Stability analysis of gravity-driven flow of a thermoviscous liquid on the exterior surface of a uniformly heated or cooled vertical cylinder is presented. The film evolution model derived using lubrication approximation consists of four dimensionless groups, namely, Marangoni number, Biot number, Bond number, and thermoviscosity number. The viscosity of the liquid is modeled as an exponentially varying function of temperature. The thermocapillary stress significantly affects the Rayleigh-Plateau instability for flow over a nonisothermal cylinder with intricate dependence on various parameters involved. For the temporally unstable system, spatiotemporal stability analysis is performed to delineate the parameter regions for convectively and absolutely unstable systems. Brigg's criterion is employed and the critical value of a composite parameter $\beta$ is evaluated to study the transition from convective to absolute instability. A proper rescaling of the dispersion relation shows that the condition on the composite parameter is $\beta <1.507$ for the existence of absolute instability, which is consistent with an earlier work on isothermal flows. Further, an expression is found for the critical composite Marangoni number beyond which the film is always absolutely unstable independent of the Bond number. This critical value is shown to be an increasing function of thermoviscosity number. Results from the nonlinear simulations are in agreement with the predictions of the linear temporal and spatiotemporal analyses.

Intermittent turbulent-laminar patterns characterize the transition to turbulence in pipe, plane Couette, and plane channel flows. The time evolution of turbulent-laminar bands in plane channel flow is studied via direct numerical simulations using the parallel pseudospectral code ChannelFlow in a narrow computational domain tilted by ${24}^{\circ }$ with respect to the streamwise direction. Mutual interactions between bands are studied through their propagation velocities. Energy profiles show that the flow surrounding isolated turbulent bands returns to the laminar base flow over large distances. Depending on the Reynolds number, a turbulent band can either decay to laminar flow or split into two bands. As with past studies of other wall-bounded shear flows, in most cases survival probabilities are found to be consistent with exponential distributions for both decay and splitting, indicating that the processes are memoryless. Statistically estimated mean lifetimes for decay and splitting are plotted as a function of the Reynolds number and lead to the estimation of a critical Reynolds number ${\mathrm{Re}}_{\text{cross}}\simeq 965$, where decay and splitting lifetimes cross at greater than ${10}^6$ advective time units. The processes of splitting and decay are also examined through analysis of their Fourier spectra. The dynamics of large-scale spectral components seem to statistically follow the same pathway during the splitting of a turbulent band and may be considered as precursors of splitting.

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.

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.

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.

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.

We investigate experimentally stratified turbulence forced by waves. Stratified turbulence is present in oceans and it is expected to be dominated by nonlinear interaction of internal gravity waves as described by the Garrett and Munk spectrum. To reach turbulent regimes dominated by stratification we use the Coriolis facility in Grenoble (France), where the large size enables us to reach regimes with both low Froude number and large Reynolds number. Stratification is obtained by using vertically linearly varying salt concentration and we force large-scale waves in a $6\times 6\times 1{\mathrm{m}}^3$ domain. We perform time-resolved particle image velocimetry to probe the space-time structure of the velocity field. We observe a wide band spectrum which is made of waves. Discrete modes are observed due to the square shape of the flow container as well as a continuum part which appears consistent with an axisymmetric superposition of random weakly nonlinear waves. Our observations support the interpretation of turbulence of a strongly stratified fluid as wave turbulence of internal waves although our spectrum is quite different from the Garrett and Munk spectrum. Weak turbulence proceeds down to a small cutoff length scale (the buoyancy wavelength) at which a transition to more strongly nonlinear turbulence is expected.

The behavior of flagellated bacteria swimming in non-Newtonian media remains an area with contradictory and conflicting results. We report on the behavior of wild-type and smooth-swimming E. coli in Newtonian, shear-thinning, and viscoelastic media, measuring their trajectories and swimming speed using a three-dimensional real-time tracking microscope. We conclude that the speed enhancement in Methocel solution at higher concentrations is due to shear thinning and an analytical model is used to support our experimental result. We argue that shear-induced normal stresses reduce wobbling behavior during cell swimming but do not significantly affect swimming speed. However, the normal stresses play an important role in decreasing the flagellar bundling time, which changes the swimming-speed distribution. A dimensionless number, the “strangulation number” (Str) is proposed and used to characterize this effect.

