We present a numerical investigation on the effect of isolation imposed on two previously correlated walking droplets. These two bouncing droplets oscillate horizontally, confined to separate cavities placed at a distance. Nachbin [Chaos 28, 096110 (2018)] showed that the droplets are coupled through the underlying wave field of the multicavity system, resulting in nonseparable subsystems: their respective probability distributions cannot be inferred through an individual solitary droplet. Beyond correlated, the droplets are statistically indistinguishable, highlighting their intrinsically related statistics. Isolation is imposed through a wide barrier which abruptly halts the long-range wave-mediated interactions between droplets. Shortly after, both droplets transition to new cycles in phase space. The postisolation phase-space histograms reflect new and effectively identical probability density distributions. The particles' new energy level is higher than if the droplets had been isolated at all times. The new energy level observed, and sustained beyond isolation, is shown to be related with long-range disturbances existing prior to isolation. The postisolation change of phase-space cycles is faster than any possible propagation of information between subsystems. The statistical droplet pairing is therefore associated to preexisting correlations between particles. The intrinsic statistical relation of the bipartite system adjusts itself to new configurations where statistical indistinguishability persists even after the particles are set into isolation.

We present a framework to quantitatively describe energy exchange in high-speed turbulent flows, also including the hypersonic regime. Governing equations are introduced which control the transport of the mean-field kinetic energy ($k_m$), the turbulence kinetic energy ($k_t$), the mean-field internal energy ($e_m$), and the turbulence internal energy ($e_t$). The common terms in the transport equations are found to represent energy exchanges and interactions among $k_m, k_t, e_m$, and $e_t$. The routes of energy exchange are then highlighted and quantified in hypersonic boundary-layer flow, with special attention paid to the effects of wall cooling.

Anguilliform and carangiform fish have a thinner and thicker body along with a smaller and larger undulating wavelength-based kinematics for their propulsion, respectively. The present work is motivated by the fact that both types of fish are observed to adopt each other's kinematics for a short duration on a needs basis. This study explores the effect of such adaptive kinematics via a 2D computational model, focusing on the underlying fluid dynamics and propulsive performance. The effect of the shape is also studied by considering various series of NACA00XX hydrofoil, based on the fineness ratio (length/thickness) of different anguilliform and carangiform fish reported in the literature. Adaptation of carangiform (anguilliform) mode of undulation kinematics by an anguilliform (carangiform)-shaped hydrofoil is found to result in an increase (decrease) in the thrust coefficient along with a decrease (increase) in the quasipropulsive efficiency. Flow characteristics, such as the pressure distribution around the hydrofoil, the strength of the vortices, and the jet behind the hydrofoil, are correlated with the propulsive performance of two naturally observed and six adaptive cases mimicking anguilliform and carangiform fish-inspired shape and swimming. Fineness ratio and undulation wavelength, as compared to the amplitude envelope, has more influence on the propulsive performance and vortex strength in the wake, except for the protovortex, which is more influenced by the amplitude envelope. Finally, a discussion is presented to connect the present 2D CFD results with some of the observed behavior of the anguilliform/carangiform fish in nature. This bioinspired and biomimetics study on naturally observed and adaptive fish-inspired swimming may assist with the need-based efficient design of underwater vehicles.

The breakup of a fluid jet into droplets has long fascinated natural scientists, with early research dating back to the 19th century. Infinitesimal perturbations to a jet grow because of surface tension, which eventually leads to breakup of the jet into droplets (Rayleigh-Plateau instability). Although this classical phenomenon has long been studied, it is not clear how it is modified when the fluid is replaced by an active fluid. In this study, we investigate instabilities of a jet of an active fluid. The active fluid is modeled by a suspension of microswimmers that propel themselves by generating surface tangential velocities, i.e., squirmers. The squirmers are assumed to be bottom-heavy and heavier than the surrounding fluid, so that a downward jet of the active fluid self-assembles under gravity. Hydrodynamic interactions between squirmers are computed using the Stokesian dynamics method, in which near-field hydrodynamics are accurately calculated. We find that jets of active fluids are unstable, with different unstable modes between pullers and pushers. For an active fluid of pullers, the jet breaks up into droplets in a varicose manner reminiscent of a Newtonian fluid. For pushers, however, the jet buckles and undergoes a waving (sinuous) instability. The physical mechanisms for these two instabilities can be understood by an inspection of the stress fields in the jets, and parametric study reveals the importance of hydrodynamic interactions in the instabilities. Although both gravity and bottom-heaviness play an essential role in realizing the downward jet, their influence on the instability is found to be limited. Our findings help reveal new features of the collective properties of active fluids.

