We investigate flow pattern formation and viscosity reduction mechanisms in active fluids by studying a generalized Navier-Stokes model that captures the experimentally observed bulk vortex dynamics in microbial suspensions. We present exact analytical solutions including stress-free vortex lattices and introduce a computational framework that allows the efficient treatment of higher-order shear boundary conditions. Large-scale parameter scans identify the conditions for spontaneous flow symmetry breaking, geometry-dependent viscosity reduction, and negative-viscosity states amenable to energy harvesting in confined suspensions. The theory uses only generic assumptions about the symmetries and long-wavelength structure of active stress tensors, suggesting that inviscid phases may be achievable in a broad class of nonequilibrium fluids by tuning confinement geometry and pattern scale selection.

Flow around a square cylinder controlled using plasma actuators (PAs) is numerically investigated by direct numerical simulation in order to clarify the most effective location of actuator installation and to elucidate the mechanism of control effect. The Reynolds number based on the cylinder diameter and the free-stream velocity is set to be 100 to study the fundamental effect of PAs on two-dimensional vortex shedding, and three different locations of PAs are considered. The mean drag and the root-mean-square of lift fluctuations are found to be reduced by 51% and 99% in the case where two opposing PAs are aligned vertically on the rear surface. In that case, a jet flow similar to a base jet is generated by the collision of the streaming flows induced by the two opposing PAs, and the vortex shedding is completely suppressed. The simulation results are ultimately revisited in the frame of linear sensitivity analysis, whose computational cost is much lower than that of performing the full simulation. A good agreement is reported for low control amplitudes, which allows further discussion of the linear optimal arrangement for any number of PAs.

We investigate the effect of nonlinearities on the frequency response of a round, incompressible jet. Experiments show that axisymmetric structures dominate the response of forced and unforced jets. In contrast, linear stability and frequency response analyses predict the asymmetric mode $\left(m=1\right)$ to be locally more unstable and globally more amplified than the axisymmetric mode $(m=0)$. We perform a weakly nonlinear expansion of the response of the flow to harmonic forcing and derive an asymptotic expression for the sum of this divergent series beyond its limit of validity. This expression compares reasonably well with the nonlinear gain up to forcing amplitudes an order of magnitude greater than the limit of validity of the weakly nonlinear expansion. For equal forcing amplitudes, the asymmetric mode dominates over the axisymmetric mode. This suggests that the projection of environmental forcing onto the individual azimuthal modes plays an important role in the preferred dynamics of round jets.

In this work, a spectral model is derived to investigate numerically unstably stratified homogeneous turbulence (USHT) at large Reynolds numbers. The modeling relies on an earlier work for passive scalar dynamics [Briard et al., J. Fluid Mech. 799, 159 (2016)] and can handle both shear and mean scalar gradients. The extension of this model to the case of active scalar dynamics is the main theoretical contribution of this paper. This spectral modeling is then applied at large Reynolds numbers to analyze the scaling of the kinetic energy, scalar variance, and scalar flux spectra and to study as well the temporal evolution of the mixing parameter, the Froude number, and some anisotropy indicators in USHT. A theoretical prediction for the exponential growth rate of the kinetic energy, associated with our model equations, is derived and assessed numerically. Throughout the validation part, results are compared with an analogous approach, restricted to axisymmetric turbulence, which is more accurate in term of anisotropy description, but also much more costly in terms of computational resources [Burlot et al., J. Fluid Mech. 765, 17 (2015)]. It is notably shown that our model can qualitatively recover all the features of the USHT dynamics, with good quantitative agreement on some specific aspects. In addition, some remarks are proposed to point out the similarities and differences between the physics of USHT, shear flows, and passive scalar dynamics with a mean gradient, the two latter configurations having been addressed previously with the same closure. Moreover, it is shown that the anisotropic part of the pressure spectrum in USHT scales in $k^{-11/3}$ in the inertial range, similarly to the one in shear flows. Finally, at large Schmidt numbers, a different spectral range is found for the scalar flux: It first scales in $k^{-3}$ around the Kolmogorov scale and then further in $k^{-1}$ in the viscous-convective range.

