We study experimentally the quasistatic displacement of an oil-air front across a localized constriction in a model open fracture. The front experiences capillary jumps at one end of the constriction in both imbibition and drainage, leading to a microscale pressure-saturation hysteresis cycle. At the other end the front is reversibly pinned. A condition of local mechanical equilibrium between the restoring elasticity of the front and the distortion produced by the local change in aperture captures all we measure quantitatively, in terms of material and geometrical properties only.

We study the effect of spherical particles on the turbulent flow of a viscoelastic fluid and find that the drag reducing effect of polymer additives is completely lost for semidense suspensions, with the drag increasing more than for suspensions in Newtonian fluids. This different behavior is due to three separate effects. First, polymer stretching is reduced by the presence of rigid particles, thus canceling the drag reducing benefit of the viscoelastic fluid. Second, drag increase is provided by the growth of the particle and polymeric shear stresses with the particles, due to larger shear rates in the vicinity of the particle surface. Third, particles migrate towards the wall due to the shear-thinning property of the fluid, thus enhancing the particle near-wall layer and further increasing the drag.

We present a new technique to study preferential concentration of droplets in a turbulent air flow. Preferential concentration is the tendency of droplets to cluster in regions of strain, while avoiding regions of rotation. We study the properties of the droplet concentration field in zero mean flow turbulence that was created using an array of synthetic jets. The droplets are made of a phosphorescent solution of Europium chelate. They are excited by a laser sheet from a pulsed UV laser, after which the glowing droplets are followed using a high-speed intensified camera. We quantify preferential concentration through measurement of moments of the coarse-grained local droplet density. At the Stokes numbers studied ($\mathrm{St}\approx 2$) the fractal dimension, a scaling property of this coarse-grained density field, points to clustering. Clustering is a consequence of the compressibility of the droplet velocity field. We also quantify the dynamical behavior of clustering by moving with this velocity field. We find a preference for clustering in the Lagrangian frame during the time interval set by the decay of the phosphorescence.

We report interpenetrating spiral vortices (ISVs), a coexisting state of upward and downward propagating spiral/helical vortices, in a neutrally buoyant suspension undergoing Taylor-Couette flow, with the inner cylinder rotating and the outer cylinder at rest. Along with ISV and Taylor vortex flow (TVF), the nonaxisymmetric patterns, such as the wavy Taylor vortices (WTVs) and spiral vortex flows (SVFs), and the coexisting states of “$\mathrm{TVF}+\mathrm{WTV}$” and “$\mathrm{TVF}+\mathrm{SVF}$” are also uncovered. It is shown that the “$\mathrm{TVF}+\mathrm{SVF}$” pattern appears as a primary transition, which gives birth to interpenetrating spirals as a secondary transition beyond a critical Reynolds number, with the final state being that of WTVs over a range of particle volume fractions and Reynolds number.

The Boltzmann equation provides a rigorous description of gas flows at all degrees of gas rarefaction. Asymptotic analyses of this equation yield valuable insight into the physical mechanisms underlying gas flows. In this article, we report an asymptotic analysis of the Boltzmann-BGK equation for a slightly rarefied gas when the acoustic wavelength is comparable to the macroscopic characteristic length scale of the flow. This is performed using a three-way matched asymptotic expansion, which accounts for the Knudsen layer, the viscous layer, and the outer Hilbert region—these are separated by asymptotically disparate length scales. Transport equations and boundary conditions for these regions are derived. The utility of this theory is demonstrated by application to three problems: (1) flow generated by uniformly heating two plates, (2) oscillatory thermal creep induced between two plates, and (3) the flow generated by an oscillating sphere. Comparisons to numerical simulations of the Boltzmann-BGK equation and previous asymptotic theories (for long wavelength) are performed. The present theory is distinct from previous asymptotic analyses that implicitly assume long or short acoustic wavelength. This theory is expected to find application in the design and characterization of nanoelectromechanical devices, which often generate acoustic oscillatory flows of a rarefied nature.

