The present paper describes a microfluidic oscillator based on facing impinging jets and operating in laminar flow conditions. Using appropriate microchannel configurations, pulsatile liquid flows are generated at the microscale from steady and equal inlet flow conditions and without moving parts or external stimuli. An experimental campaign has been carried out, using oscillator structures manufactured in silicon using conventional microfabrication techniques. This allowed us to study in detail the impact of the main geometric parameters of these structures on the oscillation frequency. The observed range of regular oscillations was found to depend on the geometry of the output channels, with highly regular oscillations occurring over a very large range of Reynolds numbers (Re) when an expansion of the output channel is added. The evolution of the self-oscillating frequency was shown to be dependent on the distance separating the impinging jets and on the average speed of the jets. Direct numerical simulations have been performed using a spectral element method. The computed dye concentration fields and nondimensional self-oscillation frequencies compare well with the experiments. The simulations enable a detailed characterization of the self-oscillation phenomenon in terms of pressure and velocity fields.

Particle image velocimetry (PIV) systems are often limited in their ability to fully resolve the spatiotemporal fluctuations inherent in turbulent flows due to hardware constraints. In this study, we develop models based on rapid distortion theory (RDT) and Taylor's hypothesis (TH) to reconstruct the time evolution of a turbulent flow field in the intermediate period between consecutive PIV snapshots obtained using a non-time resolved system. The linear governing equations are evolved forward and backward in time using the PIV snapshots as initial conditions. The flow field in the intervening period is then reconstructed by taking a weighted sum of the forward and backward estimates. This spatiotemporal weighting function is designed to account for the advective nature of the RDT and TH equations. Reconstruction accuracy is evaluated as a function of spatial resolution and reconstruction time horizon using direct numerical simulation data for turbulent channel flow from the Johns Hopkins Turbulence Database. This method reconstructs single-point turbulence statistics well and resolves velocity spectra at frequencies higher than the temporal Nyquist limit of the acquisition system. Reconstructions obtained using a characteristics-based evolution of the flow field under TH prove to be more accurate compared to reconstructions obtained from numerical integration of the discretized forms of RDT and TH. The effect of measurement noise on reconstruction error is also evaluated.

Pleated membrane filters, which offer larger surface area to volume ratios than unpleated membrane filters, are used in a wide variety of applications. However, the performance of the pleated filter, as characterized by a flux-throughput plot, indicates that the equivalent unpleated filter provides better performance under the same pressure drop. Earlier work [Sanaei, Richardson, Witelski, and Cummings, J. Fluid Mech. 795, 36 (2016)] used a highly simplified membrane model to investigate how the pleating effect and membrane geometry affect this performance differential. In this work, we extend this line of investigation and use asymptotic methods to couple an outer problem for the flow within the pleated structure to an inner problem that accounts for the pore structure within the membrane. We use our model to formulate and address questions of optimal membrane design for a given filtration application.

We study the effect of spherical particles on the turbulent flow of a viscoelastic fluid and find that the drag reducing effect of polymer additives is completely lost for semidense suspensions, with the drag increasing more than for suspensions in Newtonian fluids. This different behavior is due to three separate effects. First, polymer stretching is reduced by the presence of rigid particles, thus canceling the drag reducing benefit of the viscoelastic fluid. Second, drag increase is provided by the growth of the particle and polymeric shear stresses with the particles, due to larger shear rates in the vicinity of the particle surface. Third, particles migrate towards the wall due to the shear-thinning property of the fluid, thus enhancing the particle near-wall layer and further increasing the drag.

We report water wave experiments performed in a long tank where we consider the evolution of nonlinear deep-water surface gravity waves with the envelope in the form of a large-scale rectangular barrier. Our experiments reveal that, for a range of initial parameters, the nonlinear wave packet is not disintegrated by the Benjamin-Feir instability but exhibits a specific, strongly nonlinear modulation, which propagates from the edges of the wave packet toward the center with finite speed. Using numerical tools of nonlinear spectral analysis of experimental data, we identify the observed envelope wave structures with focusing dispersive dam break flows, a peculiar type of dispersive shock waves recently described in the framework of the semiclassical limit of the 1D focusing nonlinear Schrödinger equation (1D-NLSE). Our experimental results are shown to be in a good quantitative agreement with the predictions of the semiclassical 1D-NLSE theory. This is the first observation of the persisting dispersive shock wave dynamics in a modulationally unstable water wave system.

