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In nature, chemotactic interactions are ubiquitous and play a critical role in driving the collective behavior of living organisms. Reproducing these interactions in vitro is still a paramount challenge due to the complexity of mimicking and controlling cellular features, such as tangled metabolic networks, cytosolic macromolecular crowding, and cellular migration, on a microorganism size scale. Here, we generate enzymatically active cell-sized droplets able to move freely, and by following a chemical gradient, able to interact with the surrounding droplets in a collective manner. The enzyme within the droplets generates a pH gradient that extends outside the edge of the droplets. We discovered that the external pH gradient triggers droplet migration and controls its directionality, which is selectively toward the neighboring droplets. Hence, by changing the enzyme activity inside the droplet, we tuned the droplet migration speed. Furthermore, we showed that these cellular-like features can facilitate the reconstitution of a simple and linear protometabolic pathway and increase the final reaction product generation. Our work suggests that simple and stable membraneless droplets can reproduce complex biological phenomena, opening new perspectives as bioinspired materials and synthetic biology tools.

In this study, we delve into the intricacies of elastoviscoplastic (EVP) fluids, particularly focusing on how polymer additives influence their extensional behavior. Our findings reveal that polymer additives significantly alter the extensional properties of the EVP fluids, such as relaxation time and extensional stresses while having negligible impact on the shear rheology. Interestingly, the modified fluids exhibit a transition from yield stress-like behavior to viscoelastic-like behavior under high extensional rates, ultimately leading to destabilization under extreme deformation. This research enhances the fundamental understanding of EVP fluids and highlights potential advancements in applications, especially in precision-demanding fields like 3D printing., (© The Author(s) 2024. Published by Oxford University Press on behalf of National Academy of Sciences.)

Elastic turbulence is the chaotic fluid motion resulting from elastic instabilities due to the addition of polymers in small concentrations at very small Reynolds ( Re ) numbers. Our direct numerical simulations show that elastic turbulence, though a low Re phenomenon, has more in common with classical, Newtonian turbulence than previously thought. In particular, we find power-law spectra for kinetic energy E(k) ~ k -4 and polymeric energy E p (k) ~ k -3/2 , independent of the Deborah (De) number. This is further supported by calculation of scale-by-scale energy budget which shows a balance between the viscous term and the polymeric term in the momentum equation. In real space, as expected, the velocity field is smooth, i.e., the velocity difference across a length scale r, δu ~ r but, crucially, with a non-trivial sub-leading contribution r 3/2 which we extract by using the second difference of velocity. The structure functions of second difference of velocity up to order 6 show clear evidence of intermittency/multifractality. We provide additional evidence in support of this intermittent nature by calculating moments of rate of dissipation of kinetic energy averaged over a ball of radius r, ε r , from which we compute the multifractal spectrum., (© 2024. The Author(s).)

An unstable density stratification between two fluids mixes spontaneously under the effect of gravity, a phenomenon known as Rayleigh-Taylor (RT) turbulence. If the two fluids are immiscible, for example, oil and water, surface tension prevents intermixing at the molecular level. However, turbulence fragments one fluid into the other, generating an emulsion in which the typical droplet size decreases over time as a result of the competition between the rising kinetic energy and the surface energy density. Even though the first phenomenological theory describing this emulsification process was derived many years ago, it has remained elusive to experimental verification, hampering our ability to predict the fate of oil in applications such as deep-water spills. Here, we provide the first experimental and numerical verification of the immiscible RT turbulence theory, unveiling a unique turbulent state that originates at the oil-water interface due to the interaction of multiple capillary waves. We show that a single, non-dimensional, and time-independent parameter controls the range of validity of the theory. Our findings have wide-ranging implications for the understanding of the mixing of immiscible fluids. This includes in particular oil spills, where our work enables the prediction of the oil-water interface dynamics that ultimately determine the rate of oil biodegradation by marine bacteria., Competing Interests: Competing interests statement:The authors declare no competing interest.

We investigate the influence of dispersed solid spherical particles on the largest scales of the turbulent Arnold-Beltrami-Childress (ABC) flow. The ABC flow is an ideal instance of a complex flow: it does not have solid boundaries, but possesses an inhomogeneous and three-dimensional mean shear. By tuning the parameters of the suspension, we show that particles modulate the largest scales of the flow toward an anisotropic, quasi-two-dimensional and more energetic state. In this regime, particles move along quasistraight trajectories and exhibit anomalous transport.

We study the rheological behaviour of bidisperse suspensions in three dimensions under a non-uniform shear flow, made by the superimposition of a linear shear and a sinusoidal disturbance. Our results show that (i) only a streamwise disturbance in the shear-plane alters the suspension dynamics by substantially reducing the relative viscosity, (ii) with the amplitude of the disturbance determining a threshold value for the effect to kick-in and its wavenumber controlling the amount of reduction and which of the two phases is affected. We show that, (iii) the rheological changes are caused by the effective separation of the two phases, with the large or small particles layering in separate regions. We provide a physical explanation of the phase separation process and of the conditions necessary to trigger it. We test the results in the whole flow curve, and we show that the mechanism remains substantially unaltered, with the only difference being the nature of the interactions between particles modified by the phase separation., (© 2023. Springer Nature Limited.)

