We consider an isotropic compressible nondissipative fluid with broken parity subject to free surface boundary conditions in two spatial dimensions. The hydrodynamic equations describing the bulk dynamics of the fluid and the free surface boundary conditions depend explicitly on the parity-breaking nondissipative odd viscosity term. We construct an effective action which gives both bulk hydrodynamic equations and free surface boundary conditions. The free surface boundary conditions require an additional boundary term in the action which resembles a $1+1\mathrm{D}$ chiral boson field coupled to the background geometry. We solve the linearized hydrodynamic equations for the deep water case and derive the dispersion of chiral surface waves. We show that in the long-wavelength limit the flow profile exhibits an oscillating vortical boundary layer near the free surface. The layer thickness is controlled by the ratio between the odd viscosity (${\nu }_o$) and the sound velocity ($c_s$), $\delta \sim {\nu }_o/c_s$. In the incompressible limit, $c_s\to \infty$, the vortical boundary layer becomes singular with the vorticity within the layer diverging as $\omega \sim c_s$. The boundary layer is formed by odd viscosity coupling the divergence of velocity $\mathbf{\nabla }·\mathit{v}$ to vorticity $\mathbf{\nabla }\times \mathit{v}$. It results in nontrivial chiral free surface dynamics even in the absence of external forces. The structure of the odd-viscosity-induced boundary layer is very different from the conventional free surface boundary layer associated with dissipative shear viscosity.

We report on Rayleigh-Bénard convection with strongly varying fluid properties experimentally and theoretically. Using pressurized sulfur-hexafluoride (${\mathrm{SF}}_6$) above its critical point, we are able to make measurements at mean temperatures ($T_m$) and pressures ($P_m$) along Prandtl-number isolines in the ($T,P$) parameter space. This allows us to keep the mean Rayleigh- (${\mathrm{Ra}}_m$) and Prandtl number (${\mathrm{Pr}}_m$) constant while changing the temperature dependences of the fluid properties independently, e.g., probing the liquidlike or gaslike region that are left and right of the supercritical isochore. Hence, non-Oberbeck-Boussinesq (NOB) effects can be measured and analyzed cleanly. We measure the temperature at midheight ($T_c$) as well as the global vertical heat flux. We observe a significant heat transport enhancement of up to $112\%$ under strong NOB conditions. Furthermore, we develop a theoretical model for the global vertical heat flux based on ideas of Grossmann and Lohse (GL) in OB systems, adjusted for nonconstant fluid properties. In this model, the NOB effects influence the boundary layer and hence $T_c$, but the change of the heat flux is predominantly due to a change of the fluid properties in the bulk, in particular the heat capacity $c_p$ and density $\rho$. Predictions from our model are consistent with our experimental results as well as with previous measurements carried out in pressurized ethane and cryogenic helium.

Janus phoretic colloids (JPs) self-propel as a result of self-generated chemical gradients and exhibit spontaneous nontrivial dynamics within phoretic suspensions, on length scales much larger than the microscopic swimmer size. Such collective dynamics arise from the competition of (i) the self-propulsion velocity of the particles, (ii) the attractive/repulsive chemically mediated interactions between particles, and (iii) the flow disturbance they introduce in the surrounding medium. These three ingredients are directly determined by the shape and physicochemical properties of the colloids' surface. Owing to such link, we adapt a recent and popular kinetic model for dilute suspensions of chemically active JPs where the particle's far-field hydrodynamic and chemical signatures are intrinsically linked and explicitly determined by the design properties. Using linear stability analysis, we show that self-propulsion can induce a wave-selective mechanism for certain particles' configurations consistent with experimental observations. Numerical simulations of the complete kinetic model are further performed to analyze the relative importance of chemical and hydrodynamic interactions in the nonlinear dynamics. Our results show that regular patterns in the particle density are promoted by chemical signaling but prevented by the strong fluid flows generated collectively by the polarized particles, regardless of their chemotactic or antichemotactic nature, i.e., for both puller and pusher swimmers.

Accurate quantification of turbulent mixing induced by classical Rayleigh-Taylor instability is of fundamental importance for many natural phenomena and engineering applications. However, a systematic model to predict its evolution at different mixing levels and different density ratios ($R$) has not been established. In this paper, the mixing width is predicted by combining the principle of mass conservation and mean density profile. The mean density profile, as well as the mean profiles of mass fraction and molar/volume fraction, are predicted with $R$-invariant hybrid species profiles from asymptotic analysis. The unknown turbulent fluctuations are closed with the predicted mean quantities, yielding analytical predictions for mixing degree and mixed mass. The predictions agree very well with previous experiments and simulations, explaining the distinct differences that exist among the famous experiments.

