, who considered the opposite limit, we study this process for conditions when the diffusion length is larger than the bubble radius. It is found that history effects are important in determining the threshold conditions. Under a static ambient pressure, the time dependence of the gas concentration can arise due to the action of surface tension, which increases the gas pressure as the bubble dissolves or, when the bubble contains a mixture of two or more gases, due to the different rates at which they dissolve. In these latter cases history effects prove mostly negligible for bubbles larger than a few hundred nanometers.

The present analysis extends the author's earlier work [Lappa, Phys. Fluids 26, 093301 (2014)] on the properties of patterns formed by the spontaneous accumulation and ordering of solid particles in certain types of flow. It is shown that under certain conditions, when subjected to vibrations to induce natural flow, nonisothermal fluids with dispersed solid particles are characterized by intervals of solid-pattern-forming behavior due to particle rearrangements preceded by intervals in which no recognizable structures of solid matter can be detected. The dynamics of these systems are highly nonlinear in nature. Because this family of particle attractors is known to exhibit strong sensitivity to the symmetry properties of the considered vibrated system and related geometrical constraints, the present study attempts to clarify the related dynamics in a geometry with curved walls (cylindrical enclosure). In particular, by assuming vibrations always directed perpendicularly to the imposed temperature gradient, we show that the morphology, spatial extension (percentage of physical volume occupied), separation (spatial distance), and mechanisms responsible for the formation of the resulting particle structures change significantly according to whether the temperature gradient is parallel or perpendicular to the symmetry axis of the cylinder. This indicates that the physics is not invariant with respect to 90° rotations in space of the specific forcing considered (direction of the imposed temperature gradient and associated perpendicular vibrations). Additional insights into the problem are obtained by assessing separately the influence played by the time-averaged (mean) and oscillatory effects. According to the numerical results, the intriguing diversity of particle agglomerates results from the different role or importance played by (curved or straight) boundaries in constraining particles and from the different structure and topology of the resulting macroscopic (large-scale) thermovibrational flow oscillating in time at the same frequency of the imposed vibrations.

We show that thermocapillary-induced droplet motion is markedly enhanced when using lubricant-impregnated surfaces as compared to solid substrates. These surfaces provide weak pinning, which makes them ideal for droplet transportation and specifically for water transportation. Using a lubricant with viscosity comparable to that of water and temperature gradients as low as 2 K/mm, we observe that drops can propel at 6.5 mm/s, that is, at least 5 times quicker than reported on conventional substrates. Also in contrast with solids, the liquid nature of the different interfaces makes it possible to predict quantitatively the thermocapillary Marangoni force (and velocity) responsible for the propulsion.

Water vapor condensation on superhydrophobic surfaces has received much attention in recent years due to the ability of such surfaces to shed microscale water droplets via coalescence-induced droplet jumping, resulting in heat transfer, anti-icing, and self-cleaning performance enhancement. Here we report the coalescence-induced removal of water nanodroplets ($R\approx 500\mathrm{nm}$) from superhydrophobic carbon nanotube (CNT) surfaces. The two-droplet coalescence time is measured for varying droplet Ohnesorge numbers, confirming that coalescence prior to jumping is governed by capillary-inertial dynamics. By varying the conformal hydrophobic coating thickness on the CNT surface, the minimum jumping droplet radius is shown to increase with increasing solid fraction and decreasing apparent advancing contact angle, allowing us to explore both hydrodynamic limitations stemming from viscous dissipation and surface adhesion limitations. We find that, even for the smallest nanostructure length scale ($\le 100$ nm) and lowest surface adhesions, nonideal surface interactions and the evolved droplet morphology play defining roles in limiting the minimum size for jumping on real surfaces. The outcomes of this work demonstrate the ability to passively shed nanometric water droplets, which has the potential to further increase the efficiency of systems that can harness jumping droplets for a wide range of energy and water applications.

