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.

Bileaflet mechanical heart valves (BMHVs) have been related to the production of unphysiological turbulent flow in the ascending aorta. These valves comprise a pair of rigid blunt plates (leaflets), which are immersed in a confined flow with Reynolds numbers up to 10 000. They are prone to develop impinging leading-edge vortex (ILEV) instabilities [K. Hourigan et al., J. Fluids Struct. 15, 387 (2001); S. Deniz and T. Staubli, J. Fluids Struct. 11, 3 (1997)] on the leaflets because of their relatively large chord-to-thickness ratio and their low angle of incidence. These instabilities can produce strong disturbances between the leaflets which may contribute to the onset and intensity of turbulent flow in the wake of the valve. The complex nature of the flow around BMHVs prevents a detailed theoretical analysis of the underlying instability mechanisms. Therefore, we defined a two-dimensional submodel of the flow with fixed leaflets, which renders the problem accessible to the rich toolbox of hydrodynamic stability theory. High-order numerical simulations of this flow configuration indicated the systolic development of unstable ILEVs on the inner side of the leaflets during systolic acceleration of the flow. We found that the ILEV instabilities can only be observed with sufficiently high spatial resolution, which may explain why these phenomena have not been observed so far in most computational studies of BMHV flow. Orr-Sommerfeld eigenmodes with high growth rates confirmed the unstable character of this flow. We further identified a pocket of absolute instability which acts as a wave maker between the leaflets. Finally, we confirmed that this wave-maker region has a direct effect on the nonlinear breakdown in the wake of the valve. To this end, the leaflet geometry was modified such that the ILEV (and the associated wave maker) was eliminated and it was shown numerically that the wake remains laminar for the modified geometry. The results of this study are a first step toward a detailed understanding of the hydrodynamic instability mechanisms which lead to turbulent flow past BMHVs.

In wall-bounded parallel flows, sustained turbulence can occur even while laminar flow is still stable. Channel flow is one of such flows and displays spatiotemporal fluctuating patterns of localized turbulence along its way from and to featureless turbulence. By direct numerical simulation, we study the observed inconsistency between turbulence decay according to a two-dimensional directed-percolation $\left(2D\text{−}\mathrm{DP}\right)$ scenario and the presence of sustained oblique localized turbulent bands (LTBs) below the DP critical point. Above Reynolds number ${\mathrm{Re}}_{\mathrm{g}}\approx 700$, sustained LTBs are observed; most LTBs have the same orientation so that the spanwise symmetry of the LTB pattern is broken below ${\mathrm{Re}}_2\approx 1000$. The frequency of transversal splitting, by which an LTB generates another one with opposite obliqueness, so that turbulence spreading becomes intrinsically two dimensional, increases in the range ${\mathrm{Re}}_{\mathrm{g}}<\mathrm{Re}<{\mathrm{Re}}_2$. It reaches a critical rate at ${\mathrm{Re}}_2$, beyond which symmetry is restored. The $2D\text{−}\mathrm{DP}$ behavior is retrieved only above ${\mathrm{Re}}_2$. A mean-field model is proposed which qualitatively accounts for the above symmetry-restoring bifurcation by considering interactions between space-averaged densities of LTBs propagating in either direction.

The net movement of Lagrangian particles under water waves comprises a Stokes drift in the direction of wave propagation and an Eulerian return flow in the opposing direction. Accurate prediction of the Eulerian return flow in the ocean is of importance in modeling the transport of plastic pollution, oil, wreckage, and sediment. Herein, we derive a multiple-scales solution for the Eulerian mean flow under wave packets that is valid for all water depths, relative to both the length of the wave and the length of the wave packet. To validate this solution, we carry out particle tracking velocimetry experiments in a long flume to extract the mean motion from Lagrangian seeding particles under wave packets, finding good agreement. The extraction technique is able to deal with small background motion and subharmonic error waves associated with wave generation by the paddle, the latter being relatively large in finite-depth flume experiments. In finite depth, the return flow is forced by both the divergence of the Stokes transport on the wave-packet scale and the formation of a non-negligible mean set-down underneath the packet, which acts like a bounding streamtube in the form of a convergent-divergent duct. The magnitude of the horizontal return flow is thus enhanced, with particular relevance to transport in the finite-depth coastal environment.