The regularized versions of extended-hydrodynamic equations for a dilute granular gas, in terms of 10-, 13-, and 14-moments, are derived from the inelastic Boltzmann equation. The regularization is achieved by adding higher-order gradient terms that are obtained following a Chapman-Enskog-like gradient-expansion [H. Struchtrup, Stable transport equations for rarefied gases at high orders in the Knudsen number, Phys. Fluids, 16, 3921 (2004)]. For both granular and molecular gases, the resulting moment equations are found to be free from the well-known finite Mach-number singularity (that occurs in the Riemann problem of planar shock waves) since the regularized gradient terms yield parabolic equations in contrast to the hyperbolic nature of original moment equations. In order to clarify the advantage of these regularized equations, the 10-moment model for the plane shock-wave problem is solved numerically for both molecular and granular gases; the calculated hydrodynamic profiles compare favorably with previous simulation results for molecular gases. For a granular gas, both regularized and nonregularized equations predict asymmetric density and temperature profiles, with the maxima of both density and temperature occurring within the shock layer, and the hydrodynamic fields are found to be smooth for the regularized equations for all Mach numbers studied. It is demonstrated that, unlike in the case of molecular gases, a “second” regularization of the regularized equations must be carried out in order to arrest the unbounded growth of density within the shock layer in a granular gas.

We investigate the flow past circular, square, and triangular cylinders embedded on spherical and cylindrical surfaces and quantify the effect of the embedding surface curvature on the flow characteristics. For the circular cylinder, we examine three Reynolds numbers $\text{Re}=40,100$, and 1000 based on cylinder diameter ($D$), and vary the normalized embedding surface curvature values $\kappa D$, where $\kappa$ is the maximum principal curvature, from 0 (flat surface) to $1/12$. Measures of fluid dynamical quantities of interest: drag coefficient $\left(C_d\right)$, lift coefficient $\left(C_l\right)$, Strouhal number $\left(\text{St}\right)$, pressure coefficient ($C_p$), friction coefficient ($C_f$), vorticity magnitude (${\omega }^{*}$), street speed $\left(V_{st}\right)$, street wavelength $\left(\lambda \right)$, length of stationary vortex pair ($L$), and separation angle (${\theta }_{\text{sep}}$) show an insignificant effect of the surface curvature. For the range of embedding surface curvature values, the dynamics of the flow past a stationary circular cylinder exhibits near universality, and is essentially independent of the embedding surface curvature. Our conclusion is further consolidated by the similar insensitivity to the embedding surface curvature exhibited by flows past a stationary cylinder having a square or triangular cross-section.

Individual constituent balance equations are often used to derive expressions for species-specific segregation velocities in flows of dense granular mixtures. We propose a semiempirical expression for the interspecies momentum exchange in density-bidisperse granular flows as an extension of ideas from kinetic theory and compare it to a previous viscous drag approach that is analogous to particles settling in a fluid. The proposed model expands the range of the granular kinetic theory from short-duration binary collisions to the multiple enduring contacts characteristic of dense shear flows and incorporates the effects of particle friction, concentration ratio, and local flow conditions. The segregation velocities derived from the momentum balance equation using both interspecies drag models match the downward and upward segregation velocities of heavy and light particles obtained from DEM simulations through the flowing layer depth for different density ratios and constituent concentrations in confined shear flows. Predictions of the kinetic theory inspired approach are additionally compared to results from free surface heap flow simulations, and, again, a close match is observed.

Past studies have shown that liquid jet breakup behavior can be classified into five regimes: Rayleigh, first wind, sinuous, second wind, and atomization. By experimentally examining the breakup of superfluid and normal liquid ${}^4\mathrm{He}$ in an atmosphere of its own vapor, we investigate the evolution of the jet behavior over a large range of the traditional three-dimensional parameter space of the Ohnesorge number $[{\text{Oh}}_l\sim O({10}^{-5}$–${10}^{-2}\left)\right]$, Reynolds number $[{\text{Re}}_l\sim O({10}^2$–${10}^6\left)\right]$, and gas-liquid density ratio $[{\rho }_g/{\rho }_l\sim O({10}^{-4}$–1)]. Using dimensional analysis we find that the transition from Rayleigh to first-wind breakup occurs at a constant liquid Weber number, and that the transitions from first wind to sinuous, and sinuous to second wind occur at constant gas Weber numbers. The proposed transitions, which differ from some previous studies, are well supported by our new experimental data that extend over all three dimensions of the parameter space. We do not observe any obvious effects of superfluidity on the breakup behavior. In addition, we examine the breakup length and comment on the transition of a liquid jet to a gaseous jet as the temperature passes through the critical point.

