A mathematical study of imbibition into a converging capillary with wettability gradient that can potentially act as a liquid diode.

High-speed visualization identifies the formation mechanism of microscopic saliva droplets during the phonation of plosive consonants: as moist lips open, there is a sequence of film formation and rupture into vertically attached filaments, which subsequently extend over centimeter-scales and destabilize into droplets due to the fast airflow of speech. The formation process ties this aerosolization mechanism to drop formation in wind instruments and to meter-long, speech-driven transport important to asymptomatic transmission of airborne pathogens.

Fire whirls (FW) are whirling, turbulent, cylindrical yellow (sooting) flames that form naturally in wildfires. In contrast, the blue whirl (BW) is a laminar, blue (non-sooting) flame with an inverted conical shape, that forms at much smaller scales. The relative influence of circulation and buoyancy on the transition between these regimes is investigated with a scaling analysis. We find that FWs are generally formed in a buoyancy-dominated regime, and BWs in a circulation-dominated one. Our results support a previously suggested theory that the transition from a FW to a BW is enabled by the formation of the bubble mode of vortex breakdown.

Using classical and $ab$ $initio$ molecular dynamics simulations, we calculate the frequency-dependent shear viscosity of pure liquid water and water–glycerol mixtures. In agreement with recent experiments, we find deviations from Newtonian-fluid behavior in the THz regime, and introduce a continuum viscoelastic model (CVM) to describe the observed viscosity spectrum of pure water. We relate features of the CVM to the microscopic dynamics of water molecule clusters. Our model bridges hydrodynamic and molecular approaches to water dynamics, quantifying the viscoelastic response on short timescales where a Newtonian-fluid model breaks down.

We address uncertainties which remain in the statistical features of atoms spontaneously emitted from the liquid phase. By numerically solving the Enskog-Vlasov (EV) equation, we find that the distribution function of evaporated atoms is well approximated by a drifted bi-Maxwellian. The drift velocity and the temperature anisotropy reduce as the liquid bulk temperature decreases. Deviations from the undrifted isotropic half-Maxwellian are explained, based on a simple mathematical model, by collisions occurring in the liquid-vapor interface which preferentially backscatter atoms with lower normal-velocity component.

An investigation into what triggers flow reversals in thermal convection, especially in two-dimensional enclosures, explores whether it is due to the corner roll growth process or the core bulk region instabilities, and examines the effect of enclosure shape. Using direct numerical simulations, it is shown that the flow reversals are due to the core bulk region instabilities.

Thermal convection experiments with strongly varying fluid properties, when the Oberbeck-Boussinesq (OB) condition is violated, are presented. By using compressed sulfur hexafluoride above its critical point, measurements with different degrees of fluid property variations are conducted, while keeping the Rayleigh and Prandtl number fixed. The vertical heat transport is significantly enhanced under non-OB conditions, which is explained with an increase of the density and heat capacity in the bulk due to asymmetries in the vertical temperature profile.

An experimental study of the supercooling solidification of an axisymmetric vertical liquid bridge under the influence of gravity is carried out. An ice ring is formed at the end of the freezing process because of the instability of the liquid bridge. A model considering gravity and the supercooling effect is developed to describe the freezing of liquid bridge.

In-flight collisions between a regular stream of droplets and a continuous liquid jet enable the production of controlled structures, which may be hardened for various applications such as liquid encapsulation. Experiments show that both the drop and jet viscosities have a major, yet very different influence on the geometry of the created structures and their evolution. Models based on the hydrodynamics of the drop and jet support these observations and provide a first guide on how each viscosity can be used to better shape the structures produced by in-air microfluidics.

Linear electrokinetics often results in simple unidirectional flows in porous media. Surprisingly, for a heterogenous random media, pore-scale disorder results in vortical flow structures at the macroscopic scale, which can lead to enhanced fluid mixing and convective transport.

Using a high-accuracy-and-resolution implicit Large Eddy Simulation we study the development of the bottom boundary layer (BBL) driven by the long separation bubble which forms under an internal solitary wave (ISW) of depression propagating against a barotropic background current. We obtain insights on the structure of the initial instability in the form of a global mode with a distinct transverse structure, and that of the self-sustained transition and resulting fully developed turbulence along the bed. Comparisons are made to similar flow features previously found in shorter separation bubbles typical of applications in aerodynamics.