Convection can develop upon dissolution of a given species A in a host phase when dissolution leads to a buoyantly unstable density stratification. If A reacts with a solute B present in the host solution according to a bimolecular $\mathrm{A}+\mathrm{B}\to \mathrm{C}$ reaction, convective dissolution can be enhanced or slowed down depending on the relative contribution to density of each chemical species. We study numerically the influence of differential diffusion on such reactive convective dissolution in the nonlinear regime. In particular we compute the temporal evolution of the dissolution flux, its asymptotic value and the onset time of convection as a function of the ratio of the diffusion coefficients. We find that, when B diffuses faster than C, the density profiles can exhibit a local minimum below the reaction front where a double-diffusive instability develops. This has a destabilizing effect and leads to enhanced mixing, earlier onset of convection, and increased asymptotic fluxes. On the other hand, when B diffuses slower than C, the density profiles can contain a local minimum at the reaction front followed by a local maximum below, which gives rise to two convection zones with a diffusive-layer convection instability occurring below the reaction front. The overall dynamics is stabilizing with delayed onset of convection and with smaller asymptotic fluxes. When B and C diffuse at an equal rate but differently from A, differential diffusion can accelerate or slow down convection.

In grid turbulence, not so far behind the grid, an average flow can be observed with a close to sinusoidal velocity profile, corresponding to the wakes behind the grid bars. The kinetic energy of this mean flow decays rapidly and a close to isotropic flow is observed further downstream. We show how these wakes behind the grid bars influence the downstream turbulence. In particular, we investigate the decay rate of kinetic energy, the behavior of the normalized dissipation rate, and the sensitivity of the flow on initial conditions. We show that the initial value of the ratio of the length scale of the turbulence to the mesh-size determines the precise decay of the mean-flow and the generation of the turbulent kinetic energy. We further show how a simple turbulence model can estimate the degree of nonequilibrium and inhomogeneity of grid turbulence and how this model can be extended to take into account disequilibrium observed in direct numerical simulations of decaying isotropic turbulence.

The solidification of liquid bridges plays an important role in many applications. Previous research on droplet solidification has found that supercooling and gravity have certain effects on physical properties and droplet shape during solidification. In this paper, axisymmetric water bridge solidification is studied from theory and experiment. A fixed contact line model, considering both the effects of supercooling and gravity, is developed to describe the freezing behavior of a liquid bridge. In the experiment, two horizontal cold coaxial circular end plates are cooled simultaneously, and a liquid bridge starts freezing from the contact surfaces with the end plates and finally forms an asymmetric ice ring in the middle. A correlation expression of the three-phase contact line height evolution determined by theory and experiment is developed. Comparisons between the calculation and experiment are made, and good agreement is obtained in the first freezing stage.

We have used large-scale molecular dynamics (MD) simulations to investigate the contact-line friction of a waterlike liquid interface moving across a flat solid surface. The dynamic contact angle ${\theta }_D$ has been measured as a function of contact-line speed $U_{cl}$ using two configurations: a liquid drop spreading spontaneously on a stationary solid surface and a liquid bridge in Couette flow between two solid surfaces moving in opposite directions at a range of steady speeds. The wettability of the solid surface was systematically varied to give a range of equilibrium contact angles ${\theta }^0$ from 38 to 126 deg. The coefficient of contact-line friction $\zeta$ was determined from the expression $\zeta U_{cl}={\gamma }_L(cos{\theta }^0-cos{\theta }_D)$, where ${\gamma }_L$ is the surface tension of the liquid. This simple linear equation, which maybe derived from the molecular-kinetic theory (MKT) of dynamic wetting, is predicted to apply at sufficiently low values of $U_{cl}$. In addition, we have applied a Langevin formalism to extract the coefficients of contact-line friction directly from the equilibrium fluctuations of the contact line, without any additional theoretical interpretation or model. Both approaches yield the same values for the coefficient within the probable uncertainty, confirming that this intriguing property is determined only by equilibrium properties. Overall, our results show that contact-line friction is a real phenomenon, intrinsic to wetting and applicable to real liquids such as water. Thus, models of dynamic wetting that ignore it are incomplete. From a practical perspective, the concept of a simple linear relationship between surface tension driving force and contact-line velocity may provide a useful simplification in many areas such as nanotechnology where contact-line speeds can be low. Another finding from our study is that slip between water and a molecularly flat, partially wetted solid surface is minimal, with slip lengths of little more than the diameter of a water molecule for equilibrium contact angles of 90 deg or less. Furthermore, we have confirmed a mechanistic link between the coefficients of slip and contact-line friction, specifically $\beta =\zeta /\delta$, where $\delta$ is the thickness of the contact line when viewed at the molecular scale. Thus measurements of the dynamic contact angle or contact-line fluctuations may potentially be used to predict slip and vice versa.