The instability and rupture of nanoscale liquid threads is shown to strongly depend on thermal fluctuations. These fluctuations are naturally occurring within molecular dynamics (MD) simulations and can be incorporated via fluctuating hydrodynamics into a stochastic lubrication equation (SLE). A simple and robust numerical scheme is developed for the SLE that is validated against MD for both the initial (linear) instability and the nonlinear rupture process. Particular attention is paid to the rupture process and its statistics, where the “double-cone” profile reported by Moseler and Landmann [Science 289, 1165 (2000)] is observed, as well as other distinct profile forms depending on the flow conditions. Comparison to the Eggers' similarity solution [Phys. Rev. Lett. 89, 084502 (2002)], a power law of the minimum thread radius against time to rupture, shows agreement only at low surface tension; indicating that surface tension cannot generally be neglected when considering rupture dynamics.

We report on a numerical study of axisymmetric flow of liquid metal in a circular duct with a rectangular cross section. The flow is forced through the combination of an axial magnetic field and a radial current. Sweeping a wide range of forcing parameters, we identify the different regimes which characterize the flows and explicate the associate scaling laws. Results from different studies in the literature are interpreted in the light of our numerical simulations.

Understanding the behavior of liquid phase turbulence near gas-liquid interfaces is of great interest in many fundamental, environmental, or industrial applications. For example, near-surface liquid side turbulence is known to enhance the mass transfers between the two phases. Descriptions of this behavior for air-water systems exist in the literature, but the case of turbulence in a shear-thinning liquid phase below a flat gas-liquid interface has never been considered to the best of our knowledge. This paper consists in an experimental characterization of low Reynolds number, oscillating grid generated, near-surface turbulence in shear-thinning dilute polymer solutions, in the surface-influenced and in the viscous sublayers. The energy transfer mechanism, known in the water case, is evidenced in dilute polymer solutions. A horizontal damping mechanism, similar to the one introduced by surfactants, is evidenced. The evolution of the viscous sublayer depth can be explained by both viscous and shear-thinning effects, and it appears that a critical polymer concentration may exist within the dilute regime.

Based on the lattice Boltzmann (LB) method, pore-scale simulations are performed to investigate the differential diffusion effects on the density-driven instability (DI) with chemical reaction $A+B\to C$ in porous media. A partially miscible stratification is considered, and thus only solutes from the top fluid can diffuse down into the host fluid in pore spaces. Tests with different values of the Rayleigh number ${\text{Ra}}_r$ and the diffusion coefficient $D_r$ of species $r$ ($r=A,B,C$) are considered. The results demonstrate eight distinct scenarios of DI, and four of them are not observed in equal diffusivity simulations. Two differential diffusion effects, namely, the double-diffusive (DD) and the diffusive-layer convection (DLC) mechanisms, can act upon the gravity field and give rise to new fingering phenomena. The DD mechanism comes into play and results in a local minimum density layer if ${\text{Ra}}_B/{\text{Ra}}_C$ is small and $D_B>D_C$; and DLC becomes significant and brings in a local maximum density layer if ${\text{Ra}}_B/{\text{Ra}}_C$ is large and $D_B<D_C$. On one hand, when fluid density increases with dissolved $A$, the DD-induced minimum can act as an inhibiting barrier to suppress fingering propagation, although it can be eventually penetrated by fingering tips; and the DLC-induced maximum can introduce the second DI below the first one. On the other hand, when the dissolution of $A$ contributes to decreasing fluid density, both the DD-induced minimum and the DLC-induced maximum can help trigger the development of DI. Finally, quantitative results are provided to indicate that fingering propagates into the host fluid more deeply with larger $D_B/D_C$, and the dissolution of $A$ decreases with the increasing difference between $D_B$ and $D_C$.

