Suspensions of fluid particles with complex interfacial architecture (for instance, capsules, vesicles, polymersomes, lipid bilayers, and emulsions embedded with certain surface-active agents and surfactants) find an immense number of applications in the field of engineering and bioscience. Interfacial rheology plays an important role in the dynamics of many of these systems, yet little is understood about how these effects alter droplet deformation and breakup. In this study, we develop a theoretical model that explores the deformation and breakup of a single droplet with a viscous surface modulus suspended in an unbounded immiscible fluid under a general linear flow field. The viscous interface is modeled as a two-dimensional surface having a surface shear viscosity ${\eta }_{\mu }$, surface compression/dilational viscosity ${\eta }_{\kappa }$, and a constant surface tension over the interface, using a Boussinesq-Scriven constitutive relationship. We present the droplet breakup analysis in Stokes flow in the limit of small droplet deformation using a turning point analysis similar to that of Barthes-Biesel and Acrivos [J. Fluid Mech. 61, 1 (1973)]. In particular, we examine how the critical capillary number for breakup depends on the interfacial viscosity for different viscosity contrasts between the inner and outer fluid and different flow types. For all the flows considered, we observe that ${\eta }_{\kappa }$ is found to have a destabilizing impact on droplet breakup, whereas ${\eta }_{\mu }$ has a stabilizing effect. We explore the physical picture behind these observations in this work.

Studies on compound droplet are of emerging importance in biology and engineering. Here, we bring out unique morphodynamics of a compound droplet as a consequence of interplay between an imposed electric field and an extensional flow. As compared to the deformation characteristics of compound droplet reported in the sole presence of extensional flow [Stone and Leal, J. Fluid Mech. 211, 123 (1990)], our results implicate several nonintuitive findings on the dynamical evolution of the droplet. These exclusive new features include the interconversion of shape-evolution patterns of the compound droplet system contingent on the strength of background flow, electric field strength, electrophysical properties, and hitherto-unveiled post-breakup dynamics. Depending on these key parameters, in addition to three steady-state configurations, two new modes of droplet pinch-off are observed: Mode I: polar pinch-off; Mode II: equatorial pinch-off. Interestingly, the pinch-off time is found to vary nonmonotonically with the strength of the electric field. In sharp contrast to the extensional viscosity of a compound droplet in absence of other external fields [Stone and Leal, J. Fluid Mech. 211, 123 (1990)], we show that the additional presence of electric field brings in an intricate dependence on the electrical properties of the inner droplet; a paradigm that is not prevalent in pure extensional flow.

The flow of wall-bound liquid films on an inclined substrate is governed by viscous effects, inertia, gravity, and surface tension. It can also be significantly influenced by aerodynamic stresses if it is exposed to an external gas flow. Such film flows on nonwettable or partially wettable surfaces break up under certain conditions, when the capillary forces associated with the substrate wettability are larger than the momentum flux of the film. The dry arches which appear are separated from the wetted areas on the surface by a liquid rim, which arises due to capillary forces. In this experimental and theoretical study the dynamics of a steady flow in such rims are considered, accounting also for aerodynamic effects. Using a force balance of the rim, predictions are made for the trajectory of the rim centerline and the main geometrical properties of its cross section. The theoretical predictions agree well with the experimental data obtained in this study.

Binary fluids are present in a wide variety of systems at microscales, such as microfluidic devices containing drops, fluids with air bubbles trapped in them, and devices designed to mix fluids or to make two fluid substances react. Microfluidics devices are often, intentionally or unintentionally, subject to pulsatile forces due to the passing of drops. We demonstrate that when a binary fluid is subject to a pulsatile forcing, the compressibility of the lower viscosity phase is so important that it is able to generate resonances in the dynamic permeability of the whole system. This implies that the flow amplitude of a binary-fluid system in a zero-mean flow could be optimized at certain frequencies. The dynamic permeability is a powerful concept to describe the dynamics of the system, in the regime where the flow and the pressure gradient are related linearly in the frequency domain. We find two regimes for the frequency at which the resonance occurs: one dominated by a characteristic frequency of the system, related to the compressibility of the lower viscosity phase; and another one dominated by a more complex frequency, involving both the characteristic viscous frequency of the lower viscosity phase and a characteristic frequency related to the compressibility. In order to guide potential experiments, we calculate relevant quantities for two sets of binary fluids in standard microfluidic setups. Our calculations imply that for systems of typical microfluidic dimensions, involving a compressible fluid, the existence of the compressibility-induced resonance has to be contemplated for a correct description of the dynamics.