We numerically study the retraction of an axisymmetric viscous filament in a passive surrounding fluid. The analysis focuses on the evolution of the tip velocity, from the early stage of the filament retraction until it reaches its final equilibrium spherical shape. The problem is governed by two control parameters: the Ohnesorge number, Oh, which measures the relative importance of viscous and surface tension effects, and the initial aspect ratio of the filament, $\mathcal{A}$. We investigate the influence of Oh over a wide range of aspect ratios. The small-Oh regime is characterized by the occurrence of a spherical blob at the extremity of the filament. This feature has a key impact on the tip dynamics, which moves with an oscillating velocity whose mean value is close to the Taylor-Culick prediction. The oscillatory behavior of the tip velocity is explained through a simple mass-spring model. This regime is also characterized by the presence of capillary waves, with a phase velocity slightly larger than the Taylor-Culick velocity. Surface oscillations are also observed when the filament reaches its final spherical shape; the corresponding period agrees well with predictions of the linear theory. At intermediate Oh and large $\mathcal{A}$, the tip velocity reaches a value close to the Taylor-Culick prediction. However, for smaller aspect ratios, the maximum tip velocity is much smaller than this prediction, and does not exhibit any oscillation. The recoil dynamics is qualitatively and quantitatively different at high Oh. In this case, the radius of the filament grows uniformly over time and no blob forms, making the tip velocity decrease after a short transient. A self-similar solution is found to closely match the numerical results in this regime.

We exploit the deformation of drops spinning in a denser background fluid to investigate the effective interfacial tension (EIT) between miscible molecular fluids. We find that, for sufficiently low interfacial tension, spinning drops develop dumbbell shapes, with two large heads connected by a thinner central body. We show that this shape depends not only on the density and viscosity contrast between the drop and background fluids, but also on the fluid molecular structure, and hence on the stresses developing at their interface due to a different molecular interaction. We systematically investigate the dynamics of dumbbell-shaped drops of water-glycerol mixtures spinning in a pure glycerol reservoir. By developing a model for the deformation based on the balance of the shear stress opposing the deformation, the imposed normal stress on the drop, and an effective interfacial tension, we exploit the time evolution of the drop shape to measure the EIT. Our results show that the EIT in water-glycerol systems is orders of magnitude lower than that reported in previous experimental measurements, and in excellent agreement with values calculated via the phase field model proposed by Truzzolillo et al. [Phys. Rev. X 6, 041057 (2016)].

Designing locomotory gaits for synthetic microswimmers has been a challenge due to stringent constraints on self-propulsion at low Reynolds numbers (Re). Here, we introduce a new theoretical approach of designing a class of self-learning, adaptive (or “smart”) microswimmers via reinforcement learning. Diverging from the traditional paradigm of specifying locomotory gaits a priori, here a self-learning swimmer can develop and adapt its propulsion strategy based on its interactions with the surrounding medium. We illustrate this new approach using a minimal but representative model swimmer consisting of an assembly of spheres connected by extensible rods. Without requiring any prior knowledge of low Re locomotion, we demonstrate that this self-learning swimmer can recover a previously known propulsion strategy, identify more effective locomotory gaits, and adapt its locomotory gaits in different media. This approach opens an alternative avenue to designing the next generation of smart microrobots with robust locomotive capabilities.

Water waves in natural environments are typically broadband, nonlinear, and dynamic phenomena. Taking concepts developed for slow light in optics, we address the challenge of designing arrays to control the spatial distribution of wave energy, and amplify specific frequencies from within target frequency bands at individual locations. Meter-scale wave-flume experiments, in which incident waves interact with a chirped array of eight vertical cylinders, demonstrate significant amplifications over a broad frequency range, as predicted numerically and theoretically.

The ciliary locomotion and feeding of an axisymmetric microswimmer in a complex fluid whose viscosity depends on a surrounding nutrient field are investigated numerically in order to extend previous asymptotic results for weak nutrient-viscosity coupling. Numerical simulations capture nonlinearities inherent in the full system that are missed using perturbation-based linearization methods. The microswimmer's ciliary beating is modeled by a slip velocity, i.e., the squirmer model, and body geometry is modeled by spheroids. It is found that swimming speed and feeding are most affected by a nonuniform viscosity environment when the ratio of advection forces to diffusion transport, characterized by the nondimensional Peclét number, is moderate, i.e., $\text{Pe}=O\left(5\right)$. These changes are correlated to significant increases in the pressure force on the surface of the squirmer, as well as differences in power expenditure and hydrodynamic efficiency compared to the constant-viscosity case. Additionally, the swimming and feeding changes are found to be more significant in oblate spheroids than prolate spheroids, although the shape has a smaller effect on performance than Peclét number or surface stroke. These results suggest that nonlocal effects from viscosity variation are caused by a modification to the pressure force, as opposed to the strain rate. These results should be useful in interpreting experiments where a microswimmer affects a fluid's local rheology.