The erosion of natural sediments by a superficial fluid flow is a generic situation in many usual geological or industrial contexts. However, there is still a lack of fundamental knowledge about erosional processes, especially concerning the role of internal cohesion and adhesive stresses on issues such as the critical flow conditions for the erosion onset or the kinetics of soil mass loss. This contribution investigates the influence of cohesion on the surface erosion by an impinging jet flow based on laboratory tests with artificially bonded granular materials. The model samples are made of spherical glass beads bonded either by solid bridges made of resin or by liquid bridges made of a highly viscous oil. To quantify the intergranular cohesion, the capillary forces of the liquid bridges are here estimated by measuring their main geometrical parameters with image-processing techniques and using well-known analytical expressions. For the solid bonds, the adhesive strength of the materials is estimated by direct measurement of the yield tensile forces and stresses at the particle and sample scales, respectively, with specific traction tests developed for this purpose. The proper erosion tests are then carried out in an optically adapted device that permits a direct visualization of the scouring process at the jet apex by means of the refractive index matching technique. On this basis, the article examines qualitatively the kinetics of the scour crater excavation for both scenarios, namely, for an intergranular cohesion induced by either liquid or solid bonds. From a quantitative perspective, the critical condition for the erosion onset is discussed specifically for the case of the solid bond cohesion. In this respect, we propose here a generalized form of the Shields criterion based on a common definition of a cohesion number from yield tensile values, derived at both micro- and macroscales. The article finally shows that the proposed form manages to reconcile the experimental data for cohesive and cohesionless materials, the latter in the form of the so-called Shields curve along with some previous results of the authors which have been appropriately revisited.

The motion of a capillary interface across a deformable granular material in a confined geometry shows the complex interplay between viscous forces, solid friction, and capillary forces. In a horizontal quasi-one-dimensional geometrical confinement, a millifluidic tube, the displacement of a three-phase flow consisting of two fluids and a mobile granular phase exhibits viscous or frictional displacement regimes, as shown in [Phys. Rev. Lett. 117, 028002 (2016).]. In the present paper we explore in detail the dynamics in both regimes by making use of a new set of data. The viscous displacement regime which is characterized by a fluidization of the immersed granular material dragged by the flow driving the displacement of the capillary interface is interpreted from a rheological point of view. The frictional displacement regime which displays a self-structuring of the granular material left in the tube behind the invading capillary interface is interpreted by using a model based on the Janssen law to predict the typical size of the plugs obtained.

It is known that the turbulence in a fast-rotating volume becomes effectively two-dimensional. The latter is characterized by an inverse energy cascade leading to the formation of coherent flow in finite systems. In a rotating three-dimensional vessel this flow has the form of columnar vortices. Here we develop an analytical theory describing interaction of the vortex with turbulent pulsations. This interaction results in energy transfer from small-scale eddies to the large-scale vortex. We derive the equation for the radial velocity profile of the vortex and solve it for the simplest boundary conditions. We indicate the domain of physical parameters where our theory works.

We report water wave experiments performed in a long tank where we consider the evolution of nonlinear deep-water surface gravity waves with the envelope in the form of a large-scale rectangular barrier. Our experiments reveal that, for a range of initial parameters, the nonlinear wave packet is not disintegrated by the Benjamin-Feir instability but exhibits a specific, strongly nonlinear modulation, which propagates from the edges of the wave packet toward the center with finite speed. Using numerical tools of nonlinear spectral analysis of experimental data, we identify the observed envelope wave structures with focusing dispersive dam break flows, a peculiar type of dispersive shock waves recently described in the framework of the semiclassical limit of the 1D focusing nonlinear Schrödinger equation (1D-NLSE). Our experimental results are shown to be in a good quantitative agreement with the predictions of the semiclassical 1D-NLSE theory. This is the first observation of the persisting dispersive shock wave dynamics in a modulationally unstable water wave system.

Dense frictional particulate suspensions in a viscous liquid undergo increasingly strong continuous shear thickening as the solid packing fraction, $\varphi$, increases above a critical volume fraction, and discontinuous shear thickening is observed for even higher packing fractions. Recent studies have related shear thickening to a transition from mostly lubricated to predominantly frictional contacts with the increase in stress, with the transition determined by overcoming a repulsive force. The rheology and networks of frictional forces from two- and three-dimensional simulations of shear-thickening suspensions are studied. These are analyzed using measures of the topology of the network, including tools of persistent homology. We observe that at low stress, the frictional interaction networks are predominantly quasilinear along the compression axis. With an increase in stress, the force networks become more isotropic, forming loops in addition to chainlike structures. The topological measures of Betti numbers and total persistence provide a compact means of describing the mean properties of the frictional force networks, and provide a link between macroscopic rheology and the microscopic interactions. A total persistence measure describing the significance of loops in the force network structure, as a function of stress and packing fraction, shows behavior similar to that of relative viscosity, and displays a scaling law near the jamming fraction for both two- and three-dimensional systems considered. The total persistence measures for both dimensions are found to be very similar.