Building on its predecessor, this paper investigates the relaxation of the near-bed turbulent wake developed behind a long, laminar separation bubble induced by an internal solitary wave (ISW). The decay of the wake to a zero pressure gradient turbulent boundary layer is investigated in terms of the mean flow and turbulent kinetic energy. “Loss of memory” of the ISW-induced separation occurs faster for the mean flow than it does for its fluctuating counterpart whose far-bed component retains a persistent signature of the ISW-induced pressure gradient as compared with the near-bed turbulence.

Linear disturbance development in the Stokes layer subjected to high-frequency harmonic noise is investigated using numerical simulations. In the absence of noise, disturbances exhibit subharmonic behavior and an absolute form of instability. Inclusion of high-frequency noise establishes a strong destabilizing effect and changes the character of the absolute instability.

The large-scale flow around turbulent spots in plane shear flows decays algebraically away from the turbulent zone. The decay exponent depends only on the symmetries of the flow, independently of the Reynolds number and spot morphology.

The doubly diffusive convection of a fluid subject to horizontal gradients of temperature and salinity and placed in a closed container of large extent in the vertical direction is considered. This configuration displays a sudden transition to chaos at the parameter value where the conduction state loses stability. This transition is characterized and related to simple dynamic phenomena, hinting at its genericity.

A parametric numerical study of three-dimensional instability of steady flows in a helical pipe of arbitrary curvature and torsion is carried out. The stability results are reported as dependences of the critical Reynolds number, critical wave number, and the critical frequency on the dimensionless pipe curvature and torsion. Patterns of several most unstable modes are reported and classified. Different routes to instability by viscous and inviscid mechanisms are discussed.

Splashes are ubiquitous in nature and engineering, and they govern processes from diving to ocean oxygenation. Yet, to date, it is not understood when or why a splash sometimes seals and sometimes does not. Supported by theory and experimental observations, a detailed analysis is presented, and a critical dimensionless number that predicts the occurrence of a surface seal is uncovered.

When a water drop is deposited on a hole drilled in a superhydrophobic plate in contact with a bath of water from underneath, the liquid in the drop will transport into the bath and a jet is then produced. It is found that the evolution of the drop diameter $D(t)$ with time $t$ obeys scaling relations $D(t)\sim t^{2/7}$ and $D(t)\sim t^{1/2}$ for small drops and large puddles, respectively, arising from the competition between the surface tension and inertia.

The motion induced by osmosis of oil on a solid substrate immersed in water is investigated with two microfluidic systems. The first one allows for assessing water flux dynamics, linked to water permeability of oil, and the second one allows for probing oil removing features from a model porous system through this osmotic driven mechanism that depend on wetting properties.

Large-scale molecular dynamic simulations are used to investigate the velocity dependence of the dynamic contact angle of a waterlike liquid on a flat carbonlike solid surface and to extract the coefficients of contact-line friction. It is shown that the same coefficients are obtained from a Langevin model of contact-line fluctuations at equilibrium, without any additional theoretical interpretation or model. A mechanistic link between the coefficients of slip and contact-line friction is also confirmed.

Mode coupling is used to study two-dimensional Stokes flows produced by suction or injection flux, in which two fluids react upon contact, forming an elastic interface. The interplay of viscous and elastic effects reveals the formation of nonlinear suction-driven patterns having near-cusp structures.

Lattice Boltzmann simulations along with a diffuse interface model are used to simulate the capillary driven, symmetric spreading of a fluid drop on another fluid-fluid interface. While the equilibrium shapes of the drops with negative spreading coefficient are comprehensively represented on a phase diagram, the dynamics leading to equilibrium shapes are shown to be universal with power-law behaviors exhibited only in the limit of the small spreading coefficient.

Evaporating films consisting of binary mixtures may exhibit markedly different stability characteristics depending on their properties (e.g., different volatility ratios).

The influence of the surface roughness on the fluid flow through fracture joints is investigated through numerical simulations of the Navier-Stokes equations. Using the Hurst exponent to characterize the roughness of the self-affine surfaces that constitute the fracture, the results reveal the important interplay between geometry and inertia on the flow. A universal curve is then proposed to describe the variation of the overall hydraulic resistance of the fracture with Reynolds number at laminar flow conditions and for distinct values of the Hurst exponent.

Electro-osmotic flow is a commonly-used method to manipulate fluids in microdevices, often fabricated from soft materials like PDMS. We show that electro-osmotic flow systems may exhibit viscous-elastic interfacial instability. To provide insight on the underlying instability mechanism, we theoretically model an electro-osmotic flow interacting with an elastic substrate, and find that instability can result in asymmetric deformation, even for symmetric actuation. In addition to instability, the system nonlinearity, arising from the inverse dependence of the electro-osmotic actuation on the film thickness, results in hysteresis.