To investigate the effect of sweep on the leading-edge vortex of high aspect ratio plunging wings, this article presents force, bending moment, and volumetric velocity measurements for high aspect ratio $\mathrm{AR}=10$ wings with sweep angles of 0° and 40°. The effect of the sweep angle on the bending moment is the largest at the minimum effective angle of attack. This is because as the leading-edge vortex sheds it moves inboard on the unswept wing while moving outboard on the swept wing. Where the leg of the leading-edge vortex connects with the wing there is significant three-dimensional flow. The axial velocity along the vortex filament, which may be towards to the wing tip or the wing root (reversed flow), exhibits increasing magnitude as the effective angle of attack decreases and the vortex filament deforms. Reversed axial flow along the vortex filament has the largest magnitudes for the unswept wing. In the vortex core, jetlike, wakelike, and uniform axial velocity profiles were observed. Unlike the classical vortex breakdown, the transition from the jetlike to the wakelike axial flow does not appear to be abrupt. The measurements also revealed evidence of spanwise instabilities in the leading-edge vortex filament.

Many practical applications (e.g., coating, painting, printing, or agrochemical spraying) involve depositing complex fluids onto a solid substrate using a predominantly uniaxial extensional flow. In this work, we conduct experiments by gradually depositing non-Newtonian surfactant fluids onto a horizontal solid substrate via a vertical needle. We investigate the extent to which, the spreading dynamics of the fluid contact line on the solid substrate can affect the thinning dynamics of the fluid filament formed between the needle and the substrate. Our work considers two model viscoelastic surfactant fluids based on cetylpyridinium chloride and sodium salicylate (CPyCl/NaSal) and octadecyltrimethylammonium bromide and sodium oleate $\left({\mathrm{C}}_8\mathrm{TAB}\text{/}\mathrm{NaOA}\right)$ in deionized water. Experiments are performed using two flat substrates: a big substrate, where fluid contact line is free to move, and a finite-size substrate, where fluid contact line is pinned. The fluid wetting on the substrate is characterized by measuring the contact-line velocity and dynamic contact angle, while the extensional flow is evaluated by measuring the fluid midfilament diameter. Two novel regimes are identified: In regime I, fluid wetting and filament pinch-off dynamics are independent, while in regime II, the fluid wetting significantly affects the extensional flows by lowering the material extensional relaxation times and Trouton ratios. Our analysis shows that spreading of these viscoelastic surfactant fluids are surprisingly well captured by Tanner's law suggested for spreading of a Newtonian fluid on solid substrates. Finally, we propose a scaling analysis based on a combination of the wetting forces and viscous dissipation that can successfully explain the effects of wetting on filament pinch-off dynamics.

The tip radius $R_{\mathrm{tip}}$ of ferrofluids deformed by magnetization is typically ∼100 μm, much larger than in conducting electrified liquids, even though in both cases the capillary stress $2\gamma /R_{\mathrm{tip}}$ balances the electrostatic or magnetostatic stress. The reason for the relative dullness of magnetic tips appears to be the saturation of magnetization, $M_{\max }=M_{\mathrm{sat}}$. This hypothesis lacks quantitative experimental confirmation but is supported theoretically by the recently proposed high field asymptote $R_{\mathrm{tip}}\to \frac{4\gamma }{{\mu }_o{M}_{\mathrm{sat}}^2}$ obtained for isolated drops in strong and uniform magnetic fields. Here we confirm experimentally the controlling role of the magnetic saturation effect under more general conditions, by showing that the dimensionless group ${\mu }_o{M}_{\mathrm{sat}}^2{R}_{\mathrm{tip}}/\left(4\gamma \right)$ is always a quantity of order unity, even for ferrofluid menisci subject to the highly nonuniform magnetic fields created by supporting them at the tip of a ferrous needle facing a strong magnet. Four different ferrofluids are used, with high, medium, and low surface tensions, including highly polar and nonpolar solvents. Substantial changes in $M_{\mathrm{sat}}$ are achieved by letting the suspending solvent evaporate, with record tip radii down to 9.5 μm demonstrated at high volume fractions of magnetic particles.