This paper describes the solution of a vector function around disconnected spheres where the fields are governed by a hybrid between Stokes and Helmholtz equations. The governing relation known as Brinkman equation typically appears to represent the spatial variations in Darcy's flow in porous medium as well as in unsteady Stokesian hydrodynamics. The presented analysis provides a general solution technique of the aforementioned field equation assuming inhomogeneous Dirichlet conditions at the surface of the disconnected spheres and a decaying variation at infinity. The methodology relies on the expansions in multiple sets of vector basis functions corresponding to each sphere. The key result in the formulation is the mutual transformations between the basis functions of two such sets. This allows the derivation of the matrix relations coupling the unknown amplitudes with the given inhomogeneous boundary conditions. The presented mathematical theory is validated by complementing numerical calculations. Accordingly, the solution is constructed using the outlined method, and the error in the form of departure from the intended boundary condition is evaluated. This error vanishes very quickly with increasing number of basis solutions demonstrating high accuracy and exponential spectral convergence of the numerical scheme. The versatility of the method is also demonstrated by describing the flows under both steady and unsteady conditions around particles moving in porous and liquid medium, respectively.

We have studied experimentally particle suspension when injecting a gas at the bottom of an immersed granular layer confined in a Hele-Shaw cell. This work focuses on the dynamics of particles slightly denser than the surrounding fluid. The gas, injected at a constant flow-rate, rises through the granular bed and then forms bubbles that entrain particles in the above liquid layer. The particles settle down on the edges of the cell, avalanche on the crater formed at the granular bed free surface, and are further entrained by the continuous bubbling at the center. We report the existence of a stationary state, resulting from the competition between particle entrainment and sedimentation. The average solid fraction in the suspension is derived from a simple measurement of the granular bed apparent area. A phenomenological model based on the balance between particle lift by bubbles at the center of the cell and their settling on its sides demonstrates that most of the particles entrained by bubbles come from a global recirculation of the suspension.

Two-dimensional (2D) spectra of the streamwise velocity component, measured at friction Reynolds numbers ranging from 2400 to $26000$, are used to refine a model for the logarithmic region of turbulent boundary layers. Here we focus on the attached eddy model (AEM). The conventional AEM assumes the boundary layer to be populated with hierarchies of self-similar wall-attached (Type A) eddies alone. While Type A eddies represent the dominant energetic large-scale motions at high Reynolds numbers, the scales that are not represented by such eddies are observed to carry a significant proportion of the total kinetic energy. Therefore, in the present study, we propose an extended AEM that incorporates two additional representative eddies. These eddies, named Type ${\mathrm{C}}_{\mathrm{A}}$ and Type SS, represent the self-similar but wall-incoherent low-Reynolds-number features and the non-self-similar wall-coherent superstructures, respectively. The extended AEM is shown to better predict a greater range of energetic length scales and capture the low- and high-Reynolds-number scaling trends in the 2D spectra of all three velocity components. A discussion on spectral self-similarity and the associated $k^{-1}$ scaling law is also presented.

In a concurrent work, Villois et al. [Phys. Rev. Lett. 125, 164501 (2020)] reported the evidence that vortex reconnections in quantum fluids follow an irreversible dynamics, namely, vortices separate faster than they approach; such time asymmetry is explained by using simple conservation arguments. In this work we develop further these theoretical considerations and provide a detailed study of the vortex reconnection process for all the possible geometrical configurations of the order parameter (superfluid) wave function. By matching the theoretical description of incompressible vortex filaments and the linear theory describing locally vortex reconnections, we determine quantitatively the linear momentum and energy exchanges between the incompressible (vortices) and the compressible (density waves) degrees of freedom of the superfluid. We show theoretically and corroborate numerically, why a unidirectional density pulse must be generated after the reconnection process and why only certain reconnecting angles, related to the rates of approach and separations, are allowed. Finally, some aspects concerning the conservation of center-line helicity during the reconnection process are discussed.