The swimming characteristics achieved by flapping wings, translating motion, and shell pitching are studied from observations of shelled Antarctic pteropods (aquatic snails nicknamed “sea butterflies”). These pteropods (Limacina helicina antarctica) swim with a pair of parapodia (or “wings”) via a unique flapping propulsion mechanism that incorporates similar techniques as observed in small flying insects. The geometric scaling of the wing span ($L$), wing chord ($c$), and minor shell diameter ($d$) with respect to the major shell diameter ($D$) reveal geometric similitude. Thus, the major shell diameter ($D$) is the only length scale required to describe the size of the pteropods. The motion of swimming pteropods is characterized using flapping, translational, and rotational Reynolds numbers (i.e., ${\text{Re}}_f, {\text{Re}}_U$, and ${\text{Re}}_{\mathrm{\Omega }}$). A critical value of the flapping Reynolds number, ${\text{Re}}_f=35$, is found for the onset of translating and pitching locomotion. Finally, the relationship is obtained for the Strouhal number (${\text{St}}_A=fA/U$) for the pteropods using the geometric scalings and the translational and flapping Reynolds numbers. The Strouhal number is found to be between 0.2 and 0.4, which indicates general agreement with other oscillating organisms moving with high propulsion efficiency.

The observability of the flow away from the wall in turbulent channels is studied using noiseless, although potentially incomplete, wall measurements. Reconstructions of the velocities are generated using linear stochastic estimation. All the velocities are well reconstructed in the buffer layer, but only relatively large “wall-attached” eddies are observable farther from the wall. In particular, large-scale structures that account for approximately 50% of the total kinetic energy and of the tangential Reynolds stress are accurately captured up to $y/h\lesssim 0.2$. It is argued that this should allow the use of wall sensors for the detection (and potential control) of the large eddies populating the logarithmic region, and that it suggests a natural quantitative definition for “wall-attached” eddies.

We address numerically the deformation and fragmentation dynamics of a single liquid drop subject to impulsive acceleration by a unidirectional gas stream. The density ratio between the liquid and gaseous phases is varied in the $10–2000$ range and comparisons are made with recent drop breakup experiments. We show for low Ohnesorge numbers that the liquid-gas density contrast significantly modifies the critical Weber number for the transition between bursting and stripping fragmentation regimes, on the one hand, and for drop fragmentation, on the other hand. We suggest a simple theoretical argument to predict the transitional Weber number as a function of the density contrast and show that the stabilizing influence of small contrasts can be explained by inertial effects in the nonlinear coupling between drop stretching and centroid acceleration.

This paper is associated with a poster winner of a 2018 APS/DFD Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2018.GFM.P0002

A time-evolution of a slightly rarefied gas from a uniform equilibrium state at rest is investigated on the basis of the linearized Boltzmann equation under the acoustic time scaling. By a systematic asymptotic analysis, linearized Euler sets of equations and acoustic-boundary-layer equations are derived, together with their slip and jump boundary conditions, as well as the correction formula in the Knudsen layer. Analysis is done up to the first order of the Knudsen number ($\mathrm{Kn}$), with ${\mathrm{Kn}}^{1/2}$ being the small parameter. Several rarefaction effects, which are known as the effects of the second order in $\mathrm{Kn}$ in the diffusion scaling, are enhanced to be of the first order in $\mathrm{Kn}$. This is because the variation of the macroscopic quantities along the normal direction is steep in the boundary layer and the compressibility of the gas is comparatively strong. The occurrence of secular terms associated with the Hilbert expansion is pointed out and a remedy for it is also given. Finally, as an application example, a sound propagation in a half space caused by a sinusoidal oscillation of flat boundary is examined on the basis of the Bhatnagar–Gross–Krook equation. The asymptotic solution agrees well with the direct numerical solution.

The dynamics of an adhesive two-dimensional vesicle doublet under various flow conditions is investigated numerically using a high-order, adaptive-in-time boundary integral method. In a quiescent flow, two nearby vesicles move slowly toward each other under the adhesive potential, pushing out fluid between them to form a vesicle doublet at equilibrium. A lubrication analysis on such draining of a thin film gives the dependencies of draining time on adhesion strength and separation distance, which are in good agreement with numerical results. In a planar extensional flow, we find that a stable vesicle doublet forms only when two vesicles collide head-on around the stagnation point. In a microfluid trap where the stagnation of an extensional flow is dynamically placed in the middle of a vesicle doublet through an active control loop, novel dynamics of a vesicle doublet are observed. Numerical simulations show that there exists a critical extensional flow rate above which adhesive interaction is overcome by the diverging stream, thus providing a simple method to measure the adhesion strength between two vesicle membranes. In a planar shear flow, numerical simulations reveal that a vesicle doublet may form provided that the adhesion strength is sufficiently large at a given vesicle reduced area. Once a doublet is formed, its oscillatory dynamics is found to depend on the adhesion strength and their reduced area. Furthermore the effective shear viscosity of a dilute suspension of vesicle doublets is found to be a function of the reduced area. Results from these numerical studies and analysis shed light on the hydrodynamic and rheological consequences of adhesive interactions between vesicles in a viscous fluid.