We computationally studied the kinematics of a simple reciprocal model swimmer (asymmetric dumbbell) in a Newtonian fluid as a function of the Reynolds number (Re), and investigated how the onset and gradual increase of inertia impacts swimming behavior: a reversal in the swim direction, flow field, and the swim stroke. We divided the swim stroke into the increase and decrease in the distance between the two spheres (expansion and compression respectively) and related them to power and recovery strokes. We found that the switch in swim direction also corresponds to a switch in power and recovery strokes. We obtained expressions for the mean swimming velocity by collapsing the net displacement during expansion and compression under power-law relationships with respect to Re, the swimmer's amplitude, and the distance between the two spheres. Analyzing the fluid flows, we saw that the averaged flow field during expansion always resembles a pusher and during compression it always resembles a puller, but when averaged over the whole cycle, the flow that dominates is the one that occurs during the power stroke. We also related the power and recovery strokes to the swimming efficiency during times of expansion and compression, and found that the power stroke is, surprisingly, not always more efficient than the recovery stroke. Our results may have important implications in biology and ultimately the design of artificial swimmers.

The Leidenfrost effect, classically associated with drops levitating on their own vapor over hot solid surfaces, can also be observed over hot baths of nonvolatile liquids. In view of substrate fluidity, heat transfer through the bath to the drop should most certainly be dominated by convection and not by only conduction as in the solids, which may be instrumental for an efficient heat supply to the drop given typically poor thermal conductivity of the liquids. Here, we undertake an experimental and numerical study of the flow in a bath of silicone oil V20 induced by an overlying Leidenfrost drop, highlighting that a toroidal vortex is formed underneath the drop whose direction of circulation turns out to be different for drops of different liquids. We show that this is due to a shift in a delicate interplay between three mechanisms pulling in different directions: (i) shear stresses exerted by the vapor escaping from the gap between the bath and the drop, as well as (ii) buoyancy action and (iii) thermocapillary (Marangoni) stresses, both due to local evaporative cooling of the bath by the drop. Whatever the structure of this locally induced convection, its crucial heat transfer enhancing efficiency is readily confirmed in numerical simulations as favoring levitation.

Nature often uses capillary forces to manipulate fluids, which has inspired scientists to develop new applications, such as in microfluidics and laboratory-on-a-chip systems. Here we present a method to transport fluids in microfluidic channels, by exploiting the capillary interaction of fluid interfaces with traveling surface waves, called mechanowetting. We found that the three-phase lines of fluid slugs dynamically attach to the crests of the waves, resulting in fluid velocities that are equal to the wave speed. By comparing this microfluidic slug flow to conventional peristaltic fluid propulsion, we demonstrate that fluid velocities can be reached that are one order of magnitude larger. We quantified the efficiency numerically and theoretically in terms of the generated pressure gradient using a closed channel and measured the evolution of the pressure distribution as the wave progresses. The method was shown to work for a very wide range of contact angles. We anticipate that our results will lead to new microfluidic applications based on switchable topography technology.

Liquid jets issued from a noncircular orifice exhibit oscillation owing to the surface tension. When the orifice has an $n$-fold rotational symmetry, a material cross section of the jet interchanges two symmetric shapes alternately. This oscillation, called axis switching, is a superposition of two ripples oppositely propagating in the azimuthal direction around the axis. In this study, we used computer simulations to demonstrate that we can pick up one of the two ripples by adjusting the initial velocity profile of the orifice. As a result of the single-wave propagation in the azimuth, the jet surface shows a twisted appearance. In contrast to the swirling jets, the twisted jet has no angular momentum around the axis. We numerically demonstrated the formation of twisted jets with various cross sections, including a regular square.

One class of active particles that is especially promising for biomedical microrobotic applications is rigid magnetic microswimmers propelled via rotation by a magnetic field. For these particles there is a maximum rotational frequency, hence velocity, determined by the maximum torque exerted by the field on the particle magnetization. It has been expected that velocity can always be increased by increasing the field magnitude to increase torque. This expectation holds if magnetization is constant or responds linearly to applied field, but all real materials actually respond nonlinearly, since as field strength increases the magnetization saturates and is coerced to point along the field direction. Here we show that this saturation and coercivity limit the maximum velocity of these microparticles. These effects are particularly important for soft magnetic materials. Although soft magnetic materials are used in many microswimmers, propulsion models incorporating their magnetic response are lacking. Our results are consistent with experimental observations and we predict that the limiting behavior occurs for common magnetic materials at typical rotational frequencies and field strengths, hence is relevant for current microswimmer design.

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 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.