Using three-dimensional Voronoi analysis, we explore the local dynamics of small, settling, inertial particles in isotropic turbulence using direct numerical simulations. We independently vary the Taylor Reynolds number ${\text{Re}}_{\lambda }\in [90,398]$, Froude number $\text{Fr}\equiv a_{\eta }/g\in [0.052,\infty ]$ (where $a_{\eta }$ is the Kolmogorov acceleration, and $g$ is the acceleration due to gravity), and Kolmogorov scale Stokes number $\text{St}\equiv {\tau }_p/{\tau }_{\eta }\in [0,3]$. In agreement with previous results using global measures of particle clustering, such as the radial distribution function, we find that for small Voronoi volumes (corresponding to the most clustered particles), the behavior is strongly dependent upon St and Fr, but only weakly dependent upon ${\text{Re}}_{\lambda }$, unless $\text{St}>1$. However, larger Voronoi volumes (void regions) exhibit a much stronger dependence on ${\text{Re}}_{\lambda }$, even when $\text{St}\le 1$, and we show that this, rather than the behavior at small volumes, is the cause of the sensitivity of the standard deviation of the Voronoi volumes that has been previously reported. We also show that the largest contribution to the particle settling velocities is associated with increasingly larger Voronoi volumes as the settling parameter $\text{Sv}\equiv \text{St}/\text{Fr}$ is increased. Our local analysis of the acceleration statistics of settling inertial particles shows that clustered particles experience a net acceleration in the direction of gravity, while particles in void regions experience the opposite. The particle acceleration variance, however, is a convex function of the Voronoi volumes, with or without gravity, which seems to indicate a nontrivial relationship between the Voronoi volumes and the sizes of the turbulent flow scales. Results for the variance of the fluid acceleration at the inertial particle positions are of the order of the square of the Kolmogorov acceleration and depend only weakly on Voronoi volumes. These results call into question the “sweep-stick” mechanism for particle clustering in turbulence which would lead one to expect that clustered particles reside in the special regions where the fluid acceleration is zero (or at least small). We then consider the properties of particles in clusters, which are regions of connected Voronoi cells whose volume is less than a certain threshold. The results show self-similarity of the clusters, and that the statistics of the cluster volumes depends only weakly on St, with a stronger dependence on Fr and ${\text{Re}}_{\lambda }$. Finally, we compare the average settling velocities of all particles in the flow with those in clusters, and show that those in the clusters settle much faster, in agreement with previous work. However, we also find that this difference grows significantly with increasing ${\text{Re}}_{\lambda }$ and exhibits a nonmonotonic dependence on Fr. The kinetic energy of the particles, however, is almost the same for particles whether or not they are in clusters.

We revisit the tears of wine problem for thin films in water-ethanol mixtures and present a model for the climbing dynamics. The formulation includes a Marangoni stress balanced by both the normal and tangential components of gravity as well as surface tension which lead to distinctly different behavior. The prior literature did not address the wine tears but rather the behavior of the film at earlier stages and the behavior of the meniscus. In the lubrication limit we obtain an equation that is already well known for rising films in the presence of thermal gradients. Such models can exhibit nonclassical shocks that are undercompressive. We present basic theory that allows one to identify the signature of an undercompressive wave. We observe both compressive and undercompressive waves in new experiments, and we argue that, in the case of a preswirled glass, the famous “wine tears” emerge from a reverse undercompressive shock originating at the meniscus.

