In a spinning drop tensiometer, the interfacial tension between two immiscible fluids can be inferred from the equilibrium shape of a drop suspended in a denser rotating immiscible liquid [B. Vonnegut, Rev. Sci. Instrum. 13, 6 (1942)]. For small deformations of the droplet, an analytical solution for the droplet's shape exists [H. A. Stone and J. W. M. Bush, Q. Appl. Math. 54, 551 (1996)]. Similarly, we derive an analytical solution for the deformation dynamics of an initially spherical elastic particle suspended in a denser viscous rotating liquid. At long times, the particle attains a steady-state deformed shape that depends on the rotational Bond number, from which it is possible to get a measurement of the particle's elastic modulus, thus giving a proof of concept for a rotating tensiometer. Direct numerical simulations are used to validate the theory and identify its limits of applicability.

Viscoelastic polymer films are present in numerous industrial applications such as in paint coatings, lubricants, and optoelectronics which involve a large variation in temperatures. The present study deals with the general linear stability analysis (GLSA) of a Jeffreys viscoelastic fluid layer having a deformable free surface deposited on a perfectly conducting slippery plate. Variation in temperature results in variation in surface tension thereby inducing Marangoni stresses leading, under certain conditions, to the emergence of instability of the quiescent, heat-conducting base state which may be either stationary or oscillatory. Accounting for the deformability of the free surface of the layer, the GLSA reveals the existence of the long-wavelength Marangoni instability absent in the previous studies that assumed a nondeformable free surface. The analysis reveals a strong effect of variation in the capillary number, Ca, on the stationary mode, whereas the oscillatory mode is moderately affected. The critical parameters for the stationary mode remain unaffected by variation in the Prandtl number, Pr, and the dimensionless relaxation $L_1$ and retardation $L_2$ parameters; however, their impact on the oscillatory modes is significant. Variation in the Biot number, Bi, has a stabilizing effect on the system. Variation in the Bond number, Bo, is found to strongly influence the long-wave regime of the stationary mode, but it does not influence the short-wave regime of the stationary mode and oscillatory modes. Variation in the slip coefficient leads to a moderate increase in ${\mathrm{Ma}}_c$ in the case of the stationary mode, whereas in the case of the oscillatory mode variation of both ${\mathrm{Ma}}_c$ and $k_c$ is nonmonotonic. The energy balance analysis suggests that viscoelasticity of the fluid is responsible for the emergence of oscillatory instability. Our analysis reveals the existence of a wide parameter range where oscillatory modes determine the stability properties of the system. This result emphasizes that neglecting viscoelasticity of the fluid may lead to significant errors when the dynamics of a viscoelastic fluid is investigated. The present study further demonstrates that even for a highly elastic fluid, the interface deformability prevails and promotes the long-wave stationary instability at the expense of the oscillatory instability.

We construct a low-order thermoacoustic network model that contains the most influential physical mechanisms of a thermoacoustic system. We apply it to a laboratory-scale longitudinal combustor that has been found to be thermoacoustically unstable in experiments. We model the flame, which is behind a bluff body, by a geometric level-set method. We obtain the thermoacoustic eigenvalues of this configuration and examine a configuration in which six eigenmodes are unstable. We then derive the adjoint equations of this model and use the corresponding adjoint eigenmodes to obtain the sensitivities of the unstable eigenvalues to modifications of the model geometry. These sensitivities contain contributions from changes to the steady base flow and changes to the fluctuating flow. We find that these two contributions have similar magnitudes, showing that both contributions need to be considered. We then wrap these sensitivities within a gradient-based optimization algorithm and stabilize all six eigenvalues by changing the geometry. The required geometry changes are well approximated by the first step in the optimization process, showing that this sensitivity information is useful even before it is embedded within an optimization algorithm. We examine the acoustic energy balance during the optimization process and identify the physical mechanisms through which the algorithm is stabilizing the combustor. The algorithm works by, for each mode, reducing the work done by the flame while simultaneously increasing the work done by the system on the outlet boundary. We find that only small geometry changes are required in order to stabilize every mode. The network model used in this study deliberately has the same structure as one used in the gas turbine industry in order to ease its implementation in practice.