The relative influence of circulation and buoyancy on fire whirls (FWs), blue whirls (BWs), and the transition between these regimes of a whirling flame is investigated using a combination of experimental data and scaling analyses. FWs are whirling, turbulent, cylindrical yellow (sooting) flame structures that form naturally in fires and are here created in laboratory experiments. In contrast, a BW is a laminar, blue flame (nonsooting) with an inverted conical shape. Measurements of the circulation and heat-release rate are combined with measurements of the flame geometry, defined by the flame width and the height, to provide characteristic length scales for these whirling-flame regimes. Using these, a nondimensional circulation (${\mathrm{\Gamma }}_f^{*}$) and a heat-release rate (${\dot{Q}}_f^{*}$) were defined and shown to correspond to azimuthal and axial (buoyancy driven) momenta, respectively. The ratio ${\mathcal{R}}^{*}={\mathrm{\Gamma }}_f^{*}/{\dot{Q}}_f^{*}$, a quantity analogous to the swirl number used to characterize swirling jets, was evaluated for FWs and BWs. For FWs, ${\mathcal{R}}^{*}<1$, so that axial momentum is greater than azimuthal momentum and the flame is dominated by buoyant momentum. For BWs, ${\mathcal{R}}^{*}>1$, so that the flame is circulation dominated. This is argued to be consistent with vortex breakdown being an important part of the transition of FWs to BWs. This work presents a basis for predicting when a BW will form and remain a stable regime.

Using classical as well as ab initio molecular dynamics simulations, we calculate the frequency-dependent shear viscosity of pure water and water–glycerol mixtures. In agreement with recent experiments, we find deviations from Newtonian-fluid behavior in the THz regime. Based on an extension of the Maxwell model, we introduce a viscoelastic model to describe the observed viscosity spectrum of pure water. We find four relaxation modes in the spectrum which we attribute to (i) hydrogen–bond network topology changes, (ii) hydrogen–bond stretch vibrations of water pairs, (iii) collective vibrations of water molecule triplets, and (iv) librational excitations of individual water molecules. Our model quantitatively describes the viscoelastic response of liquid water on short timescales, where the hydrodynamic description via a Newtonian-fluid model breaks down.

Active navigation relies on effectively extracting information from the surrounding environment, and often features the tracking of gradients of a relevant signal—such as the concentration of molecules. Microfluidic networks of closed pathways pose the challenge of determining the shortest exit pathway, which involves the proper local decision-making at each bifurcating junction. Here, we focus on the basic decision faced at a T-junction by a microscopic particle, which orients among possible paths via its sensing of a diffusible substance's concentration. We study experimentally the navigation of colloidal particles following concentration gradients by diffusiophoresis. We treat the situation as a mean first passage time (MFPT) problem that unveils the important role of a separatrix in the concentration field to determine the statistics of path taking. Further, we use numerical experiments to study different strategies, including biomimetic ones such as run and tumble or Markovian chemotactic migration. The discontinuity in the MFPT at the junction makes it remarkably difficult for microscopic agents to follow the shortest path, irrespective of adopted navigation strategy. In contrast, increasing the size of the sensing agents improves the efficiency of short-path taking by harvesting information on a larger scale. It inspires the development of a run-and-whirl dynamics that takes advantage of the mathematical properties of harmonic functions to emulate particles beyond their own size.

Sweep and ejection events in turbulent boundary layer flows have been explored for half a century now to describe eddies impacting turbulent stresses. Yet, moving these studies from their current diagnostic phase to a prognostic form remains a formidable challenge. Here, a cumulant expansion is used to derive a link between the transport of shear stress and the balance of local sweep and ejection events. Cumulant expansion is further used to connect this transport to a metric of asymmetry in the streamwise velocity distribution. These relations are employed to develop two so-called structural models for predicting the turbulent stress transport, which is traditionally neglected in first-order closure of the shear stress budget. Several datasets collected in rough-wall conditions are used to show the importance of the transport term in the roughness sublayer and to demonstrate the predictive skill of the two structural models. The model parameters are invariant to the tested range of Reynolds number and surface roughness, indicating the structural similarity between the velocity asymmetry, sweep/ejection balance, and stress transport may be universal and independent of roughness. Finally, the implementation of the structural models for improved closure schemes of the shear stress budget in modeling applications and wall-modeling in large-eddy simulations are discussed.

