Solitary waves on the surface of a vertically falling liquid film in contact with an extremely confined counter-current gas flow are studied numerically. As the gas velocity is increased, traveling waves display a secondary oscillatory instability and then a catastrophic instability. The periodic amplitude modulations produced by the oscillatory instability intensify mixing and can be tuned through the gas velocity. The catastrophic instability leads to wave reversal and liquid arrest.

Small differences in the size of colliding chemically active droplets lead to three strikingly different dynamic behaviours: (i) an asymmetric rebound where both droplets reverse directions, (ii) a chasing regime leading to a bound state with both droplets swimming together, and (iii) a pausing regime where the larger droplet is temporarily stopped. Such diversity and sensitivity of the exact droplet properties may influence the complex collective dynamics of chemically active droplets.

Particles are a useful tool for studying superfluid turbulence and visualizing quantum vortices. We study the dynamics of inertial particles in finite-temperature quantum turbulence with the two-fluid Hall-Vinen-Bekarevich-Khalatnikov model. We find that, at low temperatures, when the superfluid mass fraction is dominant, particles cluster on superfluid vortex filaments regardless of their physical properties, as in the figure. Furthermore, under strong counterflow, the flow is dominated by quasi-two-dimensional large-scale structures that govern the spatial distribution of particles.

External forces, such as gravity, influence swimming microorganisms. For flagellar microorganisms, such as Chlamydomonas, gravitactic swimming has been attributed to back-heaviness. Using a simple bead-spring microswimmer model, we show that back-heaviness is not necessary for the gravitactic swimming of flagellar microorganisms. The hydrodynamic interaction among beads results in the alignment of swimming direction with external force. By modulating flagellar beating patterns a microorganism can also change its swimming direction. This understanding can aid in the design of robotic swimmers.

A first experimental characterization of low Reynolds number, oscillating grid generated, and near-surface turbulence in shear-thinning dilute polymer solutions is presented. Energy transfer and horizontal damping mechanisms are evidenced. The evolution of the viscous sublayer depth can be explained by both viscous and shear-thinning effects.

Existing studies on sound propagation in rarefied gases are extended to consider wave transmission at nonadiabatic ambient conditions, where arbitrarily large reference temperature and density gradients prevail. Asymptotic analysis of the acoustic field is carried out in the limit of small Knudsen numbers and high actuation frequencies, for both mechanical and thermal wall excitations.

We study rotary fragmentation dynamics and final droplet size distributions with a simple physical model. From animals drying their wet fur by rapidly shaking their body to automated rotary atomization in paint coating, centripetal acceleration is widely used to disintegrate liquid films into smaller fragments. However, little is known about the underlying physics and the liquid property effects on overall droplet size distributions. By performing a series of fragmentation tests with various viscous and viscoelastic liquids we are able to construct a simple and accurate physical model.

The generation and rise of bubbles in gas-liquid-solid flow systems are investigated by employing a coupled discrete element model and volume of fluid method. The calculation results disclose that the existence of solid particles has an important effect on the formation of bubbles. The causes of these results are analyzed through a velocity vector diagram of the flows, and the factors affecting the detachment time of the first bubble are also investigated.

Capitalizing on the full potential of latent heat of vaporization, boiling is among the most efficient heat transfer schemes. Further enhancement of boiling heat transfer relies on precise control of bubble dynamics, which can be realized on a surface endowed with heterogeneous wettabilities. However, such ordered bubble behavior could fail when the triple-phase contact line gets dislodged from the hydrophilic-hydrophobic border by accelerated bubble expansion. Here, a numerical study of the critical condition for the transition between the pinned- and depinned-contact-line modes is presented.

The retraction dynamics of water droplets impacting on surfaces with different wettabilities is studied. Three modes of droplet retractions can be classified as inertial, capillary, and spherical-cap. A new model is proposed to predict the inertial-mode retraction rate of water droplets on different surfaces. The scaling of retraction curves is revised to reveal the similarity behavior of droplet retraction dynamics.

When a bubble bursts at a liquid surface, it creates a jet that destabilizes into an aerosol of a few droplets. The gigantic number of bubbles that burst every second at the surface of the oceans form the sea spray. By evaporating, this spray plays a key role in the exchange between the ocean and the atmosphere. The dynamics and the evaporation of the drops generated by a large range of bubbles bursting are presented, and it is shown that they all have to be taken into account in the evaporation process.

A multicomponent lattice Boltzmann algorithm shows that droplet breakup in a generic time-dependent flow is highly dependent on the flow startup conditions. Confinement plays a crucial role as well. For a system with strong confinement, an adiabatic increase of the maximum shear intensity may drive the system into a metastable state, which has a much higher critical capillary number than the stable state.

