Microorganisms living in microfluidic environments often form multispecies swarms, where they can leverage collective motions to achieve enhanced transport and spreading. Nevertheless, there is a general lack of physical understandings of the origins of the multiscale unstable dynamics observed within these systems. In this study, we build a theoretical model to study the hydrodynamic instabilities arising in a dilute mixture of microswimmers that have different propulsion mechanisms and populations. Especially, we consider the scenario of an “activity-balanced” binary suspension that produces zero mean extra stress. We construct a continuum kinetic model that describes the transient dynamics as the system deviates from uniform isotropy. We perform linear stability analyses to show that such binary active suspensions may exhibit rich instability behavior that are far more complex than the single-species cases (e.g., pure pusher or puller suspensions) that have been well studied.

Dense suspensions that exhibit discontinuous shear thickening (DST) undergo complex stress relaxation when the flow abruptly stops. Using rotational rheometry, we study the two-step relaxation of aqueous cornstarch suspensions out of the DST state upon flow cessation and show that the DST fluid retains the memory of its shear-thickening state until the shear stress reaches a constant value at late times. We find that this residual stress at the end of the relaxation increases with the steady-state viscosity before the cessation. Furthermore, the timescales that characterize the two-step exponential decay of the shear stress exhibit near linear dependence on the steady-state viscosity. Within the current framework that ascribes DST to the breakdown of hydrodynamic lubrication layers leading to interparticle frictional contacts, the lasting effects of the steady-state viscosity suggest that the memory of frictional contacts persists until the end of the relaxation, despite the presence of repulsive forces between the particles. These results indicate that complete, spontaneous relaxation of the system out of the DST state is stalled by the partial retention of the frictional force chains, which may be caused by the stationary boundaries and the adhesion between cornstarch particles.

We consider a particle diffusing inside a wedge with absorbing boundaries and driven by a radial flow of incompressible fluid generated by a source at the apex. The survival probability decays as (time)${}^{-\beta }$ with $\beta$ depending on the opening angle of the wedge and the Reynolds number associated with the hydrodynamic flow. The computation of the exponent $\beta$ reduces to finding the ground-state energy of the quantum particle in an infinitely deep potential well with a shape determined by the radial flow velocity.

Numerical investigation of vortex induced vibration of a circular cylinder of low dimensionless mass $(m^{*}=1,2)$ near a rigid wall is carried at a Reynolds number $Re=300$ for a wide range of reduced velocity, $2\le U^{*}\le 20$. Two-dimensional computations are performed using an immersed boundary method with the cylinder initially at rest and are left to respond to the fluid forces from a height close to the wall. The cylinder is elastically mounted and has two degrees of freedom. A penalty type of collision model is employed where the repulsive force between the cylinder and wall springs into action beyond a critical separation and increases inversely with the gap. The cylinder response is synchronized with the near wake, and its transverse vibration frequency is twice the natural frequency. In the synchronization regime, three response branches are observed in the structural response curve: upper branch (UB), lower branch initial [LB(I)], and lower branch terminal [LB(T)]. Steady flow at low $U^{*}$ proceeds to the highly responsive UB at a threshold reduced velocity. The response curves remain unaltered with changes in gap ratios, whereas the critical threshold $U^{*}$ for the UB response branch moves with $m^{*}$. Transverse displacement of the cylinder is maximum in UB, followed by a dip in a narrow band of $U^{*}$ in LB(I), where the trajectories produce a perfect limit cycle. In the LB(T) branch though the transverse response stabilizes, and trajectories show quasiperiodic nature intermittently. Wake oscillations are found to peak in the UB branch with both drag and lift rms yielding high values, which subsequently settle down in the LB(T) branch at higher $U^{*}$. The wall-jet type gap flow between the cylinder and the wall deflects with the ascending and descending motion of the cylinder. We have devised a method for tracking vortex trajectories, which reveals vortex elongation, vortex merging, wake-wall interactions, and late-stage vortex merging at different response branches. We have identified a unique aspect of cylinder motion over the response branches: “impact” and “gracing.” The lift and transverse motion of the cylinder show discontinuity and rapid changes within a short time for the impact cases with a large repulsive force that has an impulsive nature. In contrast, a trivial repulsive force marks continuous lift and vertical motion of the cylinder in the gracing mode. The nature of the collision is inelastic for the impact cases for both mass and gap ratios. We have proposed a flow model for the downstream evolution of the streamwise velocity, which reveals the spatial transition. The model identifies three flow regimes: wall jet, separated shear flow, and far wake evolution. The upper branch does not favor the existence of a separated region, while the wall-jet flow becomes distinct in the LB(I). The streamwise evolution in the far wake shows a thicker reattached shear layer. The point of wall separation lies mostly upstream of the cylinder while the reattachment length becomes insensitive to $U^{*}$ for a lighter cylinder owing to a vigorous transverse vibration.