Numerical solutions of the Enskog-Vlasov equation are used to determine the velocity distribution function of atoms spontaneously evaporating into near-vacuum conditions. It is found that an accurate approximation is provided by a half-Maxwellian including a drift velocity combined with different characteristic temperatures for the velocity components normal and parallel to the liquid-vapor interface. The drift velocity and the temperature anisotropy reduce as the liquid bulk temperature decreases but persist for relatively low temperatures corresponding to a vapor behavior which is only slightly nonideal. Deviations from the undrifted isotropic half-Maxwellian are shown to be consequences of collisions in the liquid-vapor interface which preferentially backscatter atoms with lower normal-velocity component.

Traditional models of electrokinetic transport in porous media are based on homogenized material properties, which neglect any macroscopic effects of microscopic fluctuations. This perspective is taken not only for convenience but also motivated by the expectation of irrotational electro-osmotic flow, proportional to the electric field, for uniformly charged surfaces (or constant $\zeta$ potential) in the limit of thin double layers. Here, we show that the inherent heterogeneity of porous media generally leads to macroscopic vortex patterns, which have important implications for convective transport and mixing. These vortical flows originate due to competition between pressure-driven and electro-osmotic flows, and their sizes are characterized by the correlation length of heterogeneity in permeability or surface charge. The appearance of vortices is controlled by a single dimensionless control parameter, defined as the ratio of a typical electro-osmotic velocity to the total mean velocity.

Euler-Lagrange point-particle simulation has emerged as a premier methodology for studying dispersed particle-laden flows. This method's popularity stems from its ability to resolve fine-scale fluid structures while also tracking individual particles at reduced cost using an appropriate particle acceleration model. However, the point-particle model has known convergence issues in that refinement of the fluid grid can lead to changes in the predicted statistics. The reasons for nonconvergence are twofold: the point-particle two-way coupling force in the Navier-Stokes equations requires a numerical regularization and, without careful implementation, yields a singular force on the fluid with grid refinement. The second factor that yields grid-dependent statistics is that the point-particle force model in general depends on the undisturbed fluid velocity. When the undisturbed fluid velocity is not robustly modeled in a grid-insensitive way, the calculated force for both particles and fluid will be grid-dependent, contaminating their respective statistics. While the first issue regarding regularizing the point-particle source term has received attention in the literature, the consequences of robustly modeling the undisturbed velocity in the context of grid refinement of turbulence has received little attention. In this work, we consider decaying homogeneous isotropic turbulence laden with particles at different Stokes numbers. For a given Stokes number, we systematically refine the grid and demonstrate that explicitly modeling the undisturbed fluid velocity yields relative grid insensitivity for the energy of the particle and fluid phases, as well as acceleration of the particles. We also demonstrate that an appropriately defined dissipation rate is also grid-insensitive when an undisturbed fluid velocity correction is used. In contrast, when the undisturbed fluid velocity is modeled using the conventional approach of interpolating the local fluid velocity to the particle location, we show this procedure yields divergent statistics with grid refinement. In particular, we show that higher-order interpolation of the fluid velocity in two-way coupled problems is worse than lower-order interpolation, in the absence of a correction procedure to estimate the undisturbed fluid velocity. We also examine velocity derivative statistics of the fluid phase and demonstrate that these statistics are not in general convergent even when the undisturbed fluid velocity is explicitly modeled. Collectively, the observations in this work are used to present a philosophy on the types of questions which are answerable with point-particle methods.

By using direct numerical simulations of up to a resolution of $512\times 512\times 32768$ grid points we discover the existence of a metastable out-of-equilibrium state in rotating turbulence. We scan the phase space by varying both the rotation rate (proportional to the inverse of the Rossby number, $\text{Ro}$) and the dimensionless aspect ratio, $\lambda =H/L$, where $L$ and $H$ are the sizes of the domain perpendicular and parallel to the direction of rotation, respectively. We show the existence of three turbulent phases. For small $\text{Ro}$ but finite $\lambda$, we have a split cascade where the injected energy is transferred to both large and small scales. For large $\lambda$ and finite $\text{Ro}$ there is no inverse cascade and the energy is transferred downscale in Fourier space only. Surprisingly, between these two regimes, a third phase is observed as reported here. Consequently, for certain intervals of $\text{Ro}$ and $\lambda$, energy is no longer accumulated at arbitrarily large scales; rather, it stops at some characteristic intermediate length scales from where it is then redistributed forward in Fourier space, leading to a flux-loop mechanism where the flow is out of equilibrium with vanishing net flux and nonvanishing heterochiral and homochiral subfluxes. The system is further characterized by the presence of metastability explaining why previous numerical simulations were not able to detect this phenomenon, requiring an extremely long observation time and huge computational resources.