A vesicle is a common model used to represent red blood cell (RBC) in silico and in vitro. We investigate here the dynamics and the rheology of a vesicle under shear flow confined between two parallel walls in wide ranges of applied shear rate and the viscosity contrast (viscosity ratio between the internal and external fluids of the vesicle). The Helfrich model is used to describe the vesicle membrane energy and the spectral boundary integral method to compute the velocity of the vesicle membrane. Multilobe shapes are observed in a wide range of shear rates and viscosity contrasts. A phase diagram is determined in this parameter space. The cytoskeleton of a RBC is not necessary for the multilobe manifestation, in contrast with recent claims. Here we show that these shapes are due to membrane tension only. This highlights the fact that the two-dimensional (2D) vesicle model used here, besides its relevant predictions in previous studies (such as slipper and parachute shapes), can capture several other shapes and dynamics observed for RBCs. The 2D vesicle can thus be used as a reliable model, at least as an exploration basis, to investigate blood flow where the three-dimensional model may prove to be computationally demanding, especially for dense suspensions. We investigate the rheology of the multilobe shapes in the dilute regime and find that the effective viscosity exhibits a significant jump associated with a transition to multilobe dynamics. We provide simple interpretations to these findings. We discuss the stability of the centered solutions and the emergence of the off-centered ones.

In this article, we present a predictive model for the amplitude of impulse waves generated by the collapse of a granular column into a water layer. The model, which combines the spreading dynamics of the grains and the wave hydrodynamics in shallow water, is successfully compared to a large dataset of laboratory experiments, and captures the influence of the initial parameters while giving an accurate prediction. Furthermore, the role played on the wave generation by two key dimensionless numbers, i.e., the global Froude number and the relative volume of the immersed deposit, is rationalized. These results provide a simplified, yet comprehensive, physical description of the generation of tsunami waves engendered by large-scale subaerial landslides, rockfalls, or cliff collapses in a shallow water.

This work presents algebraic closure models associated with advective transport and nonlinear reactions in a Reynolds-averaged Navier-Stokes context for a system of species subject to binary reactions and transport by advection and diffusion. Expanding upon analysis originally developed for non-reactive transport in the context of Taylor dispersion of scalars, this work extends the modified gradient diffusion model explicated by Peters [N. Peters, Turbulent Combustion, Cambridge Monographs on Mechanics (Cambridge University Press, Cambridge, 2000)] and based on work by Corrsin [S. Corrsin, The reactant concentration spectrum in turbulent mixing with a first-order reaction, J. Fluid Mech. 11, 407 (1961)] beyond single-component transport phenomena and involving nonlinear reactions. The presented model forms, from this weakly nonlinear extension of the original dispersion theory, lead to an analytic expression for the eddy diffusivity matrix that explicitly captures the influence of the reaction kinetics on the closure operators. Furthermore, we demonstrate that the derived model form directly translates between flow topologies through a priori and a posteriori testing of a binary species system subject to homogeneous isotropic turbulence. Using two- and three-dimensional direct numerical simulations involving laminar and turbulent flows, it is shown that this framework improves prediction of mean quantities compared to previous results. Lastly, the presented model form, collapses to the earlier gradient diffusion and its modified version derived by Corrsin in the limits of nonreactive species and linear reactions, respectively.