The seminal Batchelor-Green's (BG) theory on the hydrodynamic interaction of two spherical particles of radii $a$ suspended in a viscous shear flow assumes unbounded fluid. In the present paper we study how a rigid plane wall modifies this interaction. Using an integral equation for the surface traction we derive the expression for the particles' relative velocity as a sum of the BG's velocity and the term due to the presence of a wall at finite distance, $z_0$. Our calculation is not the perturbation theory of the BG solution, so the contribution due to the wall is not necessarily small. We indeed demonstrate that the presence of the wall is a singular perturbation, i.e., its effect cannot be neglected even at large distances. The distance at which the wall significantly alters the particles interaction scales as $z_0^{3/5}$. The phase portrait of the particles' relative motion is different from the BG theory, where there are two singly connected regions of open and closed trajectories both of infinite volume. For finite $z_0$, besides the BG's domains of open and closed trajectories, there is a domain of closed (dancing) and open (swapping) trajectories that do not materialize in an unbounded shear flow. The width of this region grows as $1/z_0$ at smaller separations from the wall. Along the swapping trajectories, which have been previously observed numerically, the incoming particle is turning back after the encounter with the reference particle, rather than passing it by, as the BG theory anticipates. The region of dancing trajectories has infinite volume and is separated from a BG-type domain of closed trajectories that becomes compact due to presence of the wall. We found a one-parameter family of equilibrium states that were previously overlooked, whereas the pair of spheres flows as a whole without changing its configuration. These states are marginally stable and their perturbation yields a two-parameter family of the dancing trajectories, whereas the test particle is orbiting around a fixed point in a frame comoving with the reference particle. We suggest that the phase portrait obtained at $z_0\gg a$ is topologically stable and can be extended down to rather small $z_0$ of several particle diameters. We confirm this hypothesis by direct numerical simulations of the Navier-Stokes equations with $z_0=5a$. Qualitatively the distant wall is the third body that changes the global topology of the phase portrait of two-particle interaction.

The evolution of a turbulent tangle of quantum vortices in the presence of finite-size active particles is studied by means of numerical simulations of the Gross-Pitaevskii equation. Particles are modeled as potentials depleting the superfluid and described with classical degrees of freedom following a Newtonian dynamics. It is shown that particles do not modify the building-up and the decay of the superfluid Kolmogorov turbulent regime. It is observed that almost the totality of particles remains trapped inside quantum vortices, although they are occasionally detached and recaptured. The statistics of this process is presented and discussed. The particle Lagrangian dynamics is also studied. At large timescales, the velocity spectrum of particles is reminiscent of a classical Lagrangian turbulent behavior. At timescales faster than the turnover time associated with the mean intervortex distance, the particle motion is dominated by oscillations due to the Magnus effect. For light particles, a nonclassical scaling of the spectrum arises. The particle velocity and acceleration probability distribution functions are then studied. The decorrelation time of the particle acceleration is found to be shorter than in classical fluids, and related to the Magnus force experienced by the trapped particles.

We investigate the drag forces acting on objects moving through a granular packing immersed in water. In this aim, we conducted uplift experiments involving pulling out horizontal plates at a prescribed velocity vertically. During these tests, we observed that the drag force reaches to peak at a low displacement and then decays. Results show that the peak drag force strongly increases with the velocity and depends on the plate size and grain diameter. We identify empirical scaling laws for these properties and introduce a Darcy-flow mechanism that can explain them. Furthermore, we conducted tests involving suddenly stopping the motion of the plate, which evidenced a progressive relaxation of the drag force in time. We discuss how a visco-elasto-plastic mechanical analog can reproduce these dynamics. These results and analyses highlight fundamental differences in drag force between dry and immersed granular materials.

The motion of high Reynolds number objects at free surfaces is a general problem that has many industrial and ecological applications, such as hazard assessment due to driftwood in rivers or motion of plastic patches in the oceans. Modeling such object trajectories in a flow can be done assuming the object to be a tracer or using Newton's second law in the form of the Basset-Boussinesq-Oseen equation. In many studies, however, the latter approach can be difficult to implement due to the presence of complex forces at play and a high computational cost, thus knowing the validity of the tracer model can be very useful for practical applications. In this work, we study theoretically and experimentally the dynamics of high Reynolds number floating objects in one- and two-dimensional free surface flows. We first verify that the two-dimensional surface version of the Basset-Boussinesq-Oseen equation can accurately model floating object trajectories. Following our theoretical analysis, we introduce a characteristic response distance noted $\lambda$ that scales the acceleration distance of a floating object, and we show that it is about two to four times the body length in the streamwise direction. The dimensionless parameter ${\lambda }^{★}$ obtained by normalizing $\lambda$ by a flow length scale then plays a role analogous to that of the Stokes number at low particulate Reynolds number. Moreover, we show that once the floating object reaches the flow velocity, or if at any given time its velocity is equal to that of the flow, the floating object behaves like a tracer, regardless of ${\lambda }^{★}$. These results can greatly simplify the analyses and computations of the motion of floating objects at high particulate Reynolds number, first by identifying a characteristic distance $\lambda$ scaling the length of the acceleration phase, and then by showing that once the flow velocity is reached, the object is transported as a passive tracer.

