A thin-film model for a meniscus driven by Rayleigh surface acoustic waves (SAW) is analyzed, a problem closely related to the classical Landau-Levich or dragged-film problem where a plate is withdrawn at constant speed from a bath. We consider a mesoscopic hydrodynamic model for a partially wetting liquid, were wettability is incorporated via a Derjaguin (or disjoining) pressure and combine SAW driving with the elements known from the dragged-film problem. For a one-dimensional substrate, i.e., neglecting transverse perturbations, we employ numerical path continuation to investigate in detail how the various occurring steady and time-periodic states depend on relevant control parameters like the Weber number and SAW strength. The bifurcation structure related to qualitative transitions caused by the SAW is analyzed with particular attention on the appearance and interplay of Hopf bifurcations where branches of time-periodic states emerge. The latter correspond to the regular shedding of liquid ridges from the meniscus. The obtained information is relevant to the entire class of dragged-film problems.

The coalescence of two nanobubbles (NBs) in water is a process of great importance to many industrial applications. In this work, we study the coalescence of two equal-sized nitrogen NBs in water using molecular dynamics (MD) simulations and continuum-based theoretical analysis. We vary the NB diameter from 30 to 50 nm and study the coalescence characteristics including the expansion speed of the capillary bridge between two coalescing NBs, the dynamic regime of NB coalescence, the diameter of fully merged NBs, and the temperature variation of NBs during the coalescence process. For all cases, we show the MD simulation results can be well understood by the theoretical models developed in this work. Due to the large Laplace pressure in the model NBs, the diameter ratio of fully merged NBs to their daughter NBs is $\sqrt{2}$, which explains the recent experimental result showing that the size of NBs in water is distributed discretely with a uniform increment factor of $\sqrt{2}$ [Ma et al., J. Phys. Chem. B 124, 5067 (2020)]. The expansion of gas inside the coalescing NBs and the heat transfer between the gas NB and surrounding liquid leads to fluctuations of gas temperature during coalescence. From the theoretical analysis, we find the coalescence dynamics of NBs is in the crossover regime where neither viscous stress nor inertial stress in the surrounding liquid dominates even when the viscous stress is more than ten times higher than inertial stress. In the range of Ohnesorge number from 0.33 to 0.82, we show the scaling exponent for the capillary bridge radius vs time at late times of NB coalescence is around 0.75 ± 0.05, which is considerably higher than 0.5 in the viscous-dominated regime.

This investigation concerns the response of wall turbulences in a channel flow to uniform streamwise and spanwise magnetic fields through direct numerical simulations. More than 20 flow cases with different Stuart numbers were considered. It is found that the spanwise magnetic field leads to flow relaminarization at Stuart numbers significantly smaller than the streamwise magnetic field. The explanation of this phenomenon is not straightforward, and a deep analysis of the fine turbulence structure is needed for a clear understanding. This is achieved in a first step by considering Reynolds shear stress transport equations. It is shown that there are source and destruction terms directly related to the magnetic field. The destruction term overcomes the source terms under the spanwise magnetic field, leading to significant drag reduction once the Stuart number exceeds a critical value. The source term is not negligible and retards the relaminarization under the streamwise magnetic field. Subsequently, the conditional averages of the fluctuating velocity field and the electric current educed from the near wall coherent quasistreamwise vortices are discussed in detail. The electric current field is decomposed into an electromotive and conductive part. Their conditional averages are analyzed separately, in order to shed light on the topological differences. It is further shown that the quasistreamwise vortex paradigm allows an easy way to analyze the results leading to pertinent interpretations.

A wavelet-based adaptive wall-modeled large eddy simulation (WA-WMLES) method is proposed for simulations of wall-bounded compressible turbulent flows. The approach utilizes the wavelet-based adaptive large eddy simulation (WA-LES), incorporated into the anisotropic-adaptive wavelet collocation method, to resolve the outer region of turbulent boundary layer, while the inner part is approximated by the equilibrium wall-shear-stress model. Such an approach for modeling the inner layer is crucial for wavelet-based adaptive turbulent flow simulations because the mesh resolution requirement for WA-LES to resolve inner viscous sublayer becomes computationally prohibitively expensive as the Reynolds number increases. In the outer layer region WA-LES computations take advantage of the wavelet-based local mesh refinement, which not only efficiently captures the physical characteristics of flows on a nearly optimal adaptive computational mesh, e.g., massive boundary layer separation, but also actively controls the error of the solution using a priori defined wavelet filtering threshold. A flat plate turbulent boundary layer flow and a separated flow over NASA's wall-mounted hump are tested to verify and validate the WA-WMLES approach. Good agreement of the results predicted by the WA-WMLES method is achieved compared to the reference data from experiments and simulations. The finest effective mesh resolution of the WA-WMLES is consistently higher than the one used in the wall-modeled LES (WMLES) found in literature, but comparable to the wall-resolved LES, while the similar accuracy is achieved with considerably fewer degrees of freedom than in nonadaptive WMLES. These observations demonstrate both accuracy and efficiency of the WA-WMLES method.