When two drops are slowly brought together and first touch, a microscopic liquid neck or a bridge forms between them. The expansion of the neck is controlled by the capillary (Laplace) pressure which diverges when the curvature of the interface is infinite at the point where the drops first touch. The change in topology and the flows that ensue as time advances and the bridge grows from microscopic to macroscopic scales, and the two drops merge into one, are intimately coupled to this singularity in the dynamics. Despite the large volume of work dedicated to this problem, currently experiment, theory, and computation are not in complete agreement with respect to the earliest times following the initial contact of the two drops. Experiments, supported by simulations, report an initial regime where the radius of the connecting bridge grows linearly in time before a transition to either a Stokes regime or an inertial regime where either viscous or inertial force balances capillary (surface tension) force. In the initial linear regime, referred to as the inertially limited viscous (ILV) regime, all three forces are thought to be important. This is in contrast to theory which predicts that all coalescence events begin in the Stokes regime where inertia is negligible. Here we use high-accuracy numerical simulations to show that the ILV regime is only realized when the two coalescing drops are initially separated by a finite distance. Moreover, for two drops that initially just touch at a point, coalescence always begins in the Stokes regime. It is demonstrated that the linear ILV regime is more akin to a Taylor-Culick-type regime whose existence and duration are purely consequences of the use of an initial bridge of finite size that poorly approximates the point contact condition that is a cardinal feature of the coalescence singularity.

Chemically active droplets exhibit complex avoiding trajectories. While heterogeneity is inevitable in active matter experiments, it is mostly overlooked in their modeling. Exploiting its geometric simplicity, we fully resolve the head-on collision of two swimming droplets of different radii and demonstrate that even a small contrast in size critically conditions their collision and subsequent dynamics. We identify three fundamentally different regimes. The resulting high sensitivity of pairwise collisions is expected to profoundly affect their collective dynamics.

Although droplet retraction is involved in many applications, it receives less attention than droplet spreading. We present a detailed study of the retraction dynamics for water droplets with varying velocities impacting onto surfaces ranging from hydrophilic to superhydrophobic. The morphologies of retracting droplets are compared in detail. Two distinct retraction modes are classified: the inertial mode and the capillary mode. The retracting droplet with an inertial mode features a rim-lamella structure with a slowly decreasing dynamic receding contact angle while the capillary mode shows a collapsed rim and lamella and capillary wave propagation. During the retraction process, the inertial mode first takes place, and then the capillary mode occurs at a later stage. The inertial mode becomes more dominant with increasing impacting velocities. The dependencies of the retraction rate on impacting velocities and surface wettabilities are justified from the experimental measurements. The inertial-mode retraction rate increases with increasing velocity, while the capillary-mode retraction rate decreases. The retraction rate is generally higher for more hydrophobic surfaces, and its dependence on impacting velocities becomes stronger. An improved shape assumption for the retracting droplet is proposed by introducing an averaged dynamic receding contact angle and a shape factor. This semiempirical model can well explain the dependency of the inertial-mode retraction rate on impacting velocities for water droplets. Last but not the least, the normalized retraction curves generally collapse into a universal curve, revealing certain similarity behaviors for the droplet retraction on solid surfaces.

Active matter systems such as eukaryotic cells and bacteria continuously transform chemical energy to motion. Hence living systems exert active stresses on the complex environments in which they reside. One recurring aspect of this complexity is the viscoelasticity of the medium surrounding living systems: Bacteria secrete their own viscoelastic extracellular matrix, and cells constantly deform, proliferate, and self-propel within viscoelastic networks of collagen. It is therefore imperative to understand how active matter modifies, and gets modified by, viscoelastic fluids. Here we present a two-phase model of active nematic matter that dynamically interacts with a passive viscoelastic polymeric phase and perform numerical simulations in two dimensions to illustrate its applicability. Motivated by recent experiments we first study the suppression of cell division by a viscoelastic medium surrounding the cell. We further show that the self-propulsion of a model keratocyte cell is modified by the polymer relaxation of the surrounding viscoelastic fluid in a nonuniform manner and find that increasing polymer viscosity effectively suppresses the cell motility. Last, we explore the hampering impact of the viscoelastic medium on the generic hydrodynamic instabilities of active nematics by simulating the dynamics of an active stripe within a polymeric fluid. The model presented here can provide a framework for investigating more complex dynamics such as the interaction of multicellular growing systems with viscoelastic environments.