We conduct a linear analysis of axisymmetric magnetorotational instability (MRI) in a magnetized cylindrical Taylor-Couette (TC) flow for its standard version (SMRI) with a purely axial background magnetic field and two additional types—helically modified SMRI (H-SMRI) and helical MRI (HMRI)—in the presence of combined axial and azimuthal magnetic fields. This study is intended as preparatory for upcoming new cutting-edge large-scale liquid sodium MRI experiments planned within the DRESDYN project at Helmholtz-Zentrum Dresden-Rossendorf, so we explore these instability types for typical values of the main parameters: the magnetic Reynolds number, the Lundquist number, and the ratio of the angular velocities of the cylinders, which are attainable in these experiments. In contrast to previous attempts at detecting MRI in the laboratory, our results demonstrate that SMRI and its helically modified version can in principle be detected in the DRESDYN-TC device for the range of the above parameters, including the astrophysically most important Keplerian rotation, despite the extremely small magnetic Prandtl number of liquid sodium. Since in the experiments we plan to approach (H-)SMRI from the previously studied HMRI regime, we characterize the continuous and monotonous transition between these two regimes. We show that H-SMRI, like HMRI, represents an overstability (traveling wave) with nonzero frequency linearly increasing with azimuthal field. Because of its relevance to finite-size flow systems in experiments, we also analyze the absolute form of H-SMRI and compare its growth rate and onset criterion with the convective one.

Saffman and Turner [P. G. Saffman and J. S. Turner, J. Fluid Mech. 1, 16 (1956)] argued that the collision rate for droplets in turbulence increases as the turbulent strain rate increases. However, the numerical simulations of Dhanasekaran et al. [J. Dhanasekaran et al., J. Fluid Mech. 910, A10 (2021)] in a steady straining flow showed that the Saffman-Turner model is oversimplified because it neglects droplet-droplet interactions. These result in a complex dependence of the collision rate on the strain rate and on the differential settling speed. Here we show that this dependence is explained by a sequence of bifurcations in the collision dynamics. We compute the bifurcation diagram when strain is aligned with gravity and show that it yields important insights into the collision dynamics. First, the steady-state collision rate remains nonzero in the limit $\mathrm{Kn}\to 0$, contrary to the common assumption that the collision rate tends to zero in this limit (Kn is a nondimensional measure of the mean free path of air). Second, the nonmonotonic dependence of the collision rate on the differential settling speed is explained by a grazing bifurcation. Third, the bifurcation analysis explains why so-called closed trajectories appear and disappear. Fourth, our analysis predicts strong spatial clustering near certain saddle points, where the effects of strain and differential settling cancel.

Barnacle-type roughness can be considered as a hybrid form of roughness that combines some of the topographical features of traditional regular rough surfaces composed of discrete roughness elements of uniform size and shape, and of irregular rough surfaces that exhibit features with a wide distribution of sizes and shapes, covering the surface with a random areal distribution. In this study, the influence of barnacle-type rough surfaces with increasing coverage on wall-bounded turbulence is investigated using direct numerical simulations of turbulent channel flow. The barnacle-type rough surfaces were generated with an algorithm that mimics the settlement behavior of barnacles, and the set of seven different surfaces describe the evolution of barnacle fouling with increasing coverage ranging from a lightly fouled surface with small isolated barnacle clusters (10% coverage) to a surface that is fully covered by barnacles (85% coverage). The roughness function recovers the expected trend with frontal solidity, attaining its maximum at a frontal solidity of approximately 0.2. Mean flow, Reynolds stress, and dispersive stresses show signatures of the clustering of roughness features, i.e., the barnacle colonies, at low coverage. This is most distinct for the streamwise Reynolds stresses where a double peak is observed at the lowest coverage; the inner peak can be interpreted as a partial recovery of smooth-wall behavior over the large connected unfouled sections of this surface. The flow over the rough surfaces is further investigated by a topographical characterization of the blanketing layer, i.e., the effective shape of the rough surface “perceived” by the outer flow. A linear relationship between the roughness function and the effective slope of the blanketing layer is observed.

