We investigate flow in a thin liquid film over a heated solid surface in a bilayer two-dimensional gas-liquid system bounded on the gas side by an isothermal hydrophobic plate. The flow is driven by the Marangoni instability induced, in one case, by a thermal wave propagating along a flat solid substrate on the liquid side and in the other case by a left-right asymmetric topography of the thick solid substrate adjacent to the liquid phase uniformly heated at its outer surface. Using a long-wave approximation, we derive a nonlinear evolution equation governing the spatiotemporal dynamics of the liquid-gas interface and derive a closed-form expression indicating a nonzero value for a liquid flow rate in a steady state of the system, if attained. Numerical investigation is carried out to study the nonlinear dynamics of the gas-liquid interface and the resulting flow for various values of the system parameters. A linear stability analysis of the two-dimensional steady states of the system with a two-dimensional corrugated substrate on the liquid side is carried out with respect to three-dimensional out-of-plane disturbances. We demonstrate that the presence of a hydrophobic substrate enables a continuous flow for narrow systems associated with low values of the ratio between the mean thickness of the gas layer to that of the liquid, which would be impossible in its absence. This represents an extension of the conceptual methods discussed in our previous studies for the control and amplification of the average flow rate through the system for narrow systems, thus allowing for efficient thermocapillary transport in extremely small microfluidic devices.

Using three-dimensional computer simulations, we probe the thrust and swimming performance of plunging elastic fins. The simulations reveal that fin thickness tapering drastically enhances the frequency range at which fins can maintain high thrust and swimming velocity, as compared to uniformly thick fins that show high performance only at a narrow band near the fundamental frequency. Furthermore, tapered fins are characterized by superior thrust efficiency and swimming economy. We rationalize these results by showing that tapering leads to bending patterns that maintain a larger trailing edge displacement for a wide range of actuation frequencies.

The motion of a rigid spherical particle in a sheared polymeric fluid is studied via experiments and numerical simulations. We study particle mobility in highly elastic fluids, where the deformation due to the sphere's movement and the shear flow both result in significant stretching of the polymer. The shear flow is imposed in a plane perpendicular to the sphere's movement, resulting in regions of high polymer tension in the wake of the sphere that can extend well into the shear flow and gradient directions. We observe that these viscoelastic wake structures, resembling wings, are linked to an increase in the form drag, providing a mechanism for a dramatic decrease in the particle mobility.

In this study, we follow Grossmann and Lohse [Phys. Rev. Lett. 86, 3316 (2001)], who derived various scalings regimes for the dependence of the Nusselt number $\text{Nu}$ and the Reynolds number $\text{Re}$ on the Rayleigh number $\text{Ra}$ and the Prandtl number $Pr$. We focus on theoretical arguments as well as on numerical simulations for the case of large-$\text{Pr}$ natural thermal convection. Based on an analysis of self-similarity of the boundary layer equations, we derive that in this case the limiting large-$\text{Pr}$ boundary-layer dominated regime is ${\mathrm{I}}_{\infty }^{<}$, introduced and defined by Grossmann and Lohse [Phys. Rev. Lett. 86, 3316 (2001)], with the scaling relations $\text{Nu}\sim {\text{Pr}}^0{\text{Ra}}^{1/3}$ and $\text{Re}\sim {\text{Pr}}^{-1}{\text{Ra}}^{2/3}$. Our direct numerical simulations for $\text{Ra}$ from ${10}^4$ to ${10}^9$ and $Pr$ from 0.1 to 200 show that the regime ${\mathrm{I}}_{\infty }^{<}$ is almost indistinguishable from the regime ${\mathrm{III}}_{\infty }$, where the kinetic dissipation is bulk-dominated. With increasing $\text{Ra}$, the scaling relations undergo a transition to those in ${\mathrm{IV}}_u$ of Grossmann and Lohse [Phys. Rev. Lett. 86, 3316 (2001)], where the thermal dissipation is determined by its bulk contribution.