Flexible filamentous beds interacting with a turbulent flow represent a fundamental setting for many environmental phenomena, e.g., aquatic canopies in marine current. Exploiting direct numerical simulations at high Reynolds number where the canopy stems are modelled individually, we provide evidence on the essential features of the honami/monami collective motion experienced by hairy surfaces over a range of different flexibilities, i.e., Cauchy number. Our findings clearly confirm that the collective motion is essentially driven by fluid flow turbulence, with the canopy having in this respect a fully-passive behavior. Instead, some features pertaining to the structural response turn out to manifest in the motion of the individual canopy elements when focusing, in particular, on the spanwise oscillation and/or on sufficiently small Cauchy numbers., (© 2023. The Author(s).)

We use direct numerical simulations to study homogeneous and isotropic turbulent flows of dilute polymer solutions at high Reynolds and Deborah numbers. We find that for small wave numbers k , the kinetic energy spectrum shows Kolmogorov-like behavior that crosses over at a larger k to a novel, elastic scaling regime, E ( k ) ∼ k -ξ , with ξ ≈ 2.3. We study the contribution of the polymers to the flux of kinetic energy through scales and find that it can be decomposed into two parts: one increase in effective viscous dissipation and a purely elastic contribution that dominates over the nonlinear flux in the range of k over which the elastic scaling is observed. The multiscale balance between the two fluxes determines the crossover wave number that depends nonmonotically on the Deborah number. Consistently, structure functions also show two scaling ranges, with intermittency present in both of them in equal measure.

Viscous dissipation causes significant energy losses in fluid flows; in ducts, laminar flows provide the minimum resistance to the motion, whereas turbulence substantially increases the friction at the wall and the consequent energy requirements for pumping. Great effort is currently being devoted to find new strategies to reduce the energy losses induced by turbulence. Here we propose a simple and novel drag-reduction technique which achieves substantial energy savings in internal flows. Our approach consists in driving the flow with a temporally intermittent pumping, unlike the common practice of a constant pumping. We alternate "pump on" phases where the flow accelerates, and "pump off" phases where the flow decays freely. The flow cyclically enters a quasi-laminar state during the acceleration, and transitions to a more classic turbulent state during the deceleration. Our numerical results demonstrate that important energy savings can be achieved by simply modulating the power injection into the system over time. The physical understanding of this process can help the industry in reducing the waste of energy, creating economical benefits and preserving the environment by reducing harmful emissions., (© 2023. The Author(s).)

We provide a numerical validation of a recently proposed phenomenological theory to characterize the space-time statistical properties of a turbulent puff, both in terms of bulk properties, such as the mean velocity, temperature and size, and scaling laws for velocity and temperature differences both in the viscous and in the inertial range of scales. In particular, apart from the more classical shear-dominated puff turbulence, our main focus is on the recently discovered new regime where turbulent fluctuations are dominated by buoyancy. The theory is based on an adiabaticity hypothesis which assumes that small-scale turbulent fluctuations rapidly relax to the slower large-scale dynamics, leading to a generalization of the classical Kolmogorov and Kolmogorov-Obukhov-Corrsin theories for a turbulent puff hosting a scalar field. We validate our theory by means of massive direct numerical simulations finding excellent agreement. This article is part of the theme issue 'Scaling the turbulence edifice (part 2)'.

The spreading of the virus-containing droplets exhaled during respiratory events, e.g., cough, is an issue of paramount importance for the prevention of many infections such as COVID-19. According to the scientific literature, remarkable differences can be ascribed to several parameters that govern such complex and multiphysical problem. Among these, a particular influence appears associated with the different airflows typical of male and female subjects. Focusing on a typical cough event, we investigate this aspect by means of highly-resolved direct numerical simulations of the turbulent airflow in combination with a comprehensive Lagrangian particle tracking model for the droplet motion and evaporation. We observe and quantify major differences between the case of male and female subjects, both in terms of the droplet final reach and evaporation time. Our results can be associated with the different characteristics in the released airflow and thus confirm the influence of the subject gender (or other physical properties providing different exhalation profiles) on both short-range and long-range airborne transmission., Competing Interests: Conflict of interestThe authors declare that they have no conflict of interest., (© Springer Nature B.V. 2022.)