The extent and the morphology of ice forming in a differentially heated cavity filled with water are studied by means of experiments and numerical simulations. We show that the main mechanism responsible for the ice shaping is the existence of a cold upward convective current in the system. Such a current is ascribed to the peculiar equation of state of water, i.e., the nonmonotonous dependence of density with temperature. The precise form of the ice front depends on several factors, first, the temperature difference across the cell which drives the convection, and second, the wall inclination with respect to the vertical, both of which are explored here. We propose a boundary-layer model and a buoyancy-intensity model which account for the main features of the ice morphology.

Fluid mixing usually involves the interplay between advection and diffusion, which together cause any initial distribution of passive scalar to homogenize and ultimately reach a uniform state. However, this scenario only holds when the velocity field is nondivergent and has no normal component to the boundary. If either condition is unmet, such as for active particles in a bounded region, floating particles, or for filters, then the ultimate state after a long time is not uniform and may be time dependent. We show that in those cases of nonuniform mixing it is preferable to characterize the degree of mixing in terms of an $f$-divergence, which is a generalization of relative entropy, or to use the $L^1$ norm. Unlike concentration variance ($L^2$ norm), the $f$-divergence and $L^1$ norm always decay monotonically, even for nonuniform mixing, which facilitates measuring the rate of mixing. We show by an example that flows that mix well for the nonuniform case can be drastically different from efficient uniformly mixing flows.

In this Letter, we report the outcome of a spatial energy budget performed for the linear convective instability of the plane incompressible mixing layer within the inviscid framework. We find that as the critical condition for the onset of absolute instability is approached, the integrated pressure-transport term becomes increasingly more prominent as compared to the integrated production term, and the former dominates the energy budget completely at the critical condition. This implies that, near the threshold of absolute instability, the growth of disturbances is almost entirely due to the pressure-transport mechanism (rather than the more common production mechanism), which is a striking result. The part of the pressure-transport term that represents the work done by the fluctuating pressure forces is seen to be primarily responsible for the observed shift in the energy balance. The profiles of the energy terms reveal a strong coupling between velocity and pressure fluctuations at large cross-stream distances, and a region of negative production whose magnitude increases with increasing counterflow. These results can help us better understand the physical processes causing absolute instability in a mixing layer. In particular, the streamwise redistribution of disturbance energy by fluctuating pressure, which is “nonlocal” in character for incompressible flows, seems to play a key role in this respect.

Despite being intensively investigated, wetting at the nanoscale leaves a manifold of questions unresolved. In particular, the dependence of a contact angle on a droplet size for the droplets of the height of the order of a few nanometers is intensively debated. This effect is believed to be related to intermolecular (surface) forces. In the present work, we use the disjoining pressure concept and solve the Derjaguin equation numerically and analytically to model profiles of the sessile droplets of heights comparable with the range of the surface force action. We show that values of the contact angle are dramatically dependent on the droplet height as well as the way the contact angle is defined. For the axisymmetric droplets, the contact angle increases with increasing droplet height, and this dependency becomes universal for different disjoining pressure isotherms when plotted dimensionless with respect to the surface force action range. We demonstrate that for cylindrical droplets, different contact angle definitions can lead to opposite dependencies on the droplet size. We show as well that varying orders of magnitude of the apparent line tension reported can be additionally explained by the contact angle definition chosen.