The motion of a free rising skirt bubble is studied using direct numerical simulation covering the range of Eötvös (Bond) and Morton numbers where they can be observed. We investigate the skirt bubble motion (terminal velocity and drag), the flow field structure (inside the skirt film, around the bubble, and inside the gas film that forms the skirt) as well as the geometrical characteristics of the skirt (both length and thickness). A unified relation for the terminal velocity (and drag force) is provided for all bubble shapes (dimple, skirt, and spherical cap bubbles) when considering Eötvös numbers (based on bubble diameter) larger than 100. The velocity field around and inside the bubble is investigated resulting in the clarification of the wake structure with a major difference with the flow deduced from experimental observations during the 1970s. The numerical simulations reveal that only one recirculation is observed inside the bubble while two vortices are highlighted in the wake. We confirm that a parallel Poiseuille flow develops inside the skirt film resulting in an intense vorticity field. Original modeling is improved with a Reynolds correction that makes possible the prediction of the film thickness in very good agreement with the only experimental value available in the literature. Our simulations combined with experimental observations suggest the existence of a maximum value for the skirt length.

We use numerical simulations to study the dynamics of red blood cells (RBCs) in unconfined and confined Poiseuille flow. Previous numerical studies with three-dimensional (3D) vesicles have indicated that the slipper shape observed in experiments at high capillary number can be attributed to the bistability due to the interplay of wall push and outward migration tendency at higher viscosity contrasts. In this paper, we study this outward migration and bistability using numerical simulations for 3D capsules and provide phase diagrams of RBC dynamics with and without viscosity contrast. We observe a bistability of slipper and croissants in confined Poiseuille flow with viscosity contrast as observed in experiments.

The effect of initial perturbations on the evolution of the inclined Richtmyer-Meshkov turbulent mixing layer before and after reshock initiated by a shock wave with Mach number 1.55 is investigated through three-dimensional (3D) simulations using the flash code. The 3D simulations aim to reproduce both predominantly single-mode and multimode interfaces between light and heavy gases (${\mathrm{N}}_2\text{−}{\mathrm{CO}}_2$, Atwood number, $A\approx 0.22$; amplitude to wavelength ratio of 0.088) which were created in an inclined shock tube facility to analyze the effects of initial conditions on mixing development in the entire flow field. The two-dimensional center slices of 3D simulations are compared with the experimental results to validate the computational code. Mixing width, mixed mass, mixed-mass thickness, and circulation in addition to concentration fields are shown to be in good agreement with the experimental data. The three-dimensional density and vorticity fields are first presented to qualitatively describe the flow behavior before and after reshock. Several measured density/velocity-related quantities indicate that the growth of the mixing material is strongly dependent on initial conditions. Before reshock and at early times after reshock, flow is clearly maintaining the memory of initial perturbations. However, at late time after reshock, although the large wavelength feature still dominates the flow motion, and the morphology of the two different interfaces indicates several differences, by breakdown of large-scale coherent structures to much finer scales, the memory of small scales of the multimode initial perturbation is not as clear as pre-reshock. Regarding three-dimensionality of the flow, before reshock in the multimode case, the baroclinic vorticity production, circulation, turbulent kinetic energy, and turbulent mass flux suggest that the small-scale roll-up features along the large inclined wavelength quickly evolves in all three dimensions. The coherent vortex tubes break down to smaller wormlike vortex structures, and turbulent fluctuations in the out-of-plane dimension are comparable to the spanwise direction. After reshock, this three-dimensionality of mixing growth was observed in the flow for both initial conditions. The results of this work represent a significant extension of previous computational studies performed on this specific topic. A different code with a different numerical method is validated through comparison with the experimental data. The initial perturbations are directly measured from the experimental results. Moreover, the entire three-dimensional experimental shock tube domain is simulated, and more quantities are investigated to understand the mixing mechanism and instability evolution in all three dimensions.

