With the aim of finding mathematical criteria for contact line depinning from sharp corners, we have studied the equilibrium and stability of a semi-infinite planar liquid layer pinned at the vertex of a wedge. Equilibrium is compatible with a fan of apparent contact angles ${\theta }_0$ bracketed by the equilibrium contact angles of both flanks of the wedge, so the contact line could remain pinned if ${\theta }_0$ is within this fan. However, the equilibrium becomes unstable at critical depinning advancing ${\theta }_0^a$ and receding ${\theta }_0^r$ contact angles, which are found as subcritical saddle-node bifurcations. Equilibrium is possible (stable) within the interval ${\theta }_0^r<{\theta }_0<{\theta }_0^a$, but the contact line depins from the vertex beyond these critical angles if they occur within the equilibrium fan.

The observability of the flow away from the wall in turbulent channels is studied using noiseless, although potentially incomplete, wall measurements. Reconstructions of the velocities are generated using linear stochastic estimation. All the velocities are well reconstructed in the buffer layer, but only relatively large “wall-attached” eddies are observable farther from the wall. In particular, large-scale structures that account for approximately 50% of the total kinetic energy and of the tangential Reynolds stress are accurately captured up to $y/h\lesssim 0.2$. It is argued that this should allow the use of wall sensors for the detection (and potential control) of the large eddies populating the logarithmic region, and that it suggests a natural quantitative definition for “wall-attached” eddies.

Direct numerical simulations (DNSs) of two superposed fluids in a turbulent channel flow with a textured surface made of pinnacles of random height have been performed at ${\text{Re}}_{\tau }\approx 180$ and ${\text{Re}}_{\tau }\approx 395$. The texture reproduces an etched sandblasted aluminum. The viscosity ratio between the two fluids is either $m=0.02$, mimicking the viscosity ratio of a superhydrophobic surface (water over air), or $m=0.40$ (water over heptane) resembling a liquid infused surface. A parametric study has been carried out varying the position of the interface between the two fluids to assess the contribution to the drag of the portion of the texture emerging above the interface and to provide guidelines for design. Simulations with a deformable interface, at Weber numbers ${\text{We}}^{+}\approx {10}^{-2}$ and ${10}^{-3}$ have been performed. Results have been compared to those obtained assuming the ideal case of a flat interface which is slippery in the streamwise and spanwise direction (corresponding to a Weber number $\text{We}=0$). The time-averaged position of the interface has been correlated to the pressure field induced by the random-height pinnacles while the instantaneous deformation is due to the passage of the near-wall coherent structures. We attempted to reconcile the effect of superhydrophobic and liquid infused surfaces on the coherent structures by calculating how the shear rate parameter depends on the amount of drag reduction.

We present a numerical analysis of the shear viscosity of bimodal suspensions in Stokes flow. The dynamics of capsules whose membrane follows Skalak law is simulated for the total volume fraction $\varphi =0.4$. A suspension of two types of capsules with different sizes and the same deformability (capillary number) has a decreased shear viscosity compared to monomodal suspensions. Increasing the deformability of the capsules amplifies the extent of the viscosity reduction. The viscosity reduction is mainly caused by a decrease in the shear component of the stresslet of the large capsules, due to a decrease in their deformation and orientation angle with respect to the flow direction. In the case of a suspension of two types of capsules with the same size and different deformabilities, the shear viscosity is nearly the same as the weighted average of monomodal suspensions. An increase in the stresslet of the floppy capsules is counterbalanced by a decrease in the stresslet of the stiff capsules. For a suspension of two types of capsules with different sizes and the same membrane stiffness, the effects of the size difference and deformability difference coexist. The interplay of these effects decreases the stresslet for both the large and small capsules, resulting in a further viscosity reduction.

We use the multiphase magnetohydrodynamic code SFEMaNS to study the generation of electrovortex flows in liquid metal batteries. We first reproduce some well known results in a single-phase liquid metal column and then we characterize the electrovortex flow in layered multiphase fluid systems. A simple energy density balance argument accurately estimates the typical interface deformation caused by the electrovortex flow. When applied to Mg-Sb liquid metal batteries, we find that the electrovortex flows may have the capacity to cause short circuits even in moderate size batteries with radii in the range $[10,20]\mathrm{cm}$.