Liquid atomization processes generating sprays and aerosols of droplets are used in many delivery and coating systems involving pure solvents, solutions, and suspensions. In our recent experimental work, we introduced a novel liquid atomization process generating microsprays and aerosols of submicron-diameter droplets for pure solvents, solutions, and suspensions: gas jets disintegrate thin liquid films that are formed as bubbles approach a liquid surface. Here, we develop a theoretical description of droplet sizes and flow rates, using the first principles of conservation of mass and energy, and employing dimensional and scale analyses. We introduce atomization diagrams as a graphical tool to determine possible, impossible, and expected droplet diameters and specific flow rates in aerosols and sprays produced under various conditions. We find a reasonable agreement between the theory and experiments for five different liquids converted into aerosols of submicron-diameter droplets by an atomization process where gas jets disintegrate thin liquid films that are formed as bubbles approach a liquid surface, and also for five traditional pressure nozzles that produce sprays of droplets of hundreds of microns in diameter. Our study explores the overall range of mean droplet diameters between 0.1 and 100 μm and Ohnesorge numbers between 0.01 and 100, and the analysis and atomization diagrams contribute to understanding of liquid atomization and can serve as a theoretical framework for comparing different liquid atomization techniques.

In this paper, we present experimental results and reveal that strong perturbations are not necessary for elastic instability to occur in straight-channel, inertialess, viscoelastic flows at high elasticity. We show that a non-normal-mode bifurcation is followed by chaotic fluctuations, self-organized as streamwise streaks, and elastic waves due to weak disturbances generated by a small cavity at the center of the top channel wall. The chaotic flow persists in the transition, elastic turbulence, and drag reduction regimes, in agreement with previous observations for the case of strong perturbations at the inlet. Furthermore, the observed elastic waves propagate in the spanwise direction, which allows us to confirm the elastic waves' linear dispersion relation directly. In addition, the spanwise propagating elastic wave's velocity depends on Weissenberg number with the same scaling that was previously observed for streamwise propagating waves, although their velocity magnitude is significantly smaller than what was previously observed for the streamwise ones.

In this paper, we present the influence of irregular random waves on the von Kármán street in the wake of an elastically mounted cylinder. The flow is perpendicular to the long axis of the cylinder which is constrained to oscillate transversally. In our experiments, the generated waves are derived from Pierson-Moskowitz and Joint North Sea Wave Project ($\gamma =3$ or 7) spectra. It was found that the increase of the nonlinearity of the generated waves is accompanied by a decrease of the shedding frequency to half of the pic frequency of the generated waves. Furthermore, the Hilbert transformation was performed to calculate the continuous phases of irregular waves ${\theta }_{\eta }$ and that of the Kármán vortex street ${\theta }_{V_x}$. The temporal evolution of the phase combination $\theta =2{\theta }_{V_x}-{\theta }_{\eta }$ has been investigated as well. It was found that the time evolution of $\theta$ has a steplike shape, i.e., when $\theta =0$, this corresponds to a synchronizationlike effect. This approach enables the temporal variability of the synchronization to be quantified in the presence of random irregular waves.

A model for the structure function tensor is proposed, incorporating the effect of anisotropy as a linear perturbation to the standard isotropic form. The analysis extends the spectral approach of Ishihara et al. [T. Ishihara, Phys. Rev. Lett. 88, 154501 (2002)] to physical space based on Kolmogorov's theory and is valid in the inertial range of turbulence. Previous results for velocity cospectra are used to obtain estimates of the model coefficients. Structure functions measured from direct numerical simulations of channel flow and from experimental measurements in turbulent boundary layers are compared with predicted behavior and reasonable agreement is found. We note that power-law scaling is more evident in the cospectra than for the mixed structure functions. Observations are made about countergradient correlation between Fourier modes of wall-normal and streamwise velocity components for wave numbers approaching the Kolmogorov scale.