Detached eddy simulations of a Mach 3, turbulent flow over a blunt fin were performed. Past experiments have shown that this configuration generates a large, three-dimensional, unsteady, separated region. Our previously published detached eddy simulations exhibited large-scale unsteadiness even in the absence of fluctuations in the incoming flow. The introduction of synthetic turbulence at the inflow boundary altered that separation motion. With the previous simulations as a reference baseline, a parametric study was carried out of the response of the flow to time-periodic forcing of the incoming boundary layer. The disturbances were introduced into the boundary layer through momentum and energy source terms. The spatial form of the source terms was based on averages of the baseline flow, conditioned on the motion of the separation shock. The response of the separation shock motion to the imposed perturbations was found to be dependent on the frequency of forcing. With a forcing frequency representative of the characteristic large-scale separation unsteadiness in the baseline flow, the separation shock motion was phase locked to the applied force, and a larger forcing amplitude led to greater separation motion. The separation region did not, however, respond strongly to disturbances in a higher frequency range. These results show that, in a flow that oscillates in the absence of upstream disturbances, separation motion can be modulated by upstream forcing of a particular form. Similar results have been obtained in the past for flows where separation unsteadiness is directly driven by incoming turbulence, but the modulation of self-excited oscillations in the present class of flow is a different behavior. It suggests opportunities for flow control of strong shock-wave–boundary-layer interactions.

Thin liquid films play a central role in coating processes and other industrial and natural applications. Efficient optimization of these processes requires an understanding of capillary leveling, Marangoni flow, evaporation, and related phenomena. Although mathematical models are useful for gaining such understanding, it can be difficult to extract physical insight as the number of phenomena considered increases, so simplifying assumptions such as the vertical-averaging (VA) approximation for solute concentration are often employed. In this work, we consider two-component films consisting of a solute and volatile solvent and use lubrication theory to examine the performance of the VA approximation for three common evaporation models: constant, one-sided, and diffusion-limited. Whereas the VA approximation typically assumes ${\epsilon }^2\text{Pe}\ll 1$, where $\epsilon$ is the aspect ratio and Pe is the Péclet number, we find that the critical value of ${\epsilon }^2\text{Pe}$ beyond which the VA approximation breaks down is often much larger than unity and depends on the evaporation rate. Furthermore, applying the VA approximation outside of its regime of validity results in drastically different film-height and solute-distribution predictions depending on the evaporation model. Scaling relations are derived from physical arguments to show how the critical value of ${\epsilon }^2\text{Pe}$ depends on the evaporation rate under each evaporation model.

Superhydrophobic (SH) coatings have been demonstrated to reduce drag in various applications, though they have yet to be widely used or adopted due to practical issues. Various studies have demonstrated the prospect of reducing drag via SH surfaces both in turbulent and laminar flow regimes. However, the beneficial wall-slip effect produced may disappear depending on the surface geometry and flow conditions. The main mechanisms considered behind the decrease in performance are Marangoni-induced stresses and air/liquid interface deformation. In the present study, another mechanism is proposed to explain the loss of performances of SH surfaces in laminar flow regimes. Here we consider the flow of air inside the plastron and the associated momentum loss induced by roughness elements with different geometric characteristics. The effects of air motion within the plastron are coupled to the outer fluid with a homogenized boundary-condition approach. To this end, numerical simulations at the scale of the roughness elements were conducted as a function of the porosity and the tortuosity of the domain to determine the slip velocity at the air/liquid interface. The homogenized boundary condition is then implemented in a theoretical model for the outer flow to compute drag on SH spheres at low Re numbers. Experiments of laminar SH falling spheres indicate that high values of the tortuosity and low values of the porosity lead to a loss of performances when considering drag reduction. As anticipated, a three-dimensional printed sphere with low tortuosity and similar porosity demonstrated near-optimal drag reductions. A comparative study between the predicted values and experiments shows that the homogenized model is able to accurately predict the drag on SH surfaces for values of the porosity and tortuosity estimated from microscopy images of the SH textured surface.