We present a self-contained study of the dynamics of oscillating nanomenisci anchored on nanometric topographical defects around a cylindrical nanofiber with a radius below 100 nm. Using frequency-modulation atomic force microscopy (FM-AFM), we show that the friction coefficient surges as the contact angle is decreased. We propose a theoretical model within the lubrification approximation that reproduces the experimental data and provides a comprehensive description of the dynamics of the nanomeniscus. The dissipation pattern in the vicinity of the contact line and the anchoring properties are discussed as a function of liquid and surface properties in addition to the forcing conditions.

We study the statistics of principal curvatures and the surface area ratio of propagating surfaces with a constant or nonconstant propagating velocity in isotropic turbulence using direct numerical simulation. Propagating surface elements initially constitute a plane to model a planar premixed flame front. When the statistics of evolving propagating surfaces reach the stationary stage, the statistical profiles of principal curvatures scaled by the Kolmogorov length scale versus the constant displacement speed scaled by the Kolmogorov velocity scale collapse at different Reynolds numbers. The magnitude of averaged principal curvatures and the number of surviving surface elements without cusp formation decrease with increasing displacement speed. In addition, the effect of surface stretch on the nonconstant displacement speed inhibits the cusp formation on surface elements at negative Markstein numbers. In order to characterize the wrinkling process of the global propagating surface, we develop a model to demonstrate that the increase of the surface area ratio is primarily due to positive Lagrangian time integrations of the area-weighted averaged tangential strain-rate term and propagation-curvature term. The difference between the negative averaged mean curvature and the positive area-weighted averaged mean curvature characterizes the cellular geometry of the global propagating surface.

We report detailed experimental studies of statistical, scaling, and spectral properties of elastic turbulence (ET) in a von Karman swirling flow between rotating and stationary disks of polymer solutions in a wide, from dilute to semidilute entangled, range of polymer concentrations $\varphi$. The main message of the investigation is that the variation of $\varphi$ just weakly modifies statistical, scaling, and spectral properties of ET in a swirling flow. The qualitative difference between dilute and semidilute unentangled versus semidilute entangled polymer solutions is found in the dependence of the critical Weissenberg number ${\text{Wi}}_c$ of the elastic instability threshold on $\varphi$. The control parameter of the problem, the Weissenberg number $\text{Wi,}$ is defined as the ratio of the nonlinear elastic stress to dissipation via linear stress relaxation and quantifies the degree of polymer stretching. The power-law scaling of the friction coefficient on $\text{Wi}/{\text{Wi}}_c$ characterizes the ET regime with the exponent independent of $\varphi$. The torque $\mathrm{\Gamma }$ and pressure $p$ power spectra show power-law decays with well-defined exponents, which has values independent of $\text{Wi}$ and $\varphi$ separately at $100\le \varphi \le 900$ ppm and $1600\le \varphi \le 2300$ ppm ranges. Another unexpected observation is the presence of two types of the boundary layers, horizontal and vertical, distinguished by their role in the energy pumping and dissipation, which has width dependence on $\text{Wi}$ and $\varphi$ differs drastically. In the case of the vertical boundary layer near the driving disk, $w_v^v$ is independent of $\text{Wi}/{\text{Wi}}_c$ and linearly decreases with $\varphi /\varphi *$, while in the case of the horizontal boundary layer $w_v^h$ its width is independent of $\varphi /\varphi *$, linearly decreases with $\text{Wi}/{\text{Wi}}_c$, and is about five times smaller than $w_v^v$. Moreover, these $\text{Wi}$ and $\varphi$ dependencies of the vertical and horizontal boundary layer widths are found in accordance with the inverse turbulent intensity calculated inside the boundary layers $V_{\theta }^h/V_{\theta }^{h\mathrm{rms}}$ and $V_{\theta }^v/V_{\theta }^{v\mathrm{rms}}$, respectively. Specifically, the dependence of $V_{\theta }^v/V_{\theta }^{v\mathrm{rms}}$ in the vertical boundary layer on $\text{Wi}$ and $\varphi$ agrees with a recent theoretical prediction [S. Belan, A. Chernych, and V. Lebedev, Boundary layer of elastic turbulence (unpublished)].

