A small solid particle resting atop a vibrating fluid interface generates a field of outwardly propagating capillary waves due to its relative vertical motion. In this paper, we show that if the particle’s symmetry is broken, the resultant unbalanced wave stresses enable steady self-propulsion along the interface. Such “capillary surfers” interact with each other hydrodynamically at long range via their mutual wavefield and form a number of dynamic bound states. This new active system bridges the gap between dissipation- and inertia-dominated regimes and promises a number of novel collective behaviors.

The law of the wall states that, after appropriate scaling, the mean velocity of incompressible turbulent flows near flat solid walls is a universal function of the wall-normal distance. An analogous law does not exist for compressible flows due to complexities arising from mean property variations and intrinsic compressibility effects, which occur when pressure directly changes the density of fluid elements. By accounting for both these effects, we propose a new velocity scaling that transforms the mean velocity of compressible flows to the incompressible law of the wall. This transformation is more accurate than the state-of-the-art, and is applicable to a wider range of flows.

We show a mechanism for rectifying an oscillating fluid flow in a looped channel with a T-junction using geometric features. We experimentally show that a net flow is produced in a looped channel with a forcing oscillating velocity. We identify that separation at the T-junction of the looped channel induces a net flow in the looped section. We present an analytic model that captures some of the basic flow features at the T-junction.

We present a chemomechanical model to analyze the propulsion of mammalian spermatozoa. The model accounts for motor kinetics, flagellar deformations, and the hydrodynamics of the suspending fluid. Simulations demonstrate spontaneous oscillations leading to realistic swimming patterns. Notably, the swimming velocity exhibits two distinct peaks as a function of the activity of the molecular motors. These peaks are characterized by distinct waveforms and trajectories. Our findings contribute to a deeper understanding of the biophysical mechanisms involved in sperm locomotion.

We consider the conditions needed to obtain stable bound states of two spheroidal squirmers. We find that the particles must have oblate shape and non-axisymmetric distribution of surface slip in order to obtain immotile “head-to-head” pairs of identical particles. For motile “head-to-tail” pairs, the particles cannot be identical, and must satisfy certain conditions involving their self-propulsion velocities, stresslets, and shape. Overall, our results demonstrate that introducing heterogeneity in shape and interfacial actuation opens new possibilities for realizing self-organization in systems of interfacially driven microswimmers.

Biological materials such as cervical mucus and collagen gel can possess a fibrous microstructure that affects their functional behavior. Using numerical and asymptotic techniques we solve a model for stretching a thin sheet of transversely isotropic viscous fluid. We show that the emergent bulk properties are governed by an effective viscosity dependent on the evolving angle of the fibers. We also demonstrate that the center-line of the sheet need not be flat, in contrast to the Newtonian case, and capture the full center-line behavior.

Tumbling behavior of spheroidal particles in inertialess flows of shear thinning fluids is analyzed. (Top Row) A spheroid in a linear shear flow of a shear thinning fluid and the variation of its tumbling time period with Carreau number. (Bottom Row) A spheroid in a pressure driven flow of a shear thinning flow and the variation of its tumbling time period with Carreau number. The red curves illustrate trends for shear thinning fluids. The dotted black lines show the corresponding Newtonian plateaus. For linear flows, the time period shows a nonmonotonic trend with the Carreau number, while for pressure driven flows the time period decreases monotonically between the two Newtonian plateaus.

Vibration has the ability to control the convective heat transport depending on the relative direction of vibration to the gravitation. We show that horizontal vibration (perpendicular to gravitation) enhances heat transport while vertical vibration (parallel to gravitation) suppresses heat transport. The observed heat transport enhancement or suppression is indicated by the critical vibration frequency. We theoretically and numerically reveal the scaling law between the critical vibration frequency and the Rayleigh number.