Modal analysis techniques are used to identify patterns and develop reduced-order models in a variety of fluid applications. However, experimentally acquired flow fields may be corrupted with incorrect and missing entries, which may degrade modal decomposition. Here we use robust principal component analysis (RPCA) to improve the quality of flow-field data by leveraging global coherent structures to identify and replace spurious data points. RPCA is a robust variant of principal component analysis, also known as proper orthogonal decomposition in fluids, that decomposes a data matrix into the sum of a low-rank matrix containing coherent structures and a sparse matrix of outliers and corrupt entries. We apply RPCA filtering to a range of fluid simulations and experiments of varying complexities and assess the accuracy of low-rank structure recovery. First, we analyze direct numerical simulations of flow past a circular cylinder at Reynolds number 100 with artificial outliers, alongside similar particle image velocimetry (PIV) measurements at Reynolds number 413. Next, we apply RPCA filtering to a turbulent channel flow simulation from the Johns Hopkins Turbulence database, demonstrating that dominant coherent structures are preserved in the low-rank matrix. Finally, we investigate PIV measurements behind a two-bladed cross-flow turbine that exhibits both broadband and coherent phenomena. In all cases, we find that RPCA filtering extracts dominant coherent structures and identifies and fills in incorrect or missing measurements. The performance is particularly striking when flow fields are analyzed using dynamic mode decomposition, which is sensitive to noise and outliers.

The nature of the fluctuations of the dissipation rate in fluid turbulence is still under debate. One reason may be that the observed fluctuations are strong events of dissipation, which reveal the trace of spatiotemporal singularities of the Euler equations, which are the zero viscosity limit of ordinary incompressible fluids. Viscosity regularizes these hypothetical singularities, resulting in a chaotic fluctuating state in which the strong events appear randomly in space and time, making the energy dissipation highly fluctuating. Yet, to date, it is not known if smooth initial conditions of the Euler equations with finite energy do or do not blow up in finite time. We overcome this central difficulty by providing a scenario for singularity-mediated turbulence based on the self-focusing nonlinear Schrödinger equation. It avoids the intrinsic difficulty of Euler equations since it is well known that solutions of this NLS equation with smooth initial conditions do blow up in finite time. When adding viscosity, the model shows (i) that dissipation takes place near the singularities only, (ii) that such intense events are random in space and time, (iii) that the mean dissipation rate is almost constant as the viscosity varies, and (iv) the observation of an Obukhov-Kolmogorov spectrum with a power-law dependence together with an intermittent behavior using structure function correlations, in close correspondence with the one measured in fluid turbulence.

A millimetric bouncing droplet sustained on a vibrating bath becomes a moving wave source (particle) through periodically interacting with the local wave field it generates during the droplet-bath impact. By virtue of such particle-wave duality, the macroscopic hydrodynamic system imitates enigmatic behaviors of the quantum realm. Here we show that it is possible to create an integrated pilot-wave field to better prescribe the droplet trajectories, via amplified bath capillarity. This is demonstrated with a liquid metal droplet-bath system in which the local wave field generated by droplet bouncing is superposed by the global wave field induced by bath meniscus oscillation. The resulting dual pilot-wave configuration enables a class of directional chasing motions of two bound dissimilar droplets (heterodimers) in multilevel hydrodynamic traps (orbits), featuring two quantized regime parameters, namely, the interdroplet binding level and the orbit level. We investigate the dynamics of the vibrating liquid metal bath, with its level-split ring-wave field and its peculiar vortex field being highlighted. We also rationalize the exotic droplet motions by considering the interdroplet particle-wave interactions mediated by the integrated pilot-wave field. It is revealed that a temporal bouncing phase shift between the two droplets in the heterodimers, due to size mismatch, gives rise to their horizontal propulsion, while their spatial binding regime exclusively determines the collective chasing direction. It is further evidenced that the horizontal in-orbit chasing motion is directly related to vertical droplet bouncing. Our findings unveil the integrated pilot-wave field as a trail towards improved droplet guiding, thereby extending the hydrodynamic particle-wave analogy to optical systems and beyond.

Cilia and flagella are self-actuated microtubule-based structures that are present on many cell surfaces, ranging from the outer surface of single-cell organisms to the internal epithelial surfaces in larger animals. A fast and robust numerical method that simulates the coupled hydrodynamics of cilia and the constituent particles in the fluid such as rigid particles, drops, or cells would be useful to not only understand several disease and developmental pathologies due to ciliary dysfunction but also to design microfluidic chips with ciliated cultures for some targeted functionality, e.g., maximizing fluid transport or particle mixing. In this paper, we develop a hybrid numerical method that employs a boundary integral method for handling the confining geometries and the constituent rigid particles and the method of regularized Stokeslets for handling the cilia. We provide several examples demonstrating the effects of confining geometries on cilia-generated fluid mixing as well as the cilia-particle hydrodynamics.