We study the spreading and leveling of a gravity current in a Hele-Shaw cell with flow-wise width variations as an analog for flow in fractures and horizontally heterogeneous aquifers. Using phase-plane analysis, we obtain second-kind self-similar solutions to describe the evolution of the gravity current's shape during both the spreading (preclosure) and leveling (postclosure) regimes. The self-similar theory is compared to numerical simulations of the partial differential equation governing the evolution of the current's shape (under the lubrication approximation) and to table-top experiments. Specifically, simulations of the governing partial differential equation from lubrication theory allow us to compute a prefactor, which is a priori arbitrary in the second-kind self-similar transformation, by estimating the time required for the current to enter the self-similar regime. With this prefactor calculated, we show that theory, simulations and experiments agree well near the propagating front. In the leveling regime, the current's memory resets, and another self-similar behavior emerges after an adjustment time, which we estimate from simulations. Once again, with the prefactor calculated, both simulations and experiments are shown to obey the predicted self-similar scalings. For both the pre- and postclosure regimes, we provide detailed asymptotic (analytical) characterization of the universal current profiles that arise as self-similarity of the second kind.

Governing equations of swirling turbulent buoyant plumes rising from horizontal circular sources into a stationary surrounding are established with the plume function considered. In an attempt to find out the analytical solutions for both lazy and forced plumes, we derive the asymptotic approximations with first-order expansions for all swirling plume variables, including the radius, swirl ratio, axial velocity, and temperature, by applying regular perturbation methods with the swirl term being the perturbative part. Finally, the asymptotic solutions are compared with the numerical evaluations conducted through the fourth-order Runge-Kutta method. The results show that, for lazy plumes, the zeroth-order expansions are good enough to approximate the solutions for each variable, while the first-order expansions are found to match the numerical solution much better for forced plumes, indicating that swirling motions slightly influence lazy plumes but largely affect forced ones. It is also found that, in the presence of swirls, the plume radius slightly increases, while the centerline axial velocity decreases and the temperature barely changes, in both lazy and forced plumes. Additionally, as the input plume function value increases, the swirl ratio decays faster and further decreases the impact on other variables. Especially, a swirl can even turn a moderate forced plume into a lazy plume due to the dominated perturbative part in the near field, which might cause the method for categorizing plumes to be called into question.

Synthetic microswimmers offer models for cell motility and their tunability makes them promising candidates for biomedical applications. Here, we measure the acoustic propulsion of bimetallic microrods that, when trapped at the nodal plane of a MHz acoustic resonator, swim with speeds of up to $300\mu \mathrm{m}{\mathrm{s}}^{-1}$. While past acoustic streaming models predict speeds that are more than one order of magnitude smaller than our measurements, we demonstrate that the acoustic locomotion of the rods is driven by a viscous, nonreciprocal mechanism relying on shape anisotropy akin to that used by swimming cells and that reproduces our data with no adjustable parameters.

A ternary phase-field simplified multiphase lattice Boltzmann method (TPF-SMLBM) is developed and employed in numerical investigation of a compound droplet placed on solid substrate in shear flow at moderate Reynolds numbers. The TPF-SMLBM utilizes the simplified multiphase lattice Boltzmann method as the flow solver and the ternary phase-field model as the interface tracking algorithm. Compared with conventional lattice Boltzmann method, this method preserves advantages in memory cost and boundary treatment. The numerical investigations recover three major modes of motion, namely the quasisteady sliding, tumbling-sliding, and tumbling-detachment. The quasisteady sliding dynamics are analyzed from the perspective of energy conversion, which explains the exponential shrinking rate of the wetting length in early evolution stage. By using the force-balance analyses, the onset of tumbling motion is firstly elaborated as the breakup of the balance in quasisteady sliding. A dimensionless parameter named as the tumbling number $\mathrm{Tu}=\mathrm{Ca}/{\mathrm{Re}}^{-0.5}$, where Ca and Re are, respectively, capillary and Reynolds numbers, is proposed to identify the mode transition towards tumbling. The physical rational of this parameter can be established from both the force analyses and the balance of timescales, and is further validated by abundant simulation results which show that its criticality is roughly on the order of $O$(1) in the low-density–viscosity ratio scenarios. For the tumbling-sliding mode, the re-adhesion of tumbling droplet portion generates extra diffusive flow behavior and shrinks the wetted length of the sliding droplet portion. The dynamics of detachment is also investigated, showing that the critical capillary number of detachments can be scaled by ${\mathrm{Ca}}_c,{}_{\mathrm{detach}}\sim {\mathrm{Re}}^{-0.3}$.