A resolvent-based reduced-order representation is used to capture time-averaged second-order statistics in turbulent channel flow. The recently proposed decomposition of the resolvent operator into two distinct families related to the Orr-Sommerfeld and Squire operators [Rosenberg and McKeon, Efficient representation of exact coherent states of the Navier-Stokes equations using resolvent analysis, Fluid Dyn. Res. 51, 011401 (2019)] results in dramatic improvement in the ability to match all components of the energy spectra and the $uv$ cospectrum. The success of the new representation relies on the ability of the Squire modes to compete with the vorticity generated by Orr-Sommerfeld modes, which is demonstrated by decomposing the statistics into contributions from each family. It is then shown that this competition can be used to infer a phase relationship between the two sets of modes. Additionally, the relative Reynolds number scalings for the two families of resolvent weights are derived for the universal classes of resolvent modes presented by Moarref et al. [Moarref, Sharma, Tropp, and McKeon, Model-based scaling of the streamwise energy density in high-Reynolds-number turbulent channels, J. Fluid Mech. 734, 275 (2013)]. These developments can be viewed as a starting point for further modeling efforts to quantify nonlinear interactions in wall-bounded turbulence.

We study the hydrodynamic coupling between particles and solid, rough boundaries characterized by random surface textures. Using the Lorentz reciprocal theorem, we derive analytical expressions for the grand mobility tensor of a spherical particle and find that roughness-induced velocities vary nonmonotonically with the characteristic wavelength of the surface. In contrast to sedimentation near a planar wall, our theory predicts continuous particle translation transverse and perpendicular to the applied force. Most prominently, this motion manifests itself in a variance of particle displacements that grows quadratically in time along the direction of the force. This increase is rationalized by surface roughness generating particle sedimentation closer to or farther from the surface, which entails a significant variability of settling velocities.

We combine theory, numerical simulation, and experiments to investigate the breakup of two identical droplets entering a Y-junction with controlled spatial offset by which the second droplet trails the first. Based on fully resolved 3D simulations, we describe the flow physics leading to breakup. Scaling arguments, numerical simulation, and experiments consistently show that for small initial offset, breakup always occurs with the droplet fragment volume depending linearly on the offset. Above a critical offset, which increases with the capillary number, the droplets enter the constriction sequentially without breakup. Our results are relevant for understanding the breakup behavior in a dense emulsion flowing through a linearly converging channel leading to a constriction. Such geometry is commonly used for the serial interrogation of droplet content in droplet microfluidic applications, where droplet breakup can limit the maximum throughput for such process. For capillary numbers up to $\text{Ca}\simeq {10}^{-2}$, the results from the two-droplet system in a Y-junction are consistent with breakup observations in dense emulsions flowing through a linearly converging channel. The deterministic relation between initial offset and resulting breakup in the two-droplet system suggests that the stochasticity that is observed in the breakup of a dense emulsion arises from multidroplet interactions. The numerical value of the prefactor in the linear relation between initial offset and droplet fragment volume determined from experiments differs slightly from the one extracted from fully resolved numerical simulations. This discrepancy suggests that even at very high bulk surfactant concentrations, the rate-limiting surfactant adsorption kinetics allows for Marangoni stresses to develop and modify the droplet dynamics.