The emergence of turbulence in shear flows is a well-investigated field. Yet, there are some lingering issues that have not been sufficiently resolved. One of them is the apparent contradiction between the results of linear stability analysis showing a flow to be stable and yet experiments and simulations proving it to be otherwise. There is some success, in particular in astrophysical systems, based on magnetorotational instability (MRI), revealing turbulence. However, MRI requires the system to be weakly magnetized. Such instability is neither a feature of general magnetohydrodynamic (MHD) flows nor revealed in purely hydrodynamic flows. Nevertheless, linear perturbations of such flows are non-normal in nature, which argues for a possible origin of nonlinearity therein. The concept behind this is that non-normal perturbations could produce huge transient energy growth (TEG), which may lead to nonlinearity and further turbulence. However, so far, non-normal effects in shear flows have not been explored much in the presence of magnetic fields. In this spirit, here we consider the perturbed viscoresistive MHD shear flows with rotation in general. Basically we recast the magnetized momentum balance and associated equations into the magnetized version of Orr-Sommerfeld and Squire equations and their magnetic analogs. We also assume the flow to be incompressible and in the presence of Coriolis effect solve the equations using a pseudospectral eigenvalue approach. We investigate the possible emergence of instability and large TEG in three different types of flows, namely, the Keplerian flow, the Taylor-Couette (or constant angular momentum) flow, and plane Couette flow. We show that, above a certain value of magnetic field, instability and TEG both stop occurring. We also show that TEG is maximum in the vicinity of regions of instability in the wave number space for a given magnetic field and Reynolds number, leading to nonlinearity and plausible turbulence. Rotating shear flows are ubiquitous in astrophysics, especially accretion disks, where molecular viscosity is too low to account for observed data. The primary accepted cause of energy-momentum transport therein is turbulent viscosity. Hence, these results would have important implications in astrophysics.

The shear-driven drainage of capillary grooves filled with viscous liquid is a dynamic wetting phenomenon relevant to numerous industrial processes and lubricant-infused surfaces for drag reduction and antifouling. Prior work has reported that a finite length $L_{\infty }$ of the capillary groove can remain indefinitely filled with liquid even when large shear stresses are applied. The mechanism preventing full drainage is attributed to a balance between the shear-driven flow and a counterflow driven by capillary pressures caused by deformation of the free surface. In this work, we examine closely the approach to the final equilibrium length $L_{\infty }$ and report a crossover to a slow drainage regime that cannot be described by conventional dynamic models considering solely hydrodynamic and capillary forces. The slow drainage regime observed in experiments can be instead modeled by a kinetic equation describing a sequence of random thermally activated transitions between multiple metastable states caused by surface defects with nanoscale dimensions. Our findings provide insights on the critical role that natural or engineered surface roughness with nanoscale dimensions can play in the imbibition and drainage of capillaries and other dynamic wetting processes in microscale systems.

This study is inspired by the observation and hypothesis that the spreading and decay behaviors of a jet directly depend on the momentum-mixing mechanism between the jet and surrounding fluid. This mixing behavior is dictated by the kinematic viscosity $\nu$ for a laminar jet, which can be dramatically enhanced in a turbulent flow and is represented by the eddy viscosity $\varepsilon$. Similarly, pulsation in a synthetic jet is identified as another mechanism for enhancing mixing, which can be captured by an enhanced eddy viscosity beyond what is observed in a corresponding turbulent continuous jet. To this end, an effective-eddy-viscosity concept is proposed to model any excitation of a jet that could result in enhanced mixing beyond what is predicted by the kinematic viscosity. Our previous study found that $\varepsilon$ is actuator dependent and its relationship with the spreading or decay behavior of a jet is not obvious. To remove the actuator dependence, this study performs a dimensional analysis to relate the spreading and decay behaviors to a scaled effective eddy viscosity $\varepsilon /\sqrt{K}$ ($K$ is the momentum flux). This quantity physically represents a competition between the radial diffusion and the axial convection of the jet axial momentum. The experimental results confirm that $\varepsilon /\sqrt{K}$ governs the spreading and decay rates of the far field for any round jets.

Two particle image velocimetry arrangements are used to make true spatial comparisons between smooth- and rough-wall boundary layers at high Reynolds numbers across a very wide range of streamwise scales. Together, the arrangements resolve scales ranging from motions on the order of the Kolmogorov microscale to those longer than twice the boundary layer thickness. The rough-wall experiments were obtained above a continuous sandpaper sheet, identical to that used by Squire et al. [J. Fluid Mech. 795, 210 (2016)], and cover a range of friction and equivalent sand-grain roughness Reynolds numbers ($12000\lesssim {\delta }^{+}\lesssim$ 18000, $62\lesssim k_s^{+}\lesssim 104$). The smooth-wall experiments comprise new and previously published data spanning $6500\lesssim {\delta }^{+}\lesssim 17000$. Flow statistics from all experiments show similar Reynolds number trends and behaviors to recent, well-resolved hot-wire anemometry measurements above the same rough surface. Comparisons, at matched ${\delta }^{+}$, between smooth- and rough-wall two-point correlation maps and two-point magnitude-squared coherence maps demonstrate that spatially the outer region of the boundary layer is the same between the two flows. This is apparently true even at wall-normal locations where the total (inner-normalized) energy differs between the smooth and rough wall. Generally, the present results provide strong support for Townsend's [The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge, 1956), Vol. 1] wall-similarity hypothesis in high Reynolds number fully rough boundary layer flows.