Active navigation in food searching, survival, and mating has led to the evolution of diverse strategies in natural living systems. We study navigation of microscopic gradient-sensing agents that orient among possible paths via sensing of a diffusible substance’s concentration, first with experiments on colloidal particle migration along concentration gradients by diffusiophoresis. We treat particle exit time as a mean first passage time (MFPT) problem and show that a separatrix concentration gradient determines path taking statistics. We confirm numerically that an MFPT discontinuity hinders microscopic agents in following the shortest path.

In suspensions of self-propelled Janus phoretic colloids, chemically mediated interactions generate spontaneous collective dynamics. A kinetic model of such dilute phoretic suspensions demonstrates how these phenomena may be promoted, hindered, or even suppressed by the particles’ self-propulsion velocity, depending on their detailed surface properties. The long-term dynamics are characterized by the competition between the stirring effect of the flow field generated by the particles and the formulation of regular patterns resulting from chemical interactions.

A particle carried by a wall-normal flow can get critically close to the wall, depending on the particle radius compared with the flow boundary-layer thickness, on the surface effective roughness, and on the particle-to-fluid density ratio. At sufficiently large inertia, the particle bounces back. The rebound velocity of a neutrally buoyant particle at the stagnation point at the wall is examined. The rebound height of a particle pair approaching the stagnation point is surprisingly large compared with that of single particle.

We show that statistics from simulations of particle-laden turbulent flows modeled by the point-particle Euler-Lagrange methodology diverge with mesh refinement when the undisturbed fluid velocity used in the drag force that couples the dispersed and continuous phases is not properly modeled. For decaying homogeneous isotropic turbulence, fluid and particle energies, particle acceleration, and energy dissipation rates are found to be grid insensitive only when the undisturbed fluid velocity is robustly modelled. Ultimately, this work provides insight into what types of questions are answerable using two-way coupled point-particle methods.

A basis function expansion and transformation technique are generalized to find a vector variable solution around two separated spheres where the Brinkman equation governs the field. Addressing this problem can lead to a derivation of the flow field over many porous spheres and quantify how the unsteady dynamics of many Brownian particles cumulatively affects stochastic motion.

Understanding and quantifying the ability of gas to entrain and maintain particles in a liquid is a challenge in many fields. Here, an experimental study of the formation of a suspension by injecting gas at the bottom of a submerged granular bed is presented. The suspension packing fraction in the stationary state results from the balance between particle entrainment by bubble rise and sedimentation and can be well captured by a simple model.

During evaporation in a simple model porous medium, the pores occupied by gas can be refilled with liquid, snapping off a gas bubble, which then moves to a stable configuration. This phenomenon, referred to as capillary instability, is explored based on the optical images obtained from visualization experiments. For better understanding of the capillary instability induced gas-liquid displacement, a pore network model that accounts for capillary and viscous forces as well as the inertial effect is developed

The behavior of settling particles in homogeneous shear turbulence is investigated using direct numerical simulation. The two-dimensional pair-correlation distribution of particles is introduced to quantify the anisotropic clustering. Small-scale clustering displays a multifractal nature with an explicit angular distribution.

Artificial neural networks (ANNs) have recently been applied to several fluid dynamics applications. However, there are a very limited number of studies that assess the fidelity of ANN deployments, a function of algorithm choice and training data quality, by quantifying uncertainties in predictions. This diminishes their utility for practical modeling requirements. In an effort to address this, a probabilistic NN that provides confidence intervals for its predictions in a computationally effective manner is used. This approach is demonstrated in surrogate modeling and flow reconstruction tasks with promising results.

A systematic model is established to quantitatively predict the evolution of Rayleigh-Taylor turbulence at three different mixing levels and density ratios. Our predictions show great correspondence with the previous experiments and simulations and make an appropriate explanation for the distinct differences existing in experiments.

Convective dissolution, relevant to CO${}_2$ geological sequestration, occurs when a given species dissolves in a host phase and increases density. Chemical reactions have been shown to enhance this convection. If the chemical species involved diffuse at different rates, an additional convection zone due to double-diffusion processes can develop below the reaction front in addition to the dissolution-driven Rayleigh-Taylor instability below the interface. An analysis of the influence of the interaction between these various convective modes on the nonlinear dynamics and on the dissolution flux is presented.