The zero-shear first normal stress coefficient, ${\mathrm{\Psi }}_{1,0}$, is an important viscometric function used throughout rheology. It can be directly computed by using various molecular dynamics simulation methods. Homogeneous shear algorithms used in nonequilibrium molecular dynamics simulations require some type of synthetic thermostat to remove dissipated heat resulting from the work done by the shear. While it has been shown conclusively that the linear transport coefficients are unaffected by synthetic thermostats, some doubt remains for the first normal stress coefficient. This problem can be circumvented by performing inhomogeneous Poiseuille flow simulations where heat is removed by thermal conduction to thermostatted walls. Alternatively, we can use equilibrium computations to calculate the properties of interest. This is significantly more difficult for nonlinear properties than it is for the linear transport properties. Here we present three different methods of calculating the first normal stress coefficient for a model polymer solution; in one, the computations are performed in equilibrium conditions (Coleman-Markovitz equation) and in the other two they are carried out in nonequilibrium conditions (SLLOD and Poiseuille flow). We find that both nonequilibrium methods produce matching results, with ${\mathrm{\Psi }}_{1,0}=170\pm 2$ for SLLOD and ${\mathrm{\Psi }}_{1,0}=172\pm 3$ for Poiseuille flow, regardless of whether the fluid of interest is directly or indirectly thermostatted. The Coleman-Markovitz result is difficult to resolve, and much less accurate, with ${\mathrm{\Psi }}_{1,0}\approx 190$, although it still may not be fully converged, even after extensive computations. We suggest that the Coleman-Markovitz equation is unsuitable for routine determination of the first normal stress coefficient by molecular simulation.

The emergence of particle accumulation structures (PAS) in noncylindrical liquid bridges (LBs) is studied numerically for a high Prandtl number liquid considering microgravity conditions. Simulations are conducted in the framework of a finite-volume (Eulerian) approach with nonisodense particles tracked using a Lagrangian, one-way coupling scheme. First, the threshold of the Marangoni-flow instability is determined as a function of the aspect ratio and the volume of liquid held between the supporting disks, thereafter, PAS formation is investigated for supercritical conditions. The overall approach is specifically conceived to provide details about the morphological evolution of these structures as the main control parameters are varied. For this reason a set of dedicated notions and definitions (such as the linear extension of the PAS, its inner core radius, and the area of the “petals” or “blades”) are introduced to allow a precise quantification of a series of purely geometrical effects. Though the analysis is deliberately limited to illustrating the macroscopic patterning behavior and its relationship with the overarching factors, a model is proposed to interpret the increased ability of slender (concave) LBs to support the formation of PAS over extended ranges of values of the particle Stokes number. This model yet relies on essentially geometrical arguments, that is, the triadic relationship among the curvature of the free surface, the topology of fluid streamlines, and particle mass effects.

Resonance of droplets in constricted capillary tubes responding to external vibratory excitation can be theoretically characterized by the abstract coefficients such as resonant frequency and rate of damping. A physically sound model, however, is needed to relate these abstract coefficients to the fluid properties of two-phase fluid, geometric properties of tube, and features of excited waves. A hydrodynamic model, based on the moving-boundary control volume concept and the transient oscillatory velocity profile, was developed to characterize the resonance of droplets. This model was validated against computational fluid dynamics simulation results expressed in both time and frequency domains. Dominant factors including Ohnesorge number, viscosity ratio, density ratio, and aspect ratio which control resonance were systematically investigated for their influences on the resonance of droplets. The nonlinearity in light of the initial position of front droplet meniscus and the amplitude of oscillation was distinguished and validated by the theoretical model.

We examine the mobility of a chemically active particle straddling the interface between a liquid layer of finite depth and a semi-infinite layer of gas. A surface-active agent is released asymmetrically from the particle that locally lowers the interfacial surface tension. It is commonly presumed that the uneven distribution of the surface tension and the associated Marangoni flow lead to the propulsion of the active surfer opposite to the release direction, where the surface tension is higher. This is considered forward motion. However, our recent theoretical analysis—in the limits of negligible inertia and diffusion-dominated transport of the active agent—has shown that this trend may be reversed for certain shapes of the surfer and shallow enough liquid layers. Advancing beyond the Stokes regime, here, we study the Marangoni-driven motion of thin cylindrical disks and oblate spheroids for a wide range of release rates and diffusivity of the exuded chemical species, that control the effective Reynolds and Péclet numbers. We consider various degrees of confinement represented by the thickness of the liquid film, and show that indeed the surfers can undergo a forward, a backward, or an arrested motion. We also identify the links between these modes of mobility and the forces acting on the surfers as well as the flow structure in their vicinity. Rather unexpectedly, we discover that negative pressure is the primary contributor to the fluid force experienced by the surfer and that this suction force is mainly responsible for the reverse Marangoni propulsion. The reported results are based on closely corroborating numerical calculations and experimental measurements.