We construct a model to explore the hydrodynamic interactions of active inclusions in curved biological membranes. The curved membrane is modeled as a two-dimensional layer of highly viscous fluid, surrounded by external solvents of different viscosities. The active inclusions are modeled as point force dipoles. The point dipole limit is taken along a geodesic of the curved geometry, incorporating the change in orientation of the forces due to curvature. We demonstrate this explicitly for the case of a spherical membrane, leading to an analytic solution for the flow generated by a single inclusion. We further show that the flow field features an additional defect of negative index, arising from the membrane topology, which is not present in the planar version of the model. We finally explore the hydrodynamic interactions of a pair of inclusions in regimes of low and high curvature, as well as situations where the external fluid outside the membrane is confined. Our study suggests aggregation of dipoles in curved biological membranes of both low and high curvatures, under strong confinement. However, very high curvatures tend to destroy dipole aggregation, even under strong confinement.

An experimental investigation is conducted to evaluate the effect of polymer injection on the development of a zero-pressure-gradient bypass transitioning boundary layer on a flat plate. Planar particle image velocimetry and planar laser-induced fluorescence measurements conducted at multiple streamwise stations allow for a characterization of the development of the bypass transition process induced by a two-dimensional trip wire in both Newtonian and polymer-injected flow. Two different trip placements with respect to the injection slot are considered to study the effect of polymer injection within the wake of the trip wire and within the laminar boundary layer upstream of the trip. The transition process is initiated in a separated shear layer downstream of the trip wire, where a rapid amplification of the velocity perturbations via an inflectional Kelvin-Helmholtz instability leads to vortex shedding and subsequent breakdown to turbulence. A similar transition process is observed with polymer injection, but a more rapid initial growth of perturbations is observed, leading to earlier transition. Nonetheless, an onset of polymer effect is seen in the late transition stages and leads to significant levels of drag reduction in the developing turbulent boundary layer.

The physics of shock-boundary layer interactions (SBLIs) in a supersonic turbine cascade at Mach 2.0 and Reynolds number 395,000, based on the axial chord, is investigated through a wall-resolved large eddy simulation. Special attention is given to the characterization of the low-frequency dynamics of the separation bubbles using flow visualization, spectral analysis, space-time cross correlations, and flow modal decomposition. The mean flowfield shows different shock structures formed on both sides of the airfoil. On the suction side, an oblique shock impinges on the turbulent boundary layer, whereas a Mach reflection interacts with the pressure side boundary layer. The interactions taking place in the present turbine cascade show similarities and discrepancies with respect to more canonical cases. For example, the characteristic frequencies of the shock/bubble motions are comparable to those described in the literature of canonical cases. However, the suction side bubble leads to compression waves that do not coalesce into a separation shock, and a thin bubble forms on the pressure side despite the strong normal shock from the Mach reflection. Instantaneous flow visualizations illustrate elongated streamwise structures on the incoming boundary layers and their interactions with the shocks and separation bubbles. The space-time cross-correlations reveal that the near-wall streaks drive the motion of the suction side separation bubble, which in turn promotes oscillations of the reattachment shock and shear layer flapping. Organized motions in the SBLIs and their corresponding characteristic frequencies and spatial support are identified using proper orthogonal decomposition.

We experimentally investigate the curvature-driven migration and coalescence of an ethanol droplet on the free surface of an ethanol pool with an inclined bottom wall by employing a high-speed shadowgraph technique. Two distinct coalescence phenomena, migrating partial coalescence and multidrop pinch-off, in addition to the normal partial coalescence and complete coalescence are observed when the Weber number (We), liquid depth at the impact point $(d_l/D)$, and inclination angle $\left(\theta \right)$ are varied. The three-phase contact line (TPCL) formed by the air-liquid interface on the inclined bottom wall and its curvature near the TPCL cause these unique dynamics. The coalescence behaviors are clearly demarcated by the regime maps drawn in $d_l/D\text{−}\mathrm{We}$ and $\theta \text{−}{d}_l/D$ spaces. We found that the transition between partial and complete coalescence occurs at $\mathrm{We}\approx 10$, regardless of liquid depth, and that, for $\theta ={18}^{\circ }$, the influence of the inclined wall is apparent for $\mathrm{We}>2$, which increases as the inclination angle increases.