Birds have a remarkable ability to perform complex maneuvers at post-stall angles of attack such as landing, takeoff, hovering, and perching. The passive deployment of self-actuating covert feathers in response to unsteady flow separation while performing such maneuvers provides a passive, adaptive flow control paradigm for these aerodynamic capabilities. Most studies involving covert-feathers-inspired passive flow control have modeled the feathers as a rigidly attached or a freely moving flap on a wing. A flap mounted via a torsional spring enables a configuration more emblematic of the finite stiffness associated with the covert-feather dynamics (the free-flap case is the zero-stiffness limit of this more general torsional spring configuration). The performance benefits and flow physics associated with this more general case remain largely unexplored. In this work, we model covert feathers as a passively deployable, torsionally hinged flap on the suction surface of a stationary airfoil. We numerically investigate this airfoil-flap system at a low Reynolds number of $\text{Re}=1000$ and angle of attack of ${20}^{\circ }$ by performing high-fidelity nonlinear simulations using a projection-based immersed boundary method. A parametric study performed by varying the stiffness of the spring, mass of the flap and location of the hinge yielded lift improvements as high as 27% relative to the baseline flap-less case and revealed two dominant flow behavioral regimes. A detailed analysis revealed that the stiffness-dependent mean flap deflection and inertia-dependent amplitude and phase of flap oscillations altered the dominant flow characteristics in both the regimes. Of special interest for performance benefits were the flap parameters that enhanced the lift-conducive leading-edge vortex while weakening the trailing-edge vortex and associated detrimental effect of upstream propagation of reverse flow. These parameters also yielded a favorable temporal synchronization of flap oscillations with the vortex-shedding process in both regimes.

A natural and sensible way of modeling the downburst outflow that triggers thunderstorms and sandstorms is regarding it as a gravity current sustained by the cooling source, which may be quite different from the lock-release gravity current. In this paper, a unified integral model incorporating a continuous velocity transition is proposed for the lock-release and cooling-source gravity currents. It suggests that the Froude number will increase by involving the shear layer in the dense fluid, the influence of which almost vanishes in the lock-release gravity current. The integral model for the cooling-source gravity current correlates the front characteristics with the thermodynamic and geometric properties of the cooling source, in good agreement with direct numerical simulations. Both the integral model and simulations indicate that the shear layer in the dense fluid could play a dominant role in the cooling-source gravity current. Results also demonstrate that the dimensionless front velocity and the front depth are governed by the center height and the longitudinal radius of the cooling source, barely affected by the vertical radius of the cooling source. The Froude number based on the center height of the cooling source is found to manifest a minor reliance on the geometric properties of the cooling source.

Based on the conservative phase field model developed by Lowengrub and Truskinovsky [Proc. R. Soc. London A 454, 2617 (1998)] for almost incompressible liquid binary mixtures, we propose an extended scheme for studying immiscible/miscible liquids. Below a critical temperature $T_c$, the liquids are immiscible with separating interfaces. Above $T_c$, the interfacial effects vanish, and the liquids become perfectly miscible. The free-energy density of the system depends not only on the phase field variable $\varphi$ (which describes the system composition), but also on the reduced temperature $r=(T_c-T)/T_c$ which measures the distance to the critical point described by $T_c$. The free energy suffers transformations through $T_c$ in a way to permit a two-phase system in the subcritical (immiscible) regime and a monophase in the supercritical (miscible) regime. Numerical simulations in two spatial dimensions have been performed for isothermal problems (with $r$ as control parameter) as well as for nonisothermal problems with the energy equation describing the temperature distribution. These simulations reveal the behavior of liquid mixtures and droplet coalescence placed in temperature gradients with temperatures continuously varying from $T<T_c$ to $T>T_c$, problems that could be of large interest in phase transitions in micro- and nanofluidics.

Inertial microfluidics is able to focus and separate particles in microchannels based on the characteristic geometry and intrinsic hydrodynamic effect. Yet, the vertical positions of suspended particles in the microchannel cannot be manipulated in real time. In this study, we utilize the boundary slip effect to regulate the parabolic velocity distribution of fluid in the microchannel and present a scheme to actively control the vertical positions of particles in inertial microfluidics. The flow field of a microchannel with a unilateral slip boundary is equivalent to that of the microchannel widened by the relevant slip length, and the particle equilibrium positions in the two microchannels are consistent consequently. Then, we simulate the lateral migrations of three kinds of typical particles, namely, circular, elliptical, and rectangular in the microchannel. Unlike the smooth trajectories of circular particles, the motions of the elliptical and rectangular particles are accompanied by regular fluctuations and nonuniform rotations due to their noncircular geometries. The results demonstrate that the unilateral slip boundary can effectively manipulate the vertical equilibrium positions of particles. The present scheme can improve the accuracy and flexibility of particulate focusing, separating, and transport in inertial microfluidics.