The clustering of small heavy inertial particles subjected to Stokes drag in turbulence, which is the concern of present study, is known to be minimal at small and large Stokes number and substantial at $\mathrm{St}=O\left(1\right)$. This nonmonotonic trend, which has been shown computationally and experimentally, is yet to be explained analytically. In this study, we obtain an analytical expression for the Lyapunov exponents that quantitatively predicts this trend. The sum of the exponents, which is the normalized rate of change of the signed volume of a small cloud of particles, is correctly predicted to be negative and positive at small and large Stokes numbers, respectively, asymptoting to $\tau Q$ as $\tau \to 0$ and ${\tau }^{-1/2}{\left|Q\right|}^{1/4}$ as $\tau \to \infty$, where $\tau$ is the particle relaxation time and $Q\left(\tau \right)$ is the difference between the norm of the rotation- and strain-rate tensors computed along the particle trajectory, which remains negative at all $\tau$ in turbulent flows. Additionally, the trajectory crossing is predicted only in hyperbolic flows where $Q<0$ for sufficiently inertial particles with a $\tau$ that scales with ${\left|Q\right|}^{-1/2}$. Following the onset of crossovers, a transition from clustering to dispersion is predicted correctly. We show these behaviors are not unique to three-dimensional isotropic turbulence and can be reproduced closely by a one-dimensional mono-harmonic flow, which appears as a fundamental canonical problem in the study of particle clustering. Analysis of this one-dimensional canonical flow shows that the rate of clustering, quantified as the product of the Lyapunov exponent and particle relaxation time, is bounded by $-1/2$, behaving with extreme nonlinearity in the hyperbolic flows and always remaining positive in the elliptic flows. This model problem also confirms that dispersion in a hyperbolic flow will occur only if particles' trajectory cross. These findings, which stem from our analysis, are corroborated by the direct numerical simulations.

Lubrication forces depend to a high degree on elasticity, texture, charge, chemistry, and temperature of the interacting surfaces. Therefore, by appropriately designing surface properties, we may tailor lubrication forces to reduce friction, adhesion, and wear between sliding surfaces and control repulsion, assembly, and collision of interacting particles. Here, we show that variations of slippage on one of the contacting surfaces induce a lift force. We demonstrate the consequences of this force on the mobility of a cylinder traveling near a wall and show the emergence of particle oscillation and migration that would not otherwise occur in the Stokes flow regime. Our study has implications for understanding how inhomogeneous biological interfaces interact with their environment; we also propose a method of patterning surfaces for controlling the motion of nearby particles.

We demonstrate experimentally and theoretically that self-assembled precipitate membranes with dual permeability can initiate and maintain exchange nanoflows using the chemical-potential gradient of a dissolving solute. Moreover, we show how such chemical energy can drive stable, oscillatory, and explosive convective motions.

Ring-shaped deposits can be often found after a droplet evaporates on a substrate. If the fluid in the droplet is a pure liquid and its contact line remains pinned during the process, then the mechanism behind such ring-shaped deposition is the well-known coffee-stain effect. However, adding small amounts of salt to such a droplet can change the internal flow dramatically and consequently change the deposition mechanism. Due to an increase of surface tension in the contact line region, a Marangoni flow arises which is directed from the apex of the droplet toward the contact line. As a result, particles arrive at the contact line following the liquid-air interface of the droplet. Interestingly, the deposit is also ring shaped, as in the classical coffee-stain effect, but with a radically different morphology: Particles form a monolayer along the liquid-air interface of the droplet, instead of a compact three-dimensional deposit. Using confocal microscopy, we study particle-per-particle how the assembly of the colloidal monolayer occurs during the evaporation of droplets for different initial concentration of sodium chloride and initial particle dilution. Our results are compared with classical diffusion-limited deposition models and open up an interesting scenario of deposits via interfacial particle assembly, which can easily yield homogeneous depositions by manipulating the initial salt and particle concentration in the droplet.