Size and shape of a living microorganism have been recognized as important factors for its movement through a viscous fluid. Understanding how subtle variations in cellular geometry affect the hydrodynamic forces requires solving three-dimensional (3D) Stokes equations, e.g., by resolving an object's 2D surface in a boundary integral method. A reduction of these computational costs involves using available symmetries to simplify the boundary geometries, such as representing a slender body by its body centerline, known as the slender-body theory. Here, we extend the range of the aspect ratio that can be treated by a standard slender-body theory, by representing the body with a bundle of thin filaments that each still approximately satisfies the slender-body criteria. We show that this bundled slender-body theory can be used to determine the dependency of hydrodynamic forces on varying geometric factors of a moving object. As a direct application of this method, we study the optimized kinematics of a monotrichous bacterium that has a curved cell body and swims by rotating a helical flagellum. We show that the curvature in its cell body can play a nontrivial role in the swimming motility, depending on the chirality emerging from the cell-flagellum alignment.

A scaling relationship is developed for the asymptotic approach of the suspension viscosity of adhesive, rigid, and non-Brownian particles to that of nonadhesive particles in the limit of high shear-rate where the agglomerates are broken down completely. The relationship is fitted to experimental data for spherical particles, irregularly shaped particles, and biconcave, discoid-shaped, hardened red blood cells. The relationship allows us to extract a proxy for the interparticle adhesion force, which, for the case of the blood cells, is in qualitative agreement with alternative force measurements in the literature.

Oblique collisions of two wetted spheres are simulated with numerical and analytical methods. Improved expressions are developed for squeezing and sliding lubrication forces from thin fluid layers on the sphere surfaces, and a simple expression is provided for the capillary force. Previous observations of three primary collision outcomes (rebound, stick, and stick-rotate-separate) are confirmed and extended. The analytical models show close agreement with full numerical simulations of these collision outcomes and the corresponding wet coefficient of restitution. Qualitative agreement is also shown with prior experimental work. This work is expected to have relevance for future simulations of many wet particles using discrete-element methods.

The growth rate of material interfaces is an important proxy for mixing and reaction rates in fluid dynamics and can also be used to identify regions of coherence. Estimating such growth rates can be difficult, since they depend on detailed properties of the velocity field, such as its derivatives, that are hard to measure directly. When an experiment gives only sparse trajectory data, it is natural to encode planar trajectories as mathematical braids, which are topological objects that contain information on the mixing characteristics of the flow, in particular through their action on topological loops. We test such braid methods on an experimental system, the rotor-oscillator flow, which is well described by a theoretical model. We conduct a series of laboratory experiments to collect particle tracking and particle image velocimetry data, and we use the particle tracks to identify regions of coherence within the flow that match the results obtained from the model velocity field. We then use the data to estimate growth rates of material interface, using both the braid approach and numerical simulations. The interface growth rates follow similar qualitative trends in both the experiment and model, but have significant quantitative differences, suggesting that the two are not as similar as first seems. Our results shows that there are challenges in using the braid approach to analyze data, in particular the need for long trajectories, but that these are not insurmountable.

The effects of cold, hot, and adiabatic walls on flame propagation and deflagration-to-detonation transition (DDT) in a microscale channel are investigated by high-resolution numerical simulation. Results show that the conducting, cold, and hot walls lower the flame acceleration rate, while DDT can occur and originate from local explosion near the flame tip for both the hot and adiabatic walls. Furthermore, for the adiabatic wall, autoignition near the wall produces fast flames in the boundary layer, inducing two shocks propagating and colliding at the center, inducing a local explosion near the flame tip. However, for the hot wall, fast flames do not appear in the boundary layer due to heat loss at the wall; DDT occurs due to coupling of the compression waves with the stretched flame, and needs strong local explosion due to the absence of autoignition in the boundary layer. Nevertheless, compared with the adiabatic wall, occurrence of DDT is delayed while the run-up distance is reduced because of heat input from the hot wall to the fresh gas. For the cold wall, a flame propagates oscillatorily and fails to develop to detonation. It is identified that the flame retreat is caused by thermal contraction due to heat loss at the cold wall. It is further demonstrated that realistic chemistry is needed for an accurate description of the occurrence of autoignition within the boundary layer and DDT.