Counter-flow configurations, whereby two streams of fluid are brought together from opposite directions, are highly efficient mixers due to the high turbulence intensities that can be maintained. In this paper, a simplified version of the problem is introduced that is amenable to direct numerical simulation. The resulting turbulent flow problem is confined between two walls, with one nonzero mean velocity component varying in the space direction normal to the wall, corresponding to a simple shear flow. Compared to conventional channel flows, the mean flow is inflectional and the maximum turbulence intensity relative to the maximum mean velocity is nearly an order of magnitude higher. The numerical requirements and turbulence properties of this configuration are first determined. The Reynolds shear stress is required to vary linearly by the imposed forcing, with a peak at the channel centerline. A similar behavior is observed for the streamwise Reynolds stress, the budget of which shows an approximately uniform distribution of dissipation, with large contributions from production, pressure-strain, and turbulent diffusion. A viscous sublayer is obtained near the walls and with increasing Reynolds number small-scale streaks in the streamwise momentum are observed, superimposed on the large-scale structures that buffet this region. When the peak local mean Mach number reaches 0.55, turbulent Mach numbers of 0.6 are obtained, indicating that this flow configuration can be useful to study compressibility effects on turbulence.

When a symmetric regular binary mixture, subjected to a constant shear, is quenched into the unsteady region of its phase diagram under a temperature gradient, it phase separates following very complicated patterns. The phase separation process is simulated using a thermodynamics-based phase-field model where the fundamental balance equations are coupled with the constitutive equations for the diffusive fluxes of chemical species, momentum, and energy by applying the rules of nonequilibrium thermodynamics. The evolution of phase separation shows distinct features, being more complex than a simple superposition of patterns emerging in a shear flow and under a thermal gradient when taken individually. The imposed temperature gradient causes a preferential nucleation at the cooler wall, so that the emerging droplets drift towards the center of the domain while following the imposed flow field, causing a change in droplet movement as they cross the domain centerline and enhancing coalescence. The imposed temperature gradient breaks the symmetry compared to instantaneous quenching, with stable droplets which remain attached to the cooler wall and move coherently with it. The capillary number $\left(N_{\mathrm{Ca}}\right)$ determines breakup and phase separation evolving as stripes for $N_{\mathrm{Ca}}\gg 1$, while droplets nucleate and grow for $N_{\mathrm{Ca}}\ll 1$. The Lewis number $\left(N_{\mathrm{Le}}\right)$ affects the pace and propagation of phase separation: for $N_{\mathrm{Le}}>10$ phase separation takes place rather uniformly, being similar to instantaneous quenching, while for $N_{\mathrm{Le}}<0.1$ the mixture cools slowly and a phase separation front proceeds from the cooler wall. A similar behavior is induced by a composition-dependent thermal conductivity. The mixture dimensionless heat capacity $\left(N_c\right)$ has a significant effect on phase separation because, for $N_c\ll 1$, heat dissipation counterbalances the effect of the applied temperature quench, thus retarding or even reversing the process of phase separation. These results and the variety of patterns reproduced by the model highlight the necessity of integrating a consistent thermodynamic description to the hydrodynamics and heat transport in phase-field modeling.

Using fully-resolved simulations, we examine the torque experienced by a finite-length circular cylinder rotating steadily perpendicularly to its symmetry axis. The aspect ratio $\chi$, i.e., the ratio of the length of the cylinder to its diameter, is varied from 1 to 15. In the creeping-flow regime, we employ the slender-body theory to derive the expression of the torque up to order 4 with respect to the small parameter $1/ln\left(2\chi \right)$. Numerical results agree well with the corresponding predictions for $\chi \gtrsim 3$. We introduce an ad hoc modification in the theoretical prediction to fit the numerical results obtained with shorter cylinders, and a second modification to account for the increase of the torque resulting from finite inertial effects. In strongly inertial regimes, a prominent wake pattern made of two pairs of counter-rotating vortices takes place. Nevertheless the flow remains stationary and exhibits two distinct symmetries, one of which implies that the contributions to the torque arising from the two cylinder ends are identical. We build separate empirical formulas for the contributions of pressure and viscous stress to the torque provided by the lateral surface and the cylinder ends. We show that, in each contribution, the dominant scaling law may be inferred from simple physical arguments. This approach eventually results in an empirical formula for the rotation-induced torque valid throughout the range of inertial regimes and aspect ratios considered in the simulations.