Using a technique allowing for in situ measurements of concentrations fields, the evolution of scalar mixtures flowing within a porous medium made of a three-dimensional random stack of solid spheres, is addressed. Two distinct fluorescent dyes are injected from separate sources. Their evolution as they disperse and mix through the medium is directly observed and quantified, which is made possible by matching the refractive indices of the spheres and the flowing interstitial liquid. We decipher the nature of the interaction rule between the scalar sources, explaining the phenomenon that alters the concentration distribution of the overall mixture as it decays toward uniformity. Any residual correlation of the initially merged sources is progressively hidden, leading to an effective fully random interaction rule of the two distinct subfields.

This paper presents an experimental and numerical study on the structure and stability of a solutal advective flow in a horizontal shallow layer. The flow is induced by the initial longitudinal steplike density distribution caused by inhomogeneous solute concentration. It is shown that, when the density difference or the channel thickness increases, the main flow instability in the form of longitudinal convective rolls occurs in the near-wall region. This phenomenon originates from the Rayleigh-Taylor instability, which develops near both the upper and lower horizontal boundaries, where the unstable density stratification occurs due to no-slip boundary conditions. It is established that the solutal Péclet number, a measure of the relative strength of advection and diffusion, must exceed the critical value ${\text{Pe}}^{*}\approx 300$ for the instability to set in. Moreover, the Péclet number uniquely determines the spatiotemporal characteristics of the secondary flow, namely, its wavelength and formation time. The results of the laboratory experiments are in good agreement with the numerical predictions.

We numerically examine the time-dependent behavior of double emulsions in a simple shear flow using finite volume and front-tracking methods. A single inner drop is initially located eccentrically to the outer drop. When the eccentricity is contained within the plane of shear, the inner drop experiences a “revolving” motion within the plane of shear, orbiting about the center of the compound drop while slowly moving outward. The inner drop eventually experiences a limit cycle, where no more outward movement occurs because the distance between the two interfaces is reduced to a thin liquid film for portions of the revolving cycle. In addition, eccentricity in the direction normal to the plane of shear is tested. In this case, the inner droplet undergoes a “drifting” motion, slowly moving perpendicularly to the plane of shear until only a thin layer remains between the two interfaces. Finally, the revolving and drifting motions are simultaneously observed when the in-plane-of-shear eccentricity is included in addition to the off-plane-of-shear eccentricity. The observed behaviors are not qualitatively affected by the inner to outer droplet radii ratio, and are preserved when $\text{Re}\le 5,{\text{Ca}}_o\le 0.1$, and ${\text{Ca}}_i<0.2$.

Stably stratified turbulence is investigated with the aim of increasing our limited understanding of the vertical structure of this type of turbulent flow. For strongly stratified turbulence there is a theoretical prediction that the energy spectra in the vertical direction of gravity are very steep, possessing the well-known form $E_h\left(k_v\right)\propto N^2{k}_v^{-3}$, where $N$ is the Brunt-Väisälä frequency and $k_v$ is the vertical wave number, but supporting evidence from experiments and numerical simulations is lacking. We conduct direct numerical simulation (DNS) with uniform background stratification and forcing at large scales. In order to consider the large anisotropic scales only, the vertical energy spectra are decomposed into large-scale vertical spectra $E_{\mathrm{large}}\left(k_v\right)$ and small-scale vertical spectra $E_{\mathrm{small}}\left(k_v\right)$ using a horizontal demarcation scale. We find that this approach gives results that are in close agreement with $E_{\mathrm{large}}\left(k_v\right)\propto N^2{k}_v^{-3}$ for the DNS runs performed. This result holds approximately over the wave-number range $k_b\le k_v\le k_{\mathrm{oz}}$, where $k_b$ is the buoyancy wave number and $k_{\mathrm{oz}}$ is the Ozmidov wave number, in agreement with theory. Similarly, large-scale vertical spectra of potential energy are found to be $E_{p,\mathrm{large}}\left(k_v\right)\propto N^2{k}_v^{-3}$, over a narrower range of wave numbers. The evidence supports the existence of a scale-by-scale balance between inertia and buoyancy occurring in strongly stratified turbulence at large horizontal scales. Finally, the current results are put in the context of ocean turbulence by making a comparison with measurements of vertical shear spectra made in the ocean interior.