Shear thickening in stable dense colloidal suspensions is a reversible phenomenon and no hysteresis is observed in the flow curve measurements. However, a reduction in the stability of colloids promotes particle aggregation and introduces a time dependent rheological response. In this work, by using a model colloidal system of hard spherical silica particles (average diameter of 415 nm) with varying particle volume fractions 0.2 ≤ ϕ ≤ 0.56, we study the effect of particle stability on the hysteresis of the shear thickening behavior of these suspensions. The particle stability is manipulated by adding a simple monovalent salt (sodium chloride) in the silica suspension with varying concentrations α ∈ [0,0.5] M. For repulsive and weakly attractive suspensions, the flow behavior is history independent and the shear thickening behavior does not exhibit hysteresis. However, significant hysteresis is observed in rheological measurements for strongly attractive suspensions, with shear history playing a critical role due to the dynamic nature of particle clusters, resulting in time dependent hysteresis behavior. By performing numerical simulations, we find that this hysteresis behavior arises due to the competition among shear, electrostatic repulsive, van der Waals attractive, and frictional contact forces. The critical shear stress ( i.e. , the onset of shear thickening) decreases with increasing salt concentrations, which can be captured by a scaling relationship based on the force balance between particle-particle contact force and electrostatic repulsive force. Our combined experimental and simulation results imply the formation of particle contacts in our sheared suspensions.

Turbulent puffs are ubiquitous in everyday life phenomena. Understanding their dynamics is important in a variety of situations ranging from industrial processes to pure and applied science. In all these fields, a deep knowledge of the statistical structure of temperature and velocity space-time fluctuations is of paramount importance to construct models of chemical reaction (in chemistry) and of condensation of virus-containing droplets (in virology and/or biophysics) and optimal mixing strategies in industrial applications. As a matter of fact, results of turbulence in a puff are confined to bulk properties (i.e., average puff velocity and typical decay or growth time) and date back to the second half of the 20th century. There is, thus, a huge gap to fill to pass from bulk properties to two-point statistical observables. Here, we fill this gap by exploiting theory and numerics in concert to predict and validate the space-time scaling behaviors of both velocity and temperature structure functions including intermittency corrections. Excellent agreement between theory and simulations is found. Our results are expected to have a profound impact on developing evaporation models for virus-containing droplets carried by a turbulent puff, with benefits to the comprehension of the airborne route of virus contagion.

The COVID-19 pandemic is largely caused by airborne transmission, a phenomenon that rapidly gained the attention of the scientific community. Social distancing is of paramount importance to limit the spread of the disease, but to design social distancing rules on a scientific basis the process of dispersal of virus-containing respiratory droplets must be understood. Here, we demonstrate that available knowledge is largely inadequate to make predictions on the reach of infectious droplets emitted during a cough and on their infectious potential. We follow the position and evaporation of thousands of respiratory droplets by massive state-of-the-art numerical simulations of the airflow caused by a typical cough. We find that different initial distributions of droplet size taken from literature and different ambient relative humidity lead to opposite conclusions: (1) most versus none of the viral content settles in the first 1-2 m; (2) viruses are carried entirely on dry nuclei versus on liquid droplets; (3) small droplets travel less than [Formula: see text] versus more than [Formula: see text]. We point to two key issues that need to be addressed urgently in order to provide a scientific foundation to social distancing rules: (I1) a careful characterisation of the initial distribution of droplet sizes; (I2) the infectious potential of viruses carried on dry nuclei versus liquid droplets.

The backreaction of dispersed rigid fibers to turbulence is analyzed by means of a state-of-the-art fully coupled immersed boundary method. The following universal scenario is identified: turbulence at large scales looses a consistent part of its kinetic energy (via a Darcy friction term), which partially reappears at small scales where a new range of energy-containing scales does emerge. Large-scale mixing is thus depleted in favor of a new mixing mechanism arising at the smallest scales. Anchored fibers cause the same backreaction to turbulence as moving fibers of large inertia. Our results thus provide a link between two apparently separated realms: the one of porous media and the one of suspension dynamics.

Multiphase shear flows often show banded structures that affect the global behavior of complex fluids e.g. in microdevices. Here we investigate numerically the banding of emulsions, i.e. the formation of regions of high and low volume fractions, alternated in the vorticity direction and aligned with the flow (shear bands). These bands are associated with a decrease of the effective viscosity of the system. To understand the mechanism of experimentally observed banding, we have performed interface-resolved simulations of the two-fluid system. The experiments were performed starting with a random distribution of droplets, which under the applied shear, evolve in time resulting in a phase separation. To numerically reproduce this process, the banded structures are initialized in a narrow channel confined by two walls moving in opposite directions. We find that the initial banded distribution is stable when droplets are free to merge and unstable when coalescence is prevented. In this case, additionally, the effective viscosity of the system increases, resembling the rheological behavior of suspensions of deformable particles. Droplet coalescence, on the other hand, allows emulsions to reduce the total surface of the system and, hence, the energy dissipation associated with the deformation, which in turn reduces the effective viscosity.

We perform direct numerical simulations of the flow through a model of deformable porous medium. Our model is a two-dimensional hexagonal lattice, with defects, of soft elastic cylindrical pillars, with elastic shear modulus G, immersed in a liquid. We use a two-phase approach: the liquid phase is a viscous fluid and the solid phase is modeled as an incompressible viscoelastic material, whose complete nonlinear structural response is considered. We observe that the Darcy flux (q) is a nonlinear function - steeper than linear - of the pressure-difference (ΔP) across the medium. Furthermore, the flux