This study proposes a method for approximating the fully resolved flow through a monodisperse array of spherical particles using only the locations of the particles and the volume-averaged Reynolds number, both of which are available in Euler-Lagrange (EL) simulations. To achieve this, we first determine a superposable wake (SW) which best captures the behavior of direct numerical simulations (DNS). By adding the SW for all the particles, the pseudo-turbulence caused by the perturbed flow around a distribution of particles in an EL simulation can be approximated. A Reynolds stress model is then developed for use in an Euler-Lagrange framework. The range of Reynolds numbers and particle volume fractions considered in this study are $0.3\le \mathrm{Re}\le 173$ and $0.11\le \varphi \le 0.45$ accordingly.

The intermittency of an incompressible passive vector convected by homogeneous isotropic turbulence is studied by comparison with that of the velocity and passive scalar. This is used to explore the physics underlying the differences in statistical properties between the velocity vector and passive scalar. Direct numerical simulations with grid points of ${1024}^3$ and two types of forcing method are performed at Reynolds numbers of ${\text{Re}}_{\lambda }\sim 200$, 300, and 400. It is found that the probability density function (PDF) of the passive vector is wider than Gaussian. The PDFs of the logarithm of the dissipation rates of the kinetic energy, for the velocity and passive vector, are close to each other and well approximated by the log-normal distribution. Unlike the pressure PDF, which is negatively skewed, the PDF for the pseudopressure $P\left(q\right)$ is nearly symmetric. Visualization results show that the pseudoenstrophy ${\mathrm{\Omega }}_w$ for the passive vector is close to sheetlike, similar to the case of the passive scalar, while the enstrophy is tubelike. The scaling exponents of the passive vector moments are found to be anomalous, nonuniversal at high order, and intermediate between the velocity and passive scalar for the order $p\ge 4$. The pseudopressure tends to reduce the extreme events, while the linearity of the fundamental equation leads to stronger intermittency.

The mass transport induced by crossed surface waves consists of Stokes and Euler contributions, which are very different in nature. The first contribution is a generalization of Stokes drift for a plane wave in ideal fluid and the second contribution arises due to the fluid viscosity and is excited by a force applied in the viscous sublayer near the fluid surface. We study the formation and decay of the induced mass transport theoretically and experimentally and demonstrate that the two contributions have different timescales for typical experimental conditions. The evolution of the Euler contribution is described by a diffusion equation, where the fluid kinematic viscosity plays the role of the diffusion coefficient, while the Stokes contribution instantly tracks the wave pattern and therefore it evolves faster due to the additional wave damping near the system boundaries. The difference becomes more pronounced if the fluid surface is contaminated. We model the effect of contamination by a thin insoluble liquid film present on the fluid surface, with the compression modulus being the only nonzero rheological parameter of the film. Then the Euler contribution to the mass transport becomes larger and the evolution of the Stokes contribution becomes faster than in the free surface case. We infer the value of the compression modulus of the film by fitting the results of transient measurements of eddy currents and demonstrate that the obtained value leads to the correct ratio of amplitudes of horizontal and vertical velocities of the wave motion and is in reasonable agreement with the measured dissipation rate of surface waves.

In a circular channel passing overlimiting current (faster than diffusion), transient vortices of bulk electroconvection are observed in a salt-depleted region within the horizontal plane. The spatiotemporal evolution of the salt concentration is directly visualized, revealing the propagation of a deionization shock wave driven by bulk electroconvection up to millimeter scales. This mechanism leads to quantitatively similar dynamics as for deionization shocks in charged porous media, which are driven instead by surface conduction and electro-osmotic flow at micron to nanometer scales. The remarkable generality of deionization shocks under overlimiting current could be used to manipulate ion transport in complex geometries for desalination and water treatment.

In this study, realizable algebraic Reynolds stress modeling based on the square root tensor [Phys. Rev. E 92, 053010 (2015)] is further developed for extending its applicability to more complex flows. In conventional methods, it was difficult to construct an algebraic Reynolds stress model satisfying the realizability conditions when the model involves higher-order nonlinear terms on the mean velocity gradient. Such higher-order nonlinear terms are required to predict turbulent flows with three-dimensional mean velocity. The present modeling based on the square root tensor enables us to make the model always satisfy the realizability conditions, even when it involves higher-order nonlinearity. To construct a realizable algebraic Reynolds stress model applicable to turbulent flows with three-dimensional mean velocity, a quartic-nonlinear eddy-viscosity model is proposed. The performance of the model is numerically verified in a turbulent channel flow, a homogeneous turbulent shear flow, and an axially rotating turbulent pipe flow. The present model gives a good result in each turbulent flow. Note that the mean swirl flow in an axially rotating turbulent pipe flow is reproduced because the present model involves cubic nonlinearity. Such a higher-order realizable algebraic Reynolds stress model, involving quartic nonlinearity on the mean velocity, is expected to be useful in numerically stable predictions of turbulent flows with three-dimensional mean velocity.