What is the initial regime of coalescence when two drops just touch at a point? This long-standing problem has proven formidable because of the smallness of the bridge that is required to connect the drops at the initial instant in any continuum simulation. Here, initial bridge radii, heights, and radii of curvature as small as 10${}^{-6}$, 10${}^{-12}$, and 10${}^{-18}$ are achieved, showing that coalescence always begins in a Stokes regime. The inertially limited viscous regime is shown to be a Taylor-Culick-like regime seen only when drops are initially separated by a finite distance.

Beautiful, elusive shapes are obtained when a water droplet deposited on a nonwetting substrate is subjected to a strong vertical impulse. Drops are highly reshaped to form truncated cones that eventually collapse. The evolution of the geometrical features of these so-called “vase-shaped droplets” is reported and discussed.

The small-amplitude oscillation of a liquid droplet suspended in an immiscible host liquid is studied, where both liquids are assumed viscoelastic. An analytical characteristic equation is derived, and the damping rate and angular frequency that describe the droplet oscillation are numerically solved. The effect of the properties of the host liquid, including its density, viscosity and elasticity, on the viscoelastic droplet oscillation is examined for the quadrupole mode. The host liquid is found to make the droplet oscillation more complex and the mechanisms behind that are discussed.

The dynamical phase behavior of a spheroid with a magnetic dipole rotating in a shear flow and external field is investigated theoretically. Depending on the ratio of the torques due to the shear flow, a sequence of bifurcations leads to a rich complexity in the phase portraits in orientation space. We also find that the dynamics of an ideal thin rod could be very different from that of a high aspect ratio spheroid.

The cross-streamline migration of a spherical particle undergoing electrophoresis in weakly inertial or viscoelastic simple shear flow is quantified via asymptotic analysis. The findings for the migration direction and speed are in reasonable agreement with previous experimental studies on migration of electrophoretic colloids in Poiseuille microchannel flow.

A new method to predict the linear evolution of disturbances in three-dimensional inhomogeneous boundary layers is proposed, named RTPSE, in which the line-marching parabolized stability equation (PSE) is improved by applying ray tracing (RT) theory. Results show that RTPSE can accurately predict the spanwise wave number and amplitude ratio for both stationary and traveling crossflow waves, while the traditional PSE could not.

Randomized numerical algebra is incorporated into resolvent analysis to reduce large-scale resolvent operators to their low-rank approximations. The key to finding the resolvent modes accurately is to weigh the random test matrix using insights from the base flow. Turbulent flow over a NACA0012 airfoil at Re = 23,000 is used to demonstrate significant speedup and memory savings to accurately find principal resolvent modes.

In diverse applications such as enhanced oil recovery and carbon sequestration, solute A in fluid 1 diffuses into fluid 2 where it reacts with solute B following A + B → C. Pore-scale simulations based on the lattice Boltzmann method reveal intricate density-driven instability and differential diffusion effects. New fingering regimes are observed under certain combinations of density ratios, diffusivity ratios, and Rayleigh number ratios among the participating fluids and species.

A common model problem for discrete-object coating is the flow of a thin nonvolatile liquid film on the outside of a rotating cylinder. However, the behavior of a volatile particle-laden coating on rotating cylinders has yet to be studied and remains an important open problem. In this work, a lubrication-theory-based model is used to (i) examine the effects of various problem parameters on coating behavior, (ii) understand the underlying physical mechanisms, and (iii) provide guidance for improving coating uniformity.

Tears of wine, in which a thin layer of a water-ethanol mixture travel up an inclined surface against gravity and then fall down in the form of tears, have been observed in wine glasses for centuries. It has been modeled with a conservation law with a nonconvex flux and higher order diffusion due to the bulk surface tension. The resulting nonclassical “undercompressive” shock solutions are the main driver of the destabilizing front forming the “wine tears”. Prior modeling did not address the wine tears but rather the behavior of the film at earlier stages and the behavior of the meniscus.

Fingering during fluid-fluid displacement in porous media can be governed by two primitive parameters—capillary number and mobility ratio. Here, for porous media consisting of two or more distinguishable scales of pores, the dynamics of immiscible fingering under the influences of hierarchical structures are unravelled. In particular, the conditions under which the fingering pattern mode can be switched and controlled as a result of secondary pore structures are presented.

The defect-mediated turbulence occurring in the bubbly Taylor-Couette flow patterns is investigated experimentally and discussed in the framework of the Ginzburg-Landau theory using a new control parameter $\alpha$, which is the ratio between the Reynolds number of the gas and the Reynolds number of the liquid.