Using three-dimensional Voronoi analysis, we explore the local dynamics of small, settling, inertial particles in isotropic turbulence using direct numerical simulations. We independently vary the Taylor Reynolds number ${\text{Re}}_{\lambda }\in [90,398]$, Froude number $\text{Fr}\equiv a_{\eta }/g\in [0.052,\infty ]$ (where $a_{\eta }$ is the Kolmogorov acceleration, and $g$ is the acceleration due to gravity), and Kolmogorov scale Stokes number $\text{St}\equiv {\tau }_p/{\tau }_{\eta }\in [0,3]$. In agreement with previous results using global measures of particle clustering, such as the radial distribution function, we find that for small Voronoi volumes (corresponding to the most clustered particles), the behavior is strongly dependent upon St and Fr, but only weakly dependent upon ${\text{Re}}_{\lambda }$, unless $\text{St}>1$. However, larger Voronoi volumes (void regions) exhibit a much stronger dependence on ${\text{Re}}_{\lambda }$, even when $\text{St}\le 1$, and we show that this, rather than the behavior at small volumes, is the cause of the sensitivity of the standard deviation of the Voronoi volumes that has been previously reported. We also show that the largest contribution to the particle settling velocities is associated with increasingly larger Voronoi volumes as the settling parameter $\text{Sv}\equiv \text{St}/\text{Fr}$ is increased. Our local analysis of the acceleration statistics of settling inertial particles shows that clustered particles experience a net acceleration in the direction of gravity, while particles in void regions experience the opposite. The particle acceleration variance, however, is a convex function of the Voronoi volumes, with or without gravity, which seems to indicate a nontrivial relationship between the Voronoi volumes and the sizes of the turbulent flow scales. Results for the variance of the fluid acceleration at the inertial particle positions are of the order of the square of the Kolmogorov acceleration and depend only weakly on Voronoi volumes. These results call into question the “sweep-stick” mechanism for particle clustering in turbulence which would lead one to expect that clustered particles reside in the special regions where the fluid acceleration is zero (or at least small). We then consider the properties of particles in clusters, which are regions of connected Voronoi cells whose volume is less than a certain threshold. The results show self-similarity of the clusters, and that the statistics of the cluster volumes depends only weakly on St, with a stronger dependence on Fr and ${\text{Re}}_{\lambda }$. Finally, we compare the average settling velocities of all particles in the flow with those in clusters, and show that those in the clusters settle much faster, in agreement with previous work. However, we also find that this difference grows significantly with increasing ${\text{Re}}_{\lambda }$ and exhibits a nonmonotonic dependence on Fr. The kinetic energy of the particles, however, is almost the same for particles whether or not they are in clusters.

A study on the small-amplitude oscillation of a viscoelastic droplet suspended in an immiscible viscoelastic host liquid is carried out. The viscoelasticity of the inner and outer liquids is described by Jeffreys constitutive equation. The analytical characteristic equation is derived and the complex frequency is solved numerically. The effect of the outer host liquid on the oscillation of the droplet is examined for the fundamental mode $n=2$. It is found that the damping rate and the frequency of oscillation of the droplet are decreased as the host liquid gets denser in the inviscid case. The boundaries between periodic oscillation and aperiodic decay in the parametric plane of the Ohnesorge number and the relative stress relaxation time are captured. The viscosity of the outer liquid makes the supercritical and subcritical bifurcation phenomena disappear and leads to periodic oscillations of the droplet all the time. Moreover, the viscosity of the outer liquid exhibits a dual effect on the decay of the amplitude of oscillation. The elasticity of the outer liquid affects the oscillation of the droplet monotonically: the stress relaxation time decreases the damping rate and the frequency of oscillation of the droplet, whereas the strain retardation time increases them limitedly.