Autocatalytic reaction fronts between two reacting species in the absence of fluid flow propagate as solitary waves. The coupling between an autocatalytic reaction front and a forced hydrodynamic flow may lead to a stationary front whose velocity and shape depend on the underlying flow field. We focus on the chemohydrodynamic opposition between forced advection and self-sustained chemical waves, which can lead to static stationary fronts, i.e., frozen fronts (FFs). Toward that end, we perform experiments, analytical computations, and numerical simulations with the autocatalytic iodate-arsenious acid reaction (IAA) over a wide range of flow velocities around a solid disk. For the same set of control parameters, we observe two types of frozen fronts: an upstream FF, which avoids the solid disk, and a downstream FF with two symmetric branches emerging from the solid disk surface. We map the range over which we observe these frozen fronts. We also address the relevance of the so-called eikonal, thin front limit to describe the observed fronts and select the frozen front shapes.

Hot-wire measurements were performed in a zero-pressure-gradient turbulent boundary layer overlying both a smooth and a rough wall for the purpose of investigating the details of inner–outer flow interactions. The roughness considered embodies a broad range of topographical scales arranged in an irregular manner and reflects the topographical complexity often encountered in practical flow systems. Single-probe point-wise measurements with a traversing probe were made at two different regions of the rough-wall flow, which was previously shown to be heterogeneous in the spanwise direction, to investigate the distribution of streamwise turbulent kinetic energy and large scale–small scale interactions. In addition, two-probe simultaneous measurements were conducted enabling investigation of inner–outer interactions, wherein the large scales were independently sampled in the outer layer. Roughness-induced changes to the near-wall behavior were investigated, particularly by contrasting the amplitude and frequency modulation effects of inner–outer interactions in the rough-wall flow with well-established smooth-wall flow phenomena. It was observed that the rough-wall flow exhibits both amplitude and frequency modulation features close to the wall in a manner very similar to smooth-wall flow, though the correlated nature of these effects was found to be more intense in the rough-wall flow. In particular, frequency modulation was found to illuminate these enhanced modulation effects in the rough-wall flow. The two-probe measurements helped in evaluating the suitability of the interaction-schematic recently proposed by Baars et al., Exp. Fluids 56, 1 (2015) for rough-wall flows. This model was found to be suitable for the rough-wall flow considered herein, and it was found that frequency modulation is a “cleaner” measure of the inner–outer modulation interactions for this rough-wall flow.

We present measurements of the azimuthal orientation $\theta \left(t\right)$ and thermal amplitude $\delta \left(t\right)$ of the large-scale circulation (LSC) of turbulent rotating convection within a large Rossby number range $1\le \mathrm{Ro}\le 314$. Results of $\theta \left(t\right)$ reveal persistent rotation of the LSC flow in the retrograde direction over the entire Ro range. The rotation speed ratio remains a constant of $0.13\pm 0.01$ for $10\le \mathrm{Ro}\le 70$, but starts to increase with increasing Ro when $\mathrm{Ro}>70$. We identify the mechanism through which the mean retrograde rotation speed can be enhanced by stochastic cessations in the presence of weak Coriolis force and show that a low-dimensional stochastic model, with essential refinements to account for the effect of turbulence stress, provides accurate predictions of the observed LSC dynamics and interprets its retrograde rotation.

We study the evolution of the profile of a two-dimensional volatile liquid droplet that is evaporating on a flat heated substrate. We adopt a one-sided model with thermal control that, together with the lubrication approximation, results in an evolution equation for the local height of the droplet. Without requiring any presumption for the shape of the drop, the problem is formulated for the two modes of evaporation: a pinned contact line and a moving contact line with fixed contact angle. Numerical solutions are provided for each case. For the pinned contact line case, we observe that after a time interval the contact angle dynamics become nonlinear and, interestingly, the local contact angle goes to zero in advance of total evaporation of the drop. For the case of a moving contact line, in which the singularity at the contact line is treated by a numerical slip model, we find that the droplet nearly keeps its initial circular shape and that the contact line recedes with constant speed.