We report hot-wire measurements performed in two very different, co- and counterrotating flows, in normal and superfluid helium at $1.6\mathrm{K}$, $2\mathrm{K}$, and $2.3\mathrm{K}$. As recently reported, the power spectrum of the hot-wire signal in superfluid flows exhibits a significant bump at high frequency [Diribarne et al., Phys. Rev. B 103, 144509 (2021)]. We confirm that the bump frequency does not depend significantly on the temperature and further extend the previous analysis of the velocity dependence of the bump, over more than one decade of velocity. The main result is that the bump frequency depends on the turbulence intensity of the flow, and that using the turbulent Reynolds number rather than the velocity as a control parameter collapses results from both co- and counterrotating flows. The vortex shedding model previously proposed, in its current form, does not account for this observation. This suggests that the physical origin of the bump is related to the small scale turbulence properties of the flow. We finally propose some qualitative physical mechanism by which the smallest structures of the flow, at intervortex distance, could affect the heat flux of the hot wire.

We investigate the growth of short gravity-capillary waves due to wind forcing, solving the two-phase Navier-Stokes equations. The numerical method features a momentum conserving scheme, interface reconstruction using volume of fluid, and adaptive mesh refinement. A 2D laminar wind profile is used to force short gravity-capillary waves in the viscous regime, and the growth of the wave amplitude and subsurface drift layer are analyzed. The threshold for wave growth is found to depend on a balance between the growth rate and viscous dissipation rate, while the wave growth for all data can be described as a scaling depending on wind stress and a viscous correction accounting for the growth threshold. Together with the wave growth, the subsurface drift layer develops and can be described in terms of a similarity solution. The nonlinear stage of wave growth is discussed for increasing wavelength, and we recover steep capillary waves, parasitic capillary waves, and spilling breakers depending on the ratio of gravity to surface tension forces.

This paper presents a numerical study of electrohydrodynamic flow for the problem of electroconvection in a viscoelastic dielectric liquid subjected to unipolar injection. The nonlinear evolution of flow for diverse characteristic Weissenberg numbers is examined in detail. The influences of elasticity on the flow pattern, oscillation amplitude, current transfer, and power-law spectral scaling accompanying oscillatory flow are also investigated. The results demonstrate that the effect of viscoelasticity leads to hydrodynamic behaviors that are absent in Newtonian fluids. The transition sequences to the chaos of electroconvection in viscoelastic fluids are quite different from those in Newtonian fluids, and the elasticity precipitates the onset of chaos. An asymmetric steady flow pattern resulting from elasticity is observed in a perfectly symmetric geometry. The fluctuation amplitude of fluid motion is found to be suppressed for weakly elastic fluids but amplified when the fluid elasticity exceeds a certain threshold. For viscoelastic fluids, electric current transfer is reduced in most cases, but for weakly elastic fluid, it may be enhanced.

The viscodiffusive McIntyre instability [M. E. McIntyre, Geophys. Astrophys. Fluid Dyn. 1, 19 (1970)] has been suggested as a possible source for density layer formation around laboratory and oceanic vortices. This suggestion is here quantitatively addressed using idealized, axisymmetric, numerical simulations of a simple Gaussian-like vortex in thermal wind balance, floating in a rotating, stratified flow. Numerical simulations are complemented by a local stability analysis derived from the seminal study [M. E. McIntyre, Geophys. Astrophys. Fluid Dyn. 1, 19 (1970)]. It is confirmed that the McIntyre instability is responsible for the layering observed around laboratory vortices, but its relevance for explaining layering around meddies remains doubtful.

Extremely small amounts of surface-active contaminants are known to drastically modify the hydrodynamic response of the water-air interface. Surfactant concentrations as low as a few thousand molecules per square micron are sufficient to eventually induce complete stiffening. In order to probe the shear response of a water-air interface, we design a radial flow experiment that consists in an upward water jet directed to the interface. We observe that the standard no-slip effect is often circumvented by an azimuthal instability with the occurrence of a vortex pair. Supported by numerical simulations, we highlight that the instability occurs in the (inertia-less) Stokes regime and is driven by surfactant advection by the flow. The latter mechanism is suggested as a general feature in a wide variety of reported and yet unexplained observations.