Under extreme conditions, such as harsh thermodynamical environment and spatial confinement, fluids can reveal unique properties. In this work, we investigate the effects on the interfacial and transport properties of fluids confined in nanopores that are due to the spatial confinement, surface hydrophilicity, and fluid composition. We perform fully atomistic molecular dynamics of water, brine, oil, and combinations thereof, confined within amorphous silica nanopores with the radius ranging from 1.0 to 2.4 nm. We have also studied the oil infiltration on nanopores previously filled with water or brine, mimicking the natural processes when the oil is geologically formed and infiltrates a porous media. We observe that an adsorbed water/brine layer remains on the surface of the nanopores after the oil infiltration, altering the interaction of the oil with the confining surface and leading to changes of their interfacial tensions and viscosities. The presence of the ions in the brine thickens the adsorbed water layer, preventing the oil from infiltrating the nanopores with 1.0 nm radius. Thus, we have observed a limit on the pore size for oil infiltration for brine-filled pores.

In nature, liquids often circulate in channels textured with leaflets, cilia, or porous walls that deform with the flow. These soft structures are optimized to passively control flows and have inspired the design of novel microfluidic and soft-robotic devices. Yet, the relationship between the geometry of the soft structures and the flow properties remains so far poorly understood. Here, taking inspiration from the lymphatic system, we devise millifluidic valves, dressed with asymmetric soft leaflets that feature on-demand asymmetric flow properties, which we harness to induce flow rectification and pumping. We demonstrate that the functional mechanism at play involves an interplay between geometry, asymmetry, and fluid-structure interaction-induced nonlinearity. Our results open the way to a better characterization of biological leaflet malformations and to more accurate control of flows for microfluidics and soft-robotic systems.

This paper presents results of the resolved simulation of particles suspended in a fluid in shear flow. Unlike most of the existing work on this subject, the ratio of the particle density to that of the suspending fluid is not 1 but varies between 2.5 and 10, with a focus on inertial effects rather than gravity, which is not considered. Two particle Reynolds numbers are considered, 20 and 40, while the average particle volume fraction varies from 5% to 33%. The study focuses on the effects of inertia on this class of flows. It is shown that the memory of the particles' earlier state of motion associated with inertia is responsible for significant effects. Among others, the collision rate is increased and, with it, the rate of momentum transfer from the moving walls into the bulk of the fluid-particle mixture; normal stress differences become larger and the particle-rich layer near the walls becomes denser. Comparable effects are found by increasing the particle density and the particle Reynolds number. The two normal stress differences are found to be both negative and comparable in spite of their very different physical origin. Additional results concern the wall slip, the stresslet, the effects of a nonzero collisional tangential force, the wall stress, and others. The great importance of particle-particle and particle-wall collisions reveals itself in influencing the rheology of the mixture, the normal stress differences, and the transport of momentum.

The undisturbed flow of a particle is of fundamental importance since it controls both the undisturbed flow force and the perturbation force (which includes quasisteady, added-mass, and history forces). Here we use the pairwise interaction extended point particle framework to evaluate the undisturbed flow of each particle through superposition of the perturbation flow induced by all its neighbors. This approach allows calculation of various statistics related to undisturbed fluid velocity under conditions of both stationary and nonstationary particles. In a random distribution of stationary particles, while the macroscale undisturbed flow is slowly varying, the microscale undisturbed flow that arises due to the perturbation flow of neighbors varies substantially from one particle to another and this in turn leads to large variation in the hydrodynamic force exerted on the particles. The effect of particle motion is generally to increase the particle-to-particle variation in the undisturbed fluid velocity of the particles. We observe that this increase is greater for the transverse component than for the streamwise component. As a result, with increasing random particle motion, the distribution of undisturbed fluid-velocity fluctuation becomes isotropic. Three different normalized forces are defined: ${\mathrm{\Phi }}^L$ is the Lagrangian normalized force on an individual particle suitable for application in a microscale-informed Euler-Lagrange simulation, ${\mathrm{\Phi }}^E$ is the Eulerian normalized average force suitable for application in an Euler-Euler simulation, and ${\mathrm{\Phi }}^{LE}$ is the Lagrangian normalized force on an individual particle suitable for application in the standard Euler-Lagrange simulation. We establish precise relations between these different definitions. The drag laws developed based on particle-resolved direct numerical simulation results and experiments are appropriate for application only as the Eulerian normalized average force. We introduce the force consistency relation and use it to obtain an expression for ${\mathrm{\Phi }}^L$, which when applied to each particle and averaged over all the particles equals ${\mathrm{\Phi }}^E$. The results are first obtained in the limit of stationary particles and then extended to the general case of nonstationary particles.