The velocity field in a straight pipe was filtered to differentiate large-scale-motions (LSMs) and very-LSMs (VLSMs) to distinguish their contributions to wall shear stress fluctuations. A conditional averaging method was applied to examine VLSM and LSM influences on negative wall shear stress fluctuations. A pair of counter-rotating roll modes was found in VLSMs with length scales λ_x > 3R. However, in LSMs, for which 0.6R < λ_x < 3R, counter-rotating vortex pairs were not observed. The length scale threshold (3R) for generating counter-rotating vortex pairs in pipe flow is thus higher than that (1δ) reported for turbulent boundary layers.

The vortex stretching mechanism is studied in fully developed turbulence using direct numerical simulations at high Reynolds numbers with unprecedented small-scale resolution. Various statistical correlations characterizing amplification of vorticity by the strain rate are identified, especially as a function of Reynolds number and strength of vorticity fluctuations, uncovering many previously unknown aspects of the vortex stretching process.

Rotating turbulence can show two macroscopics states: split cascade state, where large vortices are formed under the fast rotation limit, and a direct cascade state, where the flow is isotropic and energy goes only to the small scales. A study shows that a third state exists in between these two, where large vortices are formed but get stuck in a crystal-like formation. As vortices cannot move and merge, the transfer of energy to the large scales of the system is halted. Evidence suggests that these new states are metastable.

We show that wall-bounded turbulence can be relaminarized and reorganized by adding nonuniform streamwise body forces. A nonuniform body force can distort the parabolic mean velocity profile, thus altering turbulence production due to mean shear. In the quasi-laminar state, all Reynolds stress tensor components are fairly weak except for streamwise fluctuations far from the wall, indicating a collapse of the near-wall turbulence self-sustaining cycle. In the recovered turbulence regime, the Reynolds shear stress has a negative range in the bulk connected with a positive range near the wall corresponding to the M-shaped velocity profile.

A quantitative link between the imbalance of sweep and ejection events, asymmetry in the velocity distribution, and the turbulent transport of shear stress in boundary-layer flows over several smooth and rough surfaces is evaluated. The linkage is captured by two model expressions that predict the turbulent stress transport. The models provide a pathway to improved shear stress closure and offer a new perspective on roughness effects in the near-wall region of the flow.

An extension to the attached eddy model (AEM) of wall turbulence is presented, where, in addition to the self-similar wall-attached eddies (Type A), we include two new eddy types for better predictions of the total kinetic energy. The first eddy type (Type SS) represents the wall-coherent very-large-scale motions, and the second eddy type (Type C${}_{\text{A}}$) is representative of the wall-incoherent but self-similar small-scale energetic motions. The extended AEM better predicts the energy spectra of all three velocity components across a broad range of Reynolds numbers.

The origin of nonclassical behavior in grid turbulence is traced back to the mean flow induced by the wakes of the grid bars. A simple model captures and explains the main nonequilibrium features of the flow.

High-resolution direct numerical simulations of incompressible turbulence with Taylor-scale Reynolds number up to 2250 show that there exists a scaling-range (approximately $100<r/\eta <400$), in which the two-point second order velocity structure functions fit well to a simple power law scaling with respect to the distance $r$ between the two points, where $\eta$ is the Kolmogorov length scale. However, the prefactor of the power law depends on the Reynolds number.

Quantum vortex reconnections represent an extremely intense (fast in time and short in length scales) process in superfluid hydrodynamics: vortices suddenly lose energy and momentum. Such a loss is compensated by the emission of a directional sound pulse. Here, a mathematical characterization of the energy and momentum exchanges between the vortical and compressible modes during a single reconnection event is provided.

The interaction between a steady open channel flow and a laterally connected cavity can trigger high-amplitude free-surface oscillations, or “seiches.” An experimental laboratory study investigates the bidirectional (waves excited in both directions simultaneously) and intermittent behavior of seiching in a square cavity as a function of the Froude number of the main stream. A combination of analytical approaches shows that the amplitude of the two excited modes fluctuates significantly in the course of a single experiment, such that bidirectional seiching cannot be considered a steady phenomenon.

We consider compressible dissipationless fluids in two dimensions with broken parity symmetry (odd viscosity) and free surface boundary conditions. In the absence of shear viscosity, compression generates dissipationless vorticity near the boundary, enabling the application of a variational principle to derive a flow and dispersion relation for surface waves. We show that this leads to the emergence of spontaneously propagating chiral surface waves. The result is applicable to compressible fluids with broken parity symmetry ranging from electron fluids in graphene to out-of-equilibrium chiral active matter.