This paper furthers our understanding of lock-on that is induced by periodic external forcing. The effect of forcing phase difference is investigated. An extended linear theory is proposed to predict the centers of various lock-on regimes, including harmonic, subharmonic, and superharmonic lock-on, in a parametric map spanned by the forcing frequency and phase difference. It reveals that when the forcing frequency is equal to the natural vortex shedding frequency or its integer multiple, harmonic or subharmonic lock-on occurs at particular forcing phase differences, whereas when the forcing frequency is a submultiple of the natural shedding frequency, superharmonic lock-on occurs. To confirm this theory and also further determine the shape and size of each lock-on regime, a series of numerical simulations is conducted on a circular-cylinder flow system with periodic external forcing being realized by a pair of synthetic jets (SJs). At a Reynolds number 100 and under moderate SJ forcing, five lock-on regimes are captured, including the primary, secondary, tertiary, and first- and second-superharmonic lock-on. It is found that these lock-on regimes are generally in a rhomboidal shape, and their size gradually reduces when the SJ frequency is away from the natural vortex shedding frequency. With these simulations, the aerodynamic forces and wake formation in each lock-on regime are analyzed and compared, with the discussion being focused on the effects of SJ frequency and phase difference. Furthermore, stability analysis is conducted to reveal more flow physics related to lock-on.

Directed assembly of colloids is an exciting field in materials science for forming structures with new symmetries and responses. We have been studying how interface curvature can be used in to guide colloidal structure formation. On a fluid interface, the area of the deformation field around adsorbed microparticles depends on interface curvature; particles move to minimize the excess area of the distortions that they make in the interface. For particles that are sufficiently small, this area decreases as particles move along principal axes to sites of high deviatoric curvature. We have studied this migration for microparticles on a curved host interface with zero mean curvature created by pinning an oil-water interface around a micropost. Here, on a similar interface, we demonstrate capillary curvature repulsion; that is, we identify conditions in which microparticles migrate away from high curvature sites. Using theory and experiment, we discuss the origin of these interactions and their relationship to the particle's undulated contact line. We discuss the implications of this type of interaction in various contexts from materials science to microrobotics.

The classical view of wall-bounded turbulence considers a near-wall inner region where all velocity statistics are universally dependent on distance from the wall when scaled with friction velocity and the kinematic viscosity of the fluid. This is referred to as an inner scaling and leads to Prandtl's law of the wall. Data from numerical simulations and experiments over the past decade or so, however, have provided compelling evidence that statistics of the fluctuating streamwise velocity do not follow inner scaling in this near-wall region and an interaction of outer and logarithmic regions exists, resulting in a Reynolds number dependence. In this paper we briefly review some of these studies and discuss the Reynolds number dependence of the streamwise turbulence intensity near the wall in terms of an inner-outer interaction. An established model for such an interaction between near-wall and logarithmic region turbulence is considered that comprises two mechanisms: superposition and modulation. Here outer-region motions, of which a fraction is wall-attached, are superimposed onto the near-wall dynamics, and concurrently the near-wall motions are modulated by this superimposed signature. We discuss to what extent the superposition effect can relate changes in the inner-scaled near-wall peak value of streamwise turbulence intensity to logarithmic region turbulence resembling features of attached eddies.