Evaporation is an effective cooling mechanism widely exploited in the thermal management of modern electronic devices, with a growing interest in the evaporation process in thin-film-based nanoporous membrane technologies. At such scales, classical approaches fail and one requires solutions of the Boltzmann equation; these are obtained here using the direct simulation Monte Carlo method. In particular, the evaporation from representative nanoporous meniscus shapes, corresponding to different operating conditions, has been investigated. Evaporation rates for the different conditions have been characterized as a function of a wide range of Knudsen numbers and free-stream Mach numbers. Additionally, the influence of porosity and evaporation coefficient on the nanoporous evaporation rates has been assessed. Investigations have also been carried out to consider cases where the meniscus has sunk within the pore, and cooling efficacy compared with cases where the meniscus is pinned to the top of the pore. This work demonstrates that the net evaporative mass flux is ultimately determined by the interplay between various physical effects, whose dominance is quantified by the Knudsen number, porosity, evaporation coefficient, and the meniscus shape. This work thus provides useful information for the design of nanoporous membrane-based cooling devices.

Flows in nanofluidic systems are controlled by the hydrodynamic boundary condition (BC), involving the friction coefficient and the hydrodynamic wall position. Here we considered a liquid nanoslab confined between two walls, where we derived, from the Stokes equation and the Navier slip BC, analytical expressions for the liquid response to an oscillatory tangential motion of the walls in terms of the wall shear stress and mean fluid velocity. By fitting these expressions to molecular dynamics simulation results, we could extract both the viscoelastic friction coefficient and hydrodynamic wall position for walls with three different wettabilities, hence fully characterizing the frequency-dependent hydrodynamic boundary condition. The proposed method could be applied to a variety of liquid-solid interfaces of interest, e.g., for flows of complex fluids or fluids at a low temperature. It should also support methodological developments on the characterization of the hydrodynamic slip in general.

In pipes and channels, the onset of turbulence is initially dominated by localized transients, which lead to sustained turbulence through their collective dynamics. In the present work, we study numerically the localized turbulence in pipe flow and elucidate a state space structure that gives rise to transient chaos. Starting from the basin boundary separating laminar and turbulent flow, we identify transverse homoclinic orbits, the presence of which necessitates a homoclinic tangle and chaos. A direct consequence of the homoclinic tangle is the fractal nature of the laminar-turbulent boundary, which was conjectured in various earlier studies. By mapping the transverse intersections between the stable and unstable manifold of a periodic orbit, we identify the gateways that promote an escape from turbulence.

We study the dynamics of a viscous fluid confined within an elastic pipe that is being stretched and twisted in the axial and azimuthal directions, respectively. A comprehensive numerical exploration of self-similar flows has been conducted for a wide range of stretching and twisting acceleration rates. Up to eight different families of steady flows have been identified and tracked. For purely axial stretching, the presented computations recover the results obtained by former authors in the past. However, the twisting mechanism, seen as a homotopy parameter, has been crucial in this study to explain how different families of equilibria interact and azimuthal swirl is induced. The explorations conclude that stable time-periodic flows may also take over the dynamics when the pipe is contracting in the axial direction, with mild or absent azimuthal twist. These time-periodic flows may destabilize through different codimension-two bifurcation scenarios, sometimes leading to unstable tori that have been genuinely identified by means of edge-tracking techniques.

In many applications it is important to estimate a fluid flow field from limited and possibly corrupt measurements. Current methods in flow estimation often use least squares regression to reconstruct the flow field, finding the minimum-energy solution that is consistent with the measured data. However, this approach may be prone to overfitting and sensitive to noise. To address these challenges we instead seek a sparse representation of the data in a library of examples. Sparse representation has been widely used for image recognition and reconstruction, and it is well-suited to structured data with limited, corrupt measurements. We explore sparse representation for flow reconstruction on a variety of fluid data sets with a wide range of complexity, including vortex shedding past a cylinder at low Reynolds number, a mixing layer, and two geophysical flows. In addition, we compare several measurement strategies and consider various types of noise and corruption over a range of intensities. We find that sparse representation has considerably improved the estimation accuracy and robustness to noise and corruption compared with least squares methods. We also introduce a sparse estimation procedure on local spatial patches for complex multiscale flows that preclude a global sparse representation. Based on these results, sparse representation is a promising framework for extracting useful information from complex flow fields with realistic measurements.