Experiments on evaporating droplets on structured surfaces have shown that the contact line does not move with constant speed, but rather in a steplike “stick-slip” fashion. As a first step in understanding such behavior, we study the evaporation of a two-dimensional volatile liquid droplet on a nonplanar heated solid substrate with a moving contact line and fixed contact angle. The model for the flat case is adapted to include curved substrates, numerical solutions are achieved for various periodic and quasiperiodic substrate profiles, and the dynamics of the contact line and the apparent contact angle are studied. In contrast with our results for a flat substrate, for which the contact line recedes in a nearly constant speed, we observe that the contact line speed and position show significant time variation and that the contact line moves in an approximate steplike fashion on relatively steep substrates. For the simplest case of a periodic substrate, we find that the apparent contact angle is periodic in time. For doubly periodic substrates, we find that the apparent contact angle is periodic and that the problem exhibits a phase-locking behavior. For multimode quasiperiodic substrates, we find the contact line behavior to be temporally complex and not only limited to a stick-slip motion. In all cases, we find that the overall evaporation is increased relative to the flat substrate.

When does a drop, deposited on a cold substrate, stop spreading? Despite the practical relevance of this question, for example, in airplane icing and three-dimensional metal printing, the detailed mechanism of arrest in solidifying spreading drops has remained debated. Here we consider the spreading and arrest of hexadecane drops of constant volume on two smooth wettable substrates: copper with a high thermal conductivity and glass with a low thermal conductivity. We record the spreading radius and contact angle in time for a range of substrate temperatures. The experiments are complemented by a detailed analysis of the temperature field near the rapidly moving contact line, by means of similarity solutions of the thermohydrodynamic problem. Our combined experimental and theoretical results provide strong evidence that the spreading of solidifying drops is arrested when the liquid at the contact line reaches a critical temperature, which is determined by the effect of kinetic undercooling.

We report on the coefficient of restitution of bubble collision on a free surface in the presence of surfactants. In pure fluids, the collision process is well described by a competition between thin film drainage and interfacial tension. When surfactants are introduced in pure water, they generate Marangoni stresses on both the bubble interface and free surface, which provides an additional mechanism affecting the collision process. We investigate this mechanism for the bubble collision process in surfactant solutions through a combination of experimental and numerical approaches, with results showing a reduced rebound velocity during the collision process in surfactant solutions compared with that in pure water. Furthermore, by varying both bubble size and surfactant concentration, our experiments show that bubbles experience elastic, partially inelastic, and perfectly inelastic collisions. We identify the Langmuir number, the ratio between absorption and desorption rates, as the fundamental parameter that quantifies the Marangoni effect on the collision process. The effect of Marangoni stress on the bubble's coefficient of restitution is nonmonotonic, where the coefficient of restitution first decreases with Langmuir number and then increases.

Swimming at low Reynolds number in Newtonian fluids is only possible through nonreciprocal body deformations due to the kinematic reversibility of the Stokes equations. We consider here a model swimmer consisting of two linked spheres, wherein one sphere is rigid and the other an incompressible neo-Hookean solid. The two spheres are connected by a rod that changes its length periodically. We show that the deformations of the body are nonreciprocal despite the reversible actuation and hence the elastic two-sphere swimmer propels forward. Our results indicate that even weak elastic deformations of a body can affect locomotion and may be exploited in designing artificial microswimmers.

In this study, a dynamic model for large-eddy simulations is proposed in order to describe the motion of small inertial particles in turbulent flows. The model is simple, involves no significant computational overhead, contains no adjustable parameters, and is flexible enough to be deployed in any type of flow solvers and grids, including unstructured setups. The approach is based on the use of elliptic differential filters to model the subgrid-scale velocity. The only model parameter, which is related to the nominal filter width, is determined dynamically by imposing consistency constraints on the estimated subgrid energetics. The performance of the model is tested in large-eddy simulations of homogeneous-isotropic turbulence laden with particles, where improved agreement with direct numerical simulation results is observed in the dispersed-phase statistics, including particle acceleration, local carrier-phase velocity, and preferential-concentration metrics.