Predicting the flows of dense granular media is still a challenging issue. Here, numerical discrete element method simulations are used to investigate the diversity of patterns within granular jumps that accompany height, velocity, and density discontinuities in gravity-driven free-surface flows. It is demonstrated that standing granular jumps can serve as a useful gauge for evaluating the dissipation mechanisms that govern the flowability of granular media.

Computational fluid dynamics–discrete element method simulation results demonstrate the bubble collapse phenomenon observed in a prior experimental study when two bubbles are injected side-by-side into an incipiently fluidized bed. Results confirm that one of the bubbles collapses when there is a slight size difference between the two bubbles and its extent is beyond a critical value. The collapse occurs because of a preferential gas channeling toward the larger bubble, which leaves the smaller bubble without sufficient gas flow to support its shape.

Fluid-particle interaction is studied in plane Couette flow by considering a nontrivial equilibrium solution that features exact coherent structures representative of wall-bounded shear flows. Despite the advantage of a much reduced complexity in comparison with a true turbulent flow, this strategy is shown to reproduce the phenomena of particle preferential concentration. The proposed approach is expected to be fruitful in future studies on various aspects of particulate flow, and perspectives for future works are also discussed.

We use three-dimensional Voronoi tessellation to perform a local analysis of particle motion in isotropic turbulence while independently varying the flow Reynolds and Froude number, and particle Stokes number. Among other interesting findings, our local analysis shows that in flow regions where particles are clustered, fluid accelerations at the particle positions are significant. These results call into question the validity of the “sweep-stick” mechanism for particle clustering in turbulence, which states that inertial particles cluster in flow regions where the fluid acceleration is zero.

Dense frictional particulate suspensions in a viscous liquid respond to applied shear in a complex manner that includes continuous or discontinuous shear thickening. This change in rheology as a function of particle packing fraction and/or applied stress is associated with a formation of complex interaction networks that develop on a mesoscopic scale. The properties of these networks, analyzed by the newly developed tools based on persistent homology in both two and three spatial dimensions, are found to be closely related to the macroscopic system response.

The erosion onset and kinetics of weakly cohesive granular materials based on experimental data from optically adapted jet erosion tests is investigated. The scouring kinetics are examined qualitatively for samples with an intergranular cohesion induced by either liquid or solid bonds. From a quantitative perspective, the erosion onset for the case of solid bond cohesion is here described by a generalized form of the usual Shields criterion including a cohesion number defined from yield tensile values considering both the micro- and macroscales.

When granular matter is involved in a confined two-phase flow, three ingredients that do not usually occur together must be considered in parallel: viscosity, capillarity, and solid friction. The displacement regimes of a gas-liquid interface along a horizontal millifluidic tube containing a sedimented granular phase are documented in detail. Experimental observations are made with a simple setup, and an associated theoretical interpretation that can describe a spectrum of capillary bulldozing regimes is developed.

Synthetic turbulent boundary flow fields generated based on the attached eddy model are compared to experimental data in wall-parallel and wall-normal planes. In doing so, a modification to the placement of the representative eddies in the attached eddy model is proposed that incorporates the meandering of the flow structures. Results reveal that this subtle modification provides a superior spatial representation of a turbulent boundary layer from the attached eddy model.

Fundamental results in nonequilibrium thermodynamics are shown to be associated with small-scale features of turbulent flows. The estimation of entropies allows the selection of distinct realizations of turbulent cascade trajectories through a hierarchy of spatial scales. Entropy-consuming cascade trajectories lead to small-scale intermittent structures with piling up of velocity increments and finite “jumps.” This finding is of interest for fundamental questions on singularities or rare extreme velocity gradients.

Turbulent flows famously display a net cascade of energy from the injection scales to the dissipation scales. This cascade can be interpreted as the interplay of an emergent turbulent stress and a scale-dependent strain rate, which reveals the key role of geometric alignment in the energy transfer process. It is argued that the constraints placed on the cascade process by geometry are surprisingly significant and may provide important but under-appreciated ingredients for understanding turbulence phenomenology.

The turbulence in a fast rotating fluid becomes effectively two-dimensional. The inverse energy cascade leads to formation of coherent columnar vortices. An analytical theory describing interaction of such a vortex with turbulent pulsations is developed. The radial velocity profile of the vortex is established.

Nonuniform stratification and vertical confinement significantly restricts the development of triad resonant instability for low mode internal gravity waves with and without background rotation.

The Benjamin-Feir, or modulational, instability has been regarded as the main mechanism of spontaneous disintegration of broad weakly nonlinear wavepackets in deep water waves. We report water wave experiments with another result. For a range of initial parameters, a nearly rectangular initial wavepacket develops a strongly nonlinear modulation with two dispersive shock waves expanding from the edges of the wavepacket towards the center at finite speed. This is supported by theory based on the semiclassical limit of the one-dimensional focusing nonlinear Schrodinger equation.