Droplet impact onto a solid substrate leads to substrate erosion and we find that erosion on a superhydrophobic substrate is mainly caused by droplet retraction and jump-off (the jump-off force), rather than droplet spreading (the inertia-dominated impact force). We measure the jump-off force exerted onto the substrate and attribute it to the sudden horizontal- to-vertical redirection of momentum when the receding droplet squeezes, that is, flow focusing. New scaling models based on the observation of flow focusing are proposed to express the relevant timescale and the magnitude of the jump-off force.

Above a critical voltage, ion transport near ion-selective surfaces leads to electroconvection of the liquid electrolyte, causing significant fluctuations in ion flux. Our simulation shows that applying a magnetic field can greatly modify the electroconvection by inducing a Lorentz force. The combined electro-magneto-hydrodynamic effects produce a cross-flow that advects electroconvective vortices and effectively suppresses the local high-ion-flux regions from reaching the ion-selective surfaces.

The spontaneous generation of a magnetic field by the movement of an electrically conducting material is known as the dynamo effect. It occurs in most astrophysical objects, such as the Earth’s core or the Sun’s convection zone. We show that, in liquid metal, the dynamo effect is made possible by the simple rotation of an immersed solid, provided the latter is made of a material with anisotropic electrical conductivity.

A typical fluid gets denser as it gets colder. Cold, fresh water is an exception to this rule, as it reaches a temperature of maximum density at 4 degrees Celsius. We can do experiments where we release a volume of fluid at one temperature into an ambient volume at a different temperature. When one uses a “typical” fluid, some experiments with different initial set-ups create intruding volumes that evolve into identical shapes. For our investigation we performed those experiments with cold, fresh water instead and found that the intruding volumes evolved into very different shapes. In the manuscript we discuss the geophysical implications of these results.

Jets-in-supersonic-crossflow (JISCF) have many influential areas of technical applications, amongst them the field of separation control when implemented as air-jet vortex generators. We present results of a combined experiments-numerical work, where we characterize the effects of changing jet-pipe length and jet-exit velocity profiles on the jet-induced structures and the associated separation control effectiveness. The results indicate a strong influence of the state and development of the flow in the pipe on the JISCF field. Consequently, the strength and downstream longevity of streamwise vortices induced by the jets also affect the separation-control effectiveness.

We explore the global stability of flow in a U-bend (180${}^{\circ }$-bend) and compare the results with those in an elbow (90${}^{\circ }$-bend) and toroidal pipes. These findings may have relevance for piping systems as well as bends in blood vessels. We identify a Hopf bifurcation at Re${}_b$=2528, which is consistent with the elbow flow but significantly lower than the torus, suggesting different underlying transition mechanisms in developing and periodic geometries. In our numerical approach, we utilize a novel method that employs adaptive meshes individually designed for the base flow, direct and adjoint disturbances, optimized for both efficiency and accuracy.

The viscous-fingering instability that emerges when gas is injected into a liquid-filled Hele-Shaw cell is a paradigm of pattern formation that has been extensively studied. Here, we examine a previously neglected aspect of the problem: The compressibility of the injected gas. We use experiments, numerical simulations, and an axisymmetric model to show that gas compression controls the time-dependent injection rate and systematically delays the onset of viscous fingering at high capillary number. We quantify the importance of gas compression with a single dimensionless compressibility number.

“Capillary surfers” are small objects that self-propel while floating at the interface of a vibrating fluid bath. In this paper, we construct and analyze a theoretical model for the waves generated by such surfers and thus the hydrodynamic forces exerted by one surfer on another. Our model recovers the dynamical modes of surfer pairs found in experiments, and predicts that surfer collectives may lock into a variety of quantized bound states. Generally, our work shows that capillary surfers are a promising platform for studying wave-coupled active matter.