Motion in fluids at the micro(nano)metric scale is dominated by viscosity. One efficient propulsion method relies on a weak uniform rotating magnetic field that drives a chiral object. From bacterial flagella to artificial magnetic micro- or nanohelices, rotation of a corkscrew is considered as a universally efficient propulsion gait in viscous environments. However, recent experimental studies have demonstrated that geometrically achiral microscale objects or random-shaped magnetic aggregates can propel similarly to helical micromotors. Although approximate theories concerning dynamics of helical magnetic propellers are available, propulsion of achiral particles or objects with complex shapes is not understood. Here we present a general theory of rotation and propulsion of magnetized object of arbitrary shape driven by a rotating magnetic field. Intrinsic symmetries of the viscous mobility tensors yield compact classification of stable rotational states depending on the orientation of the magnetic moment with respect to principal rotation axes of the object. Propulsion velocity can be written in terms of geometry-dependent chirality matrix $\mathbf{Ch}$, where both the diagonal elements (owing to orientation-dependent handedness) and off-diagonal entries (that do not necessitate handedness) contribute in a similar way. In general, the theory anticipates multiplicity of stable rotational states corresponding to two (complimentary to $\pi$) angles the magnetization forms with the field rotation axis. Thus, two identical magnetic objects may propel with different speeds or even in opposite directions. However, for a class of simple achiral objects, there is a particular magnetization whereas the pair of symmetric rotational states gives rise to a unique chiral-like propulsion gait, closely resembling that of an ideal helical propeller. In other words, a geometrically achiral object can acquire apparent chirality due to its interaction with the external magnetic field. The developed theory is further applied to study the dynamics of achiral, chiral, and random-shaped magnetic propellers, rationalizing previously unexplained experimental observations. The genetic search algorithm based on the proposed theory reveals that an arc-shaped segment is the optimal (fastest) achiral propeller, while the optimal skew-symmetric shape deviates considerably from a helix. Remarkably, an optimized arc-shaped propeller warrants propulsion speeds comparable to those of the optimally magnetized helix. Although random shaped magnetic aggregates appear to be poor swimmers at low actuation frequency, at higher frequency, whereas the helical propeller ceases to rotate in-sync with the field, the propulsion speed of the aggregates could be comparable, or even higher, than that of a helix.

The inertial migration of neutrally buoyant spherical particles suspended in tube flows of square cross sections was investigated experimentally in the range of Reynolds numbers ($\text{Re}$) from 1 to 800 for particle-to-tube-size ratios from 0.075 to 0.175. Direct observations of the particle distribution in the cross section at various distances from the tube inlet revealed that at low $\text{Re}$, smaller than a certain critical value, particles were focused on four equilibrium positions, located at the center of channel faces, consistent with previous studies on microchannel flows, whereas at higher $\text{Re}$, larger than another critical value, four additional equilibrium positions were observed near the channel corners. At intermediate $\text{Re}$, between these two critical values, we observed new focusing positions of particles, located on a heteroclinic orbit joining the channel face and corner equilibrium positions. Comparing these results with corresponding numerical simulations, we examined the migration properties in detail and categorized their types. It was found that the critical $\text{Re}$ values depended considerably on the particle-to-tube-size ratio.

Despite our reasonably advanced understanding of the dynamics and flow of glasses made of spherical colloids, the role of shape, i.e., the respective behavior of glasses formed by rodlike, particles is virtually unexplored. Recently, long, thin and highly charged rods (fd-virus particles) were found to vitrify in aqueous suspensions at low ionic strength [Phys. Rev. Lett. 110, 015901 (2013)]. The glass transition of these long-ranged repulsive rods occurs at a concentration far above the isotropic-nematic coexistence region and is characterized by the unique arrest of both the dynamics of domains that constitute the chiral-nematic orientational texture, as well as individual rods inside the domains. Hence, two relevant length scales exist: the domain size of a few hundreds of microns, and the rod-cage size of a few microns, inside the domains. We show that the unique dual dynamic arrest and the existing of two widely separated length scales imparts an unprecedented, highly heterogeneous flow behavior with three distinct signatures. Beyond a weak stress plateau at very small shear rates that characterizes the glass, the kinetic arrest of the domain dynamics gives rise to internal fracture, as a result of domain-domain interactions, as well as wall partial slip. It is shown that, on increasing the shear rate, the fractured plug flow changes to a shear-banded flow profile due to the stress response of the kinetically arrested aligned rods within the domains. Shear-gradient banding occurs due to the strong thinning of the uniform chiral-nematic phase within the domains, i.e., complying with the classic shear-banding scenario, giving rise to a stress plateau in the flow curve. Finally, a linear (uniform) velocity profile is found at the highest shear rates. Vorticity banding is also observed at intermediate and high shear rates. These results point to the crucial role of particle shape in tailoring the flow properties of dense colloidal suspensions. Moreover, they strongly support the argument that the origin of shear banding in soft-particle glasses with long-ranged repulsive interactions is fundamentally different from that of hard-particle glasses with short-ranged repulsive interactions.