Understanding the role of frictional drag in diffusive transport is an important problem in the field of active turbulence. Using a generic continuum model that applies well to living systems, we investigate the role of Ekman friction on the passive transport of Lagrangian tracers that go with the local flow. We find that the crossover from ballistic to diffusive regime happens at a timescale ${\tau }_c$ that attains a minimum at zero friction, meaning that both injection and dissipation of energy delay the relaxation of tracers. We explain this by proposing that ${\tau }_c\sim {\ell }^{*}/u_{\text{rms}}$, where ${\ell }^{*}$ is a dominant length scale extracted from energy spectrum peak, and $u_{\text{rms}}$ is a velocity scale that sets the kinetic energy at steady state; both scales monotonically decrease with friction. Finally, we predict friction scaling laws for ${\ell }^{*},u_{\text{rms}}$, and the diffusion coefficient $\mathcal{D}\sim {\ell }^{*}{u}_{\text{rms}}/2$, that are valid over a wide range of fluid friction. The findings of our report should apply to transport phenomena in generic active systems such as dense bacterial suspensions, microtubule networks, or even artificial swimmers, to name a few.

Evaporation along a curved liquid vapor interface, such as that of a wetting meniscus, is a classic multiscale problem of vital significance to many fields of science and engineering. However, a complete description of the local evaporative flux over all length scales, especially without arbitrary tuning of boundary conditions, is lacking. A multiscale method to model evaporation from steady meniscus is described such that a need for tuning of boundary conditions and additional assumptions are alleviated. A meniscus submodel is used to compute evaporation flux in the bulk meniscus while a transition film submodel is used to account for enhanced evaporation near the contact line. A unique coupling between the meniscus and transition film submodels ensures smooth continuity of both film and mass flux profiles along the meniscus. The local mass flux is then integrated over the interfacial area to investigate the contribution from the different regions on the surface. The model is evaluated with data from cryoneutron phase-change tests conducted previously at National Institute for Standards and Technology (NIST) [K. Bellur et al., Cryogenics 74, 131 (2016)]. It is found that the peak mass flux in the transition region is two orders of magnitude greater than the flux at the apex. Despite the enhanced evaporation in the thin film region, it was found that 78–95% of the evaporation occurs in the bulk meniscus due to the large area. The bulk meniscus contribution increases with increase in vapor pressure and Bond number but decreases with an increase in thermal conductivity of the substrate. Using a nonuniform temperature boundary suggests that there is a possibility that the adsorbed film may have a nonzero mass flux.

We investigate the impact of buoyancy on the solute mass transport in an evaporating liquid mixture (nonvolatile solute $+$ solvent) confined in a slit perpendicular to the gravity. Solvent evaporation at one end of the slit induces a solute concentration gradient which in turn drives free convection due to the difference between the densities of the solutes and the solvent. From the complete model coupling mass transport and hydrodynamics, we first use a standard Taylor-like approach to derive a one-dimensional nonlinear advection-dispersion equation describing the solute concentration process for a dilute mixture. We then perform a complete analysis of the expected regimes using both scaling analysis and asymptotic solutions of this equation. The validity of this approach is confirmed using a thorough comparison with the numerical resolution of both the complete model and the 1D advection-dispersion equation. Our results show that buoyancy-driven free convection always impacts solute mass transport at long timescales, dispersing solutes in a steadily increasing length scale along the slit. Beyond this confined drying configuration, our work also provides an easy way for evaluating the relevance of buoyancy on mass transport in any other microfluidic configuration involving concentration gradients.

Coupled mixed convective and stratified systems are common in natural flows. To study experimentally the associated dynamics, we use a singular property of water: its nonlinear equation of state is characterized by a maximum density close to $4°\mathrm{C}$. By heating the top of a tank at $35°\mathrm{C}$ and cooling the bottom at $0°\mathrm{C}$, a two-layer configuration spontaneously appears. The convective motion in the bottom layer consists mostly of a large-scale circulation and rising cold plumes. This turbulent flow generates propagating internal gravity waves in the upper stably stratified layer. Particle image velocimetry measurements are performed and spectral characteristics of the convection and internal gravity waves are presented. An horizontal large-scale reversing flow in the stratified layer is observed which is viscously driven by a third, intermediate layer. This buffer layer is located between the convective and stratified layers and is thermally coupled with the convective one, hence sustaining a strong horizontal shear. Three-dimensional direct numerical simulations with geometry and physical parameters close to the experimental ones corroborate our experimental results.