We experimentally investigate coherent structures of low-Stokes-number particles in the thermocapillary liquid bridge. Particle accumulation structures are found in the $m=1$ azimuthal wave number flow in the liquid bridge $\mathcal{O}$(${10}^{-3}$ m), with spatial structure different from previous research for particles heavier than the test liquid. Coherent structures for particles suspended in the liquid bridge are illustrated in the laboratory and rotating frames. Particles with Stokes number St $\mathcal{O}$(${10}^{-5}$) are tracked to examine formation of coherent structures. We find that two major coherent structures simultaneously emanate from inside the liquid bridge of aspect ratio $\mathrm{\Gamma }=1.6$.

Thermocapillary flow in droplets attached to a heated or cooled wall can undergo various hydrodynamic instabilities. In this work, we explain these instabilities by means of linear stability analysis and present their dependence on the contact angle, Prandtl number, and the heating or cooling mode of operation.

Viscosity gradients induced by heating are ubiquitous in three-dimensional printing, oil extraction, heat exchangers, and other applications where viscous flows and temperature fields are coupled. We investigate the influence of wall heating conditions on the pressure drop-flow rate relationship in narrow pipe flows and determine the asymptotic behavior of the pressure drop in both low and high-Peclet number limits.

Microparticles migrate in gradients of solute concentration through a process known as diffusiophoresis. Several classic works have examined the phenomenon in two dimensions in microfluidic devices where streams of distinct solute concentration meet. We expand on such works by considering, experimentally, numerically, and theoretically, the dynamics of fluid, solute, and particles in three dimensions. We find that diffusioosmotic flow along walls of nonzero surface charge, which yields structures we call “convection rolls,” can be significant to the dynamics.

Wall-pressure fluctuations are of greatest interest in cavitating flows - a threshold phenomenon determined by pressure fields, which are an important source of the corresponding significant vibrations and loud noise in many practical applications. In this article, we measure the wall pressure fluctuations in attached compressible turbulent cavitating flows, and firstly report their statistical behaviors which are independent of cavity regimes.

Compared with Saffman-Taylor fingers, which result from long-range viscous forces, ‘frictional fingers’ are a distinct hydrodynamic phenomenon that is entirely governed by short range forces. Here we develop a theory that describes the shape of a single frictional finger as a function of the ratio between effective surface tension and friction. The width and shape of the finger are those that minimize the power needed to form them as a balance is established between fluid pressure, capillary, and frictional forces.

A novel approach is introduced to measure flow anisotropy at all length scales. It is valid for general fields, including inhomogeneous flows with complex boundaries where traditional Fourier approaches face difficulties. Application to two- and three-dimensional Rayleigh-Taylor turbulence reveals the markedly distinct anisotropy at different scales due to differing energy cascade directions.

In global weather and climate models, the turbulent exchange of momentum, heat, moisture and carbon dioxide between the Earth’s surface and the atmosphere is described by Monin-Obukhov similarity theory (MOST) since 1954. A fundamental assumption of MOST is that velocity near the surface does not follow a logarithmic profile due to buoyancy effects driven by stratification. In contrast to MOST, we find that buoyancy does not change the logarithmic nature of velocity profiles but instead modifies the slope of the log law. The proposed logarithmic profile can serve as an alternative to MOST, possibly leading to more realistic predictions of weather and climate, especially in polar regions.

The vortex dynamics of laminar flow past a rectangular cavity is investigated using numerical simulations and microfluidic experiments. Classical bubble-type vortex breakdown is observed within the cavity, and the evolution and dynamical transitions of the breakdown regions are investigated. The stability and bifurcations of the stagnation points and their transitions to stable/unstable limit cycles are analyzed.

We are interested in the dilution of exhaust gases in aircraft wakes due to the combined effect of wake, mixing, and atmospheric stratification. The aim is to predict the properties of early contrails as a function of the aircraft’s main properties and the state of the atmosphere. Two-dimensional simulations of a passive scalar field representing jets under the action of wake vortices are carried out in a framework that allows a wide parametric study of aircraft and atmospheric parameters. The figure shows the evolution of vortex position (dashed lines) and ice mass (solid colors) for a B777 with a relative humidity of 140% and two atmospheric stratification conditions.