The geometry of passive tracer trajectories is studied in two different types of rotating turbulent flows; rotating Rayleigh-Bénard convection (RBC; experiments and direct numerical simulations) and rotating electromagnetically forced turbulence (EFT; experiments). This geometry is fully described by the curvature and torsion of trajectories, and from these geometrical quantities we can subtract information on the typical flow structures at different rotation rates. Previous studies, focusing on nonrotating homogeneous isotropic turbulence (HIT), show that the probability density functions (PDFs) of curvature and torsion reveal pronounced power laws. However, the set-ups studied here involve inhomogeneous turbulence, and in RBC the flow near the horizontal plates is definitely anisotropic. We investigate how the typical shapes of the curvature and torsion PDFs, including the pronounced scaling laws, are influenced by this level of anisotropy and inhomogeneity and how this effect changes with rotation. A first effect of rotation is observed as a shift of the curvature and torsion PDFs towards higher values in the case of RBC and towards lower values in the case of EFT. This shift is related to the length scale of typical vortical structures that decreases with rotation in RBC, but increases with rotation in EFT, explaining the opposite shifts of the curvature (and torsion) PDFs. A second remarkable observation is that in RBC the HIT scaling laws are always recovered, as long as the boundary layer (BL) is excluded. This suggests that these scaling laws are very robust and hold as long as we measure in the turbulent bulk. In the BL of the RBC cell, however, the scaling deviates from the HIT prediction for lower rotation rates. This scaling behavior is found to be consistent with the coupling between the boundary layer dynamics and the bulk flow, which changes under rotation. In particular, it is found that the active coupling of the Ekman-type boundary layer with the bulk flow suppresses anisotropy in the BL region for increasing rotation rates.

This study addresses the fluid dynamics of two-dimensional falling films flowing underneath an inclined plane using the weighted integral boundary layer (WIBL) model and direct numerical simulations (DNSs). Film flows under an inclined plane are subject to hydrodynamic and Rayleigh-Taylor instabilities, leading to the formation of two- and three-dimensional waves, rivulets, and eventually dripping. The latter can only occur in film flows underneath an inclined plane such that the gravitational force acts in a destabilizing manner by pulling liquid into the gaseous atmosphere. The DNSs are performed using the solver interFoam of the open-source code OpenFOAM with a gradient limiter approach that avoids artificial oversharpening of the interface. We find good agreement between the two model approaches for wave amplitude and wave speed irrespectively of the orientation of the gravitational force and before the onset of dripping. The latter cannot be modeled with the WIBL model by nature as it is a single-value model. However, for large-amplitude solitarylike waves, the WIBL model fails to predict the velocity field within the wave, which is confirmed by a balance of viscous dissipation and the change in potential energy. In the wavy film flows, different flow features can occur such as circulating waves, i.e., circulating eddies in the main wave hump, or flow reversal, i.e., rotating vortices in the capillary minima of the wave. A phase diagram for all flow features is presented based on results of the WIBL model. Regarding the transition to circulating waves, we show that a critical ratio between the maximum and substrate film thickness (approximately 2.5) is also universal for film flows underneath inclined planes (independent of wavelength, inclination, viscous dissipation, and Reynolds number).

A water bell forms when a fluid jet impacts upon a target and separates into a two-dimensional sheet. Depending on the angle of separation from the target, the sheet can curve into a variety of different geometries. We show analytically that harmonic perturbations of water bells have linear wave solutions with geometry-dependent growth. We test the predictions of this model experimentally with a custom target system, and observe growth in agreement with the model below a critical forcing amplitude. Once the critical forcing amplitude is exceeded, a nonlinear transcritical bifurcation occurs; the response amplitude increases linearly with increasing forcing amplitude, albeit with a fundamentally different spatial form, and distinct nodes appear in the amplitude envelope.