This work explores the turbulence anisotropy behavior of a fluidized gas-particle suspension obtained from highly resolved kinetic-theory-based two-fluid model simulations. Therein, the phase-filtered anisotropy Reynolds stress tensor is considered to classify the possible states of turbulence in the barycentric anisotropy invariants map. The temporal turbulence trajectories have revealed a nonlinear converging demarcation line that evolved differently on the gas and solid phases. It isolates the prolate-like cluster's turbulence from the oblate-like background strain on the solid phase, while on the gas phase, the trajectories turn from nearly three-dimensional (3-D) turbulence inside the clusters to 1-D turbulence in the transition regions (from dense to dilute), which then develops into 2-D turbulence in the dilute areas. The converged trajectories at the demarcation lines are found to move always toward isotropy, revealing the return-to-isotropy problem and the tendency to extinguish the bulk anisotropy. The prevalent turbulence type on the solid phase has indicated a 1-D turbulence preference, which is consistent with the reported cluster-induced turbulence in the literature. Moreover, the granular temperature as a quantitative measure of uncorrelated particle agitation is found to accumulate predominantly in 1-D turbulence (dominant solid divergence and strain) and moderately in 2-D turbulence (dominant solid convergence) at the upstream parts of clusters. Similar disclosure of turbulence types is adopted as well, for the variance of solid concentration, drag production, and the magnitudes of the gas-phase Reynolds stress and rate-of-strain tensors. They have demonstrated a similar preferential turbulence anisotropy, which in turn promotes the applicability of the eddy-viscosity approach for modeling the gas-phase Reynolds stress contributions.

We consider three-dimensional turbulence from which vortex stretching is removed. Using direct numerical simulations, we show that in this system a dual cascade is observed, consisting of a forward enstrophy cascade and an inverse helicity cascade. In the inverse cascade range the energy spectrum scaling is proportional to $k^{-7/3}$, with $k$ being the wave number. In the forward cascade range the spectrum is proportional to $k^{-3}$ with a logarithmic correction.

Viscous flows through configurations manufactured or naturally assembled from soft materials apply both pressure and shear stress at the solid-liquid interface, leading to deformation of the fluidic conduit's cross section, which, in turn, affects the flow rate-pressure drop relation. Conventionally, calculating this flow rate-pressure drop relation requires solving the complete elastohydrodynamic problem, which couples the fluid flow and elastic deformation. In this Letter, we use the reciprocal theorems for Stokes flow and linear elasticity to derive a closed-form expression for the flow rate-pressure drop relation in deformable microchannels, bypassing the detailed calculation of the solution to the fluid-structure-interaction problem. For small deformations (under a domain perturbation scheme), our theory provides the leading-order effect of the interplay between the fluid stresses and the compliance of the channel on the flow rate-pressure drop relation. Our approach uses solely the fluid flow solution and the elastic deformation due to the corresponding fluid stress distribution in an undeformed channel, eliminating the need to solve the coupled elastohydrodynamic problem. Unlike previous theoretical studies that neglected the presence of lateral sidewalls (and considered shallow geometries of effectively infinite width), our approach allows us to determine the influence of confining sidewalls on the flow rate-pressure drop relation. In particular, for the flow-rate-controlled situation and the Kirchhoff-Love plate-bending theory for the elastic deformation, we show a trade-off between the effect of compliance of the deforming top wall and the drag due to sidewalls on the pressure drop. Whereas compliance decreases the pressure drop, the drag due to sidewalls increases it. Our theoretical framework may provide insight into existing experimental data and pave the way for the design of novel optimized soft microfluidic configurations of different cross-sectional shapes.