We present a lattice-gas (generalized Ising) model for liquid droplets on solid surfaces. The time evolution in the model involves two processes: (1) single-particle moves which are determined by a kinetic Monte Carlo algorithm, which incorporate into the model particle diffusion over the surface and within the droplets and also evaporation and condensation, i.e., the exchange of particles between droplets and the surrounding vapor, and (2) larger-scale collective moves, modeling advective hydrodynamic fluid motion, determined by considering the dynamics predicted by a thin-film equation. The model enables us to relate how macroscopic quantities such as the contact angle and the surface tension depend on the microscopic interaction parameters between the particles and with the solid surface. We present results for droplets joining, spreading, sliding under gravity, dewetting, the effects of evaporation, the interplay of diffusive and advective dynamics, and how all this behavior depends on the temperature and other parameters.

We report on an instability arising when surface gravity waves propagate in a rotating frame. The Stokes drift associated to the uniform wave field, together with global rotation, drives a mean flow in the form of a horizontally invariant Ekman-Stokes spiral. We show that the latter can be subject to an instability that triggers the appearance of an additional horizontally-structured cellular flow. We determine the instability threshold numerically, in terms of the Rossby number Ro associated to the Stokes drift of the waves and the Ekman number E. We confirm the numerical results through asymptotic expansions at both large and low Ekman number. At large E the instability reduces to that of a standard Ekman spiral driven by the wave-induced surface stress instead of a wind stress, while at low E the Stokes-drift profile crucially determines the shape of the unstable mode. In both limits the instability threshold asymptotes to an Ekman-number-independent critical Rossby number, which in both cases also corresponds to a critical Reynolds number associated to the Lagrangian base-flow velocity profile. Parameter values typical of ocean swell fall into the low-E unstable regime: the corresponding “anti-Stokes” flows are unstable, with possible consequences for particle dispersion and mixing.

Classical modes of one-dimensional (1D) detonation characterized by a simplified reaction model are reproduced by using a real chemical kinetics for the ${\mathrm{H}}_2-{\mathrm{O}}_2$ system with argon dilution. As Ar dilution is varied, the bifurcation points of pulsating instability are identified and a formed bifurcation diagram is compared with that obtained by the one-step reaction model. Eventually, the numerical results demonstrate that, for real detonations with detailed chemistry, the criterion of Ng et al. works well on prediction of the 1D detonation instability. Furthermore, the detonability limits are found respectively at low and high Ar dilutions. Above the high Ar dilution limit, detonations decays to the minimum level where long autoignition time and small heat release rate make reestablishment impossible for both 1D and 2D simulations. However, below the low Ar dilution limit, a 1D detonation cannot be sustained due to high instability, while the corresponding cellular detonation can propagate sustainably due to the role of transverse instability.

A modified electrokinetic model is presented in which hydrated ions are represented as charged dielectric spheres so that the electrolyte solution becomes a nonhomogeneous fluid characterized by permittivity and viscosity values that are both functions of the local ionic concentrations. This modifies both the Poisson-Nernst-Planck and the Navier-Stokes equations and also introduces additional Born and dielectrophoretic forces acting on the ions. The model is numerically solved for a plane charged interface both in equilibrium and under the action of an applied tangential DC electric field, which makes it possible to determine the electrophoretic mobility of a suspended particle in the Smoluchowski limit. The obtained results show that the strong increase of the electrophoretic mobility due to steric and permittivity related effects is countered by the viscosity dependence on the ionic concentrations leading to values that are moderately higher than those predicted by the standard electrokinetic model. This behavior suggests that the proposed model may be used to improve the interpretation of experimental electrophoretic mobility data.

The dynamics of the displacement of one fluid by another in porous media or Hele–Shaw cells depends on the viscosity contrast due to the Saffman–Taylor instability. If the less viscous fluid is displaced by the more viscous fluid, the interface is hydrodynamically stable and, thus, fingering does not occur. Herein, we show experimentally the occurrence of fingering for hydrodynamically stable displacement in a partially miscible system using an aqueous two-phase system. Quantitative correlation between the interfacial deformation and a proposed dimensionless number demonstrates that body force driven by spinodal decomposition induces the fingering instability. Moreover, the fingering observed in this study is completely different from previously reported fingering phenomena in hydrodynamically stable displacement in immiscible and fully miscible systems.