In a wall-bounded shear flow, deformable particles form a crystal-like structure [Phys. Rev. Lett. 120, 268102 (2018)]. To expand the applicability of microfluidic devices to particle sorting, we performed a lattice Boltzmann simulation. In this study, the crystal structure of capsules can be utilized to segregate capsules of different sizes. We add small capsules into a system where large capsules form a crystal structure, and find that the movement of the small capsules changes significantly with size ratio $R_a$. When the sizes of the small capsules were comparable to those of the large capsules $(R_a\sim 1)$, the small capsules are trapped in the crystal structure. In addition, they composed the crystal with the large capsules and traveled in a diffusive manner. However, when $R_a\sim 0.6$ or lower, the small capsules were depleted from the crystal layer due to the low lift velocity, and they continuously traveled in an advective manner. Furthermore, we found that the stiffness of the small capsules had only a slight influence on this phenomenon. The results suggest that the crystal structure of capsules can be used to trap capsules of comparable sizes or to exclude capsules of smaller sizes. The findings of this study can serve as practical basis for microfluidic applications for segregating and sorting different types of soft particles.

In this numerical study, we investigate the mixing properties of an acoustic driven flow in a parallelepipedic cavity with square basis in view of applications in photovoltaic crystal growth configurations. A single acoustic source is used, but, relying on non-normal reflections, an acoustic beam with a square path is obtained, generating a global complex flow in the cavity. Depending on the power of the source, the flow field may be steady, periodic in time, or chaotic. We restrict here on the steady and periodic cases and show that those flow fields enable chaotic advection. In the case of oscillating periodic flow fields, the chaotic region invades the whole cavity, as shown by numerical simulations of Poincaré sections and animations of mixing. This illustrates that acoustic streaming at moderate powers can be used successfully as a nonintrusive tool to mix efficiently.

We introduce a closure model for coarse-grained kinetic theories of polar active fluids. Based on a quasiequilibrium approximation of the particle distribution function, the model closely captures important analytical properties of the kinetic theory, including its linear stability and the balance of conformational entropy production and dissipation. Nonlinear simulations show the model reproduces the qualitative behavior and nonequilibrium statistics of the kinetic theory, unlike commonly used closure models. We use the closure model to simulate highly turbulent suspensions in both two and three dimensions in which we observe complex multiscale dynamics, including large concentration fluctuations and a proliferation of polar and nematic defects.

This article develops a leaky-dielectric model to study the axisymmetric breakup of an electrified jet, using the phase field method to treat interfacial phenomena. The model is used to analyze the breakup in a wide range of the Taylor number ($\mathrm{\Gamma }$), the Ohnesorge number (Oh), and the wave number relevant to electrosprays operating in the cone-jet mode. The phase field technique accurately captures the behavior of the jet after pinch-off and predicts the formation of primary and satellite droplets. The numerical results are compared with existing experimental and numerical studies, extending them to account for the formation of sub-satellite droplets. It is found that for highly viscous jets, $\text{Oh}\gg 1$, the number of subsatellite droplets generated increases with the Taylor number when compared to low viscous jets, hence widening the size distribution of droplets. At fixed $\mathrm{\Gamma }$ and Oh the primary droplets are charged to an approximately constant ratio of the Rayleigh charge limit, regardless of the wave number. Furthermore, the primary droplets are charged below the Rayleigh limit for $\mathrm{\Gamma }\lesssim 1.5$ and charged above the Rayleigh limit when $\mathrm{\Gamma }\gtrsim 1.5$. Thus, most primary droplets are expected to be unstable at Taylor numbers exceeding 1.5.

An experiment is presented showing enhanced water transport across a porous layer compared to pure water vapor diffusion. The enhanced transport is explained by the presence of brine in the layer and the dependence of the equilibrium vapor pressure with the dissolved salt concentration. The impact of the salt presence is further demonstrated by a comparison with the case of pure water. A significantly longer period of sustained evaporation is obtained in the presence of salt. The transport enhancement effect can last over long periods of time when the conditions are such that the porous layer reaches a dynamic equilibrium between condensation and evaporation. Also, the porous layer can adapt to changes in the boundary conditions via changes in the brine saturation and associated modifications in the salt concentration and the equilibrium vapor pressure. The transport enhancement effect is also illustrated in relation with the dynamics of salt crusts.