We consider the gravity-driven flow of a perfect dielectric, viscous, thin liquid film, wetting a flat substrate inclined at a nonzero angle to the horizontal. The dynamics of the thin film is influenced by an electric field which is set up parallel to the substrate surface—this nonlocal physical mechanism has a linearly stabilizing effect on the interfacial dynamics. Our particular interest is in fluid films that are hanging from the underside of the substrate; these films may drip depending on physical parameters, and we investigate whether a sufficiently strong electric field can suppress such nonlinear phenomena. For a non-electrified flow, it was observed by Brun et al. [Phys. Fluids 27, 084107 (2015)] that the thresholds of linear absolute instability and dripping are reasonably close. In the present study, we incorporate an electric field and analyze the absolute and convective instabilities of a hierarchy of reduced-order models to predict the dripping limit in parameter space. The spatial stability results for the reduced-order models are verified by performing an impulse-response analysis with direct numerical simulations (DNS) of the Navier–Stokes equations coupled to the appropriate electrical equations. Guided by the results of the linear theory, we perform DNS on extended domains with inflow and outflow conditions (mimicking an experimental setup) to investigate the dripping limit for both non-electrified and electrified liquid films. For the latter, we find that the absolute instability threshold provides an order-of-magnitude estimate for the electric-field strength required to suppress dripping; the linear theory may thus be used to determine the feasibility of dripping suppression given a set of geometrical, fluid, and electrical parameters.

The cooling process associated with the flow induced by a spark plasma discharge generated between a pair of electrodes is measured using stereoscopic particle image velocimetry (S-PIV) and background oriented schlieren (BOS). Density measurements show that the hot gas kernel initially cools fast by convective cooling, which is followed by a slower cooling process. The cooling rates during the fast regime range from 2 to 10 times those in the slower regime. An analytical model is developed to relate the cooling observed in the fast regime using BOS to the total entrainment of cold ambient fluid per unit volume of the hot gas kernel, measured using S-PIV. The model calculates the cooling ratio to characterize the cooling process and shows that the cooling ratios estimated from the density measurements are in close agreement with those calculated from the entrainment. These measurements represent quantitative density and velocity measurements of the flow induced by a spark discharge and reveal the role of entrainment in the cooling of the hot gas kernel. These results underscore that convective cooling of the hot gas kernel, in the fast regime, leads to approximately 50% of the cooling and occurs within the first millisecond of the induced flow.

We derive a generalized induced-charge electrokinetic (ICEK) velocity around a conducting object placed in an arbitrary multimodal electric field. The generalized model allows consideration of asymmetric rectified electric fields (AREFs), which have recently been established to occur in liquids where the ions present have unequal mobilities. Including the AREF yields fluid velocities in which both the direction and the magnitude depend sensitively on the applied potential, frequency, ionic type and strength, and even the exact placement of the object between parallel electrodes. The results provide an explanation for the long-standing question of flow reversals observed in ICEK systems.

The transient growth in thermocapillary liquid layers is examined by nonmodal stability theory. Two kinds of thermocapillary liquid layers including linear flow and return flow are considered. The transient growth is measured by a growth function, which depends on both the velocity and temperature. It was found that rather large transient growth occurs in subcritical flows at small Prandtl numbers (Pr), while the temperature field on the surface has a negative effect on the transient growth. In particular, the transient growth function increases significantly with the Reynolds number, but decreases with Pr. The most amplified perturbation is characterized by counter-rotating vortices and streaks, which are both nearly streamwise. Energy analysis shows that the energy of transient growth mainly comes from the basic flow, while the work done by Marangoni forces on the surface is negligible.

We study numerically the hydrodynamics of a self-propelled particle system consisting of spherical squirmers sedimented on a flat surface. We observe the emergence of dynamic structures, due to the interplay of particle-particle and particle-wall hydrodynamic interactions. At low coverages, our results demonstrate the formation of small chiral spinners: two or three particles are bound together via near-field hydrodynamic interactions and form a rotating dimer or trimer, respectively. The stability of the self-organized spinners can be tuned by the strength of the sedimentation. Increasing the particle concentration leads more interactions between particles and the spinners to become unstable. At higher area fractions we find that pusher particles can align their swimming directions, leading to a stable polar order and enhanced motility. Further, we test the stability of the polar order in the presence of a solid boundary. We observe the emergence of a particle vortex in a cylindrical confinement.