As an underlying mechanism, cross-chirality transfer of kinetic energy and helicity plays an essential role in the turbulent dynamics, which is as important as cross-scale transfer especially in broken mirror-symmetry turbulence. The effects of helicity on the properties of turbulent flows in previous studies highlight the role of cross chirality, which may be developed into an efficient method of turbulence control. We numerically study the cross-chirality transfer of kinetic energy and helicity in this paper, particularly under the influence of compressibility in stationary helical homogeneous and isotropic turbulence. Through combining the Helmholtz decomposition and helical wave decomposition, a general helical wave decomposition is proposed to provide three orthogonal bases for velocity. Within the scope of chiral helicity, there also exists chiral kinetic energy based on chiral velocity. They are defined as the left- and right-chirality kinetic energy, and the remaining compressible component of velocity corresponds to free-chirality kinetic energy. Although there exists no difference in the definition of helicity in incompressible and compressible turbulence, its space-time evolution equation in compressible turbulence involves the compressible component of velocity. The compressibility has a great influence on the homochiral kinetic energy and helicity cascade, and it also plays an essential role in the chirality transfer process like cross-chirality kinetic energy and helicity transfer. The amplitude of cross-chirality kinetic energy transfer is comparable with cross-scale kinetic energy transfer at relatively large scales, and also with viscous dissipation at relatively small scales. The triple nonlinear interactions dominate the cross-chirality transfer relative to pairwise interaction of chiral modes, and it is less sensitive to compressibility. Relative to the compression, the expansion of fluid elements can lead to inverse chirality transfer and strengthen the lack of mirror symmetry. The only discrepancy of cross-chirality helicity transfer between incompressible and compressible turbulence lies in the medium role of the compressible component of velocity. The helicity transfer via the compressible component is weak, and even the kinetic energy of the compressible component relative to that of the other two chiral modes is highest. In addition, the inverse helicity transfer is always statistically associated with the compressible component of velocity via triple interaction extracted from nonlinear interactions.

The influence of coherent turbulent structures on the entrainment characteristics of a separated shear layer in a Mach-2.49 longitudinal cylinder wake is investigated using stereoscopic particle image velocimetry (SPIV). Three thousand non-time-correlated velocity field measurements, acquired along a plane coincident with the central axis, were decomposed into modes using the snapshot proper orthogonal decomposition (POD) method. The second and third POD modes identified high-energy velocity fluctuations aligned with consistent directions in the separated shear layers, near the boundaries of the recirculation region. Previous work by the authors has demonstrated, using tomographic PIV, that these directionally consistent velocity fluctuations identified by the POD modes are caused by three-dimensional (3D) coherent upright and inverted hairpin vortex structures in this flow. The SPIV velocity field snapshots were conditionally sorted based on the value of their corresponding POD amplitude coefficients, and conditional statistics from these subsets of snapshots were used to derive results in the current work. It is demonstrated that a higher statistical prevalence of upright hairpin vortices in the shear layer directly correlates with reduced shear layer growth rates, and a subsequent increase in the reattachment length. Conversely, a higher statistical prevalence of inverted hairpin vortices correlates with increased shear layer growth rates, and a subsequent reduction in the reattachment length. Comparisons of conditional statistics for the SPIV data are drawn with previous laser Doppler velocimetry measurements acquired in a $5^{\circ }$ boat-tailed cylinder configuration of this flow. These comparisons demonstrate clear similarities of important features between the two flows, such as an increase in the reattachment length when compared to the unconditional blunt-based cylinder flow, which is indicative of higher cylinder base pressures and subsequently reduced pressure drag.