Sedimenting particles and motile organisms are ubiquitously found in oceans and lakes, where density stratification naturally occurs due to temperature or salinity gradients. We explore the effects of stratification on the fundamental hydrodynamics of settling particles, rising drops, and small organisms. The results of our direct numerical simulations of the sedimentation of particles show that the presence of vertical density gradients in the water column can substantially affect the settling dynamics of a particle, interaction between a pair of particles, and settling rates and microstructure of suspension of particles. We show that elongation of particles affects both the settling orientation and the settling rate of particles in stratified fluids, which will have direct consequences on the vertical flux of particulate matter and carbon flux in the ocean. We further demonstrate an unexpected effect of buoyancy, potentially affecting a broad range of processes at pycnoclines in oceans and lakes. In particular, stratification has a major effect on the flow field, energy expenditure, and nutrient uptake of small organisms. In addition, the role of stratification in pattern formation of bioconvection plumes of algal cells and in biogenic mixing is investigated. In particular, the numerical approach allows for considering the effects of background turbulence and hydrodynamic perturbations produced by swimming organisms, shedding light on the contribution of organisms in the mixing process in aqueous environments.

Low-dimensional models of experimental and simulation data for a complex supersonic jet were fused to reconstruct time-dependent proper orthogonal decomposition (POD) coefficients. The jet consists of a multistream rectangular single expansion ramp nozzle, containing a core stream operating at Mach number $M_{j,1}=1.6$ and bypass stream at $M_{j,3}=1.0$ with an underlying deck. Proper orthogonal decomposition was applied to schlieren and particle image velocimetry data to acquire the spatial basis functions. These eigenfunctions were projected onto their corresponding time-dependent large-eddy simulation (LES) fields to reconstruct the temporal POD coefficients. This reconstruction was able to resolve spectral peaks that were previously aliased due to the slower sampling rates of the experiments. Additionally, dynamic mode decomposition was applied to the experimental and LES data sets and the spatiotemporal characteristics were compared to POD.

Some species of semiaquatic arthropods including water striders and springtails can jump from the water surface to avoid sudden dangers like predator attacks. It was reported recently that the jump of medium-sized water striders is a result of surface-tension-dominated interaction of thin cylindrical legs and water, with the leg movement speed nearly optimized to achieve the maximum takeoff velocity. Here we describe the mathematical theories to analyze this exquisite feat of nature by combining the review of existing models for floating and jumping and the introduction of the hitherto neglected capillary forces at the cylinder tips. The theoretically predicted dependence of body height on time is shown to match the observations of the jumps of the water striders and springtails regardless of the length of locomotory appendages. The theoretical framework can be used to understand the design principle of small jumping animals living on water and to develop biomimetic locomotion technology in semiaquatic environments.

The present paper draws upon the experience of the author to illustrate the potential of advanced optical metrology for understanding near-wall-turbulence physics. First the canonical flat plate boundary layer problem is addressed, initially very near to the wall and then in the outer region when the Reynolds number is high enough to generate an outer turbulence peak. The coherent structure organization is examined in detail with the help of stereoscopic particle image velocimetry (PIV). Then the case of a turbulent boundary layer subjected to a mild adverse pressure gradient is considered. The results obtained show the great potential of a joint experimental-numerical approach. The conclusion is that the insight provided by today's optical metrology opens the way for significant improvements in turbulence modeling in upcoming years.

Fluid mechanics is a discipline with rich phenomena, with motions occurring over an enormous range of length scales, and spanning a wide range of laminar and turbulent flows, instabilities, and applications in industry, nature, biology, and medicine. The subfield of complex fluids typically refers to those flows where the complexity is introduced, for example, by the presence of suspended particles, multiple phases, soft boundaries, and electrokinetic effects; several distinct multiphase flows of Newtonian fluids make up the examples in this article. Interfaces play a significant role and modify the flow with feedback that further changes the shapes of the interfaces. I will provide examples of our work highlighting (i) new features of classical instabilities triggered by changes in geometry, (ii) multiphase flows relevant to the design of liquid-infused substrates exhibiting effective slip while retaining the trapped liquid, and (iii) unexpected dynamics in flow at a T-junction. The interplay of experiments and mathematical models and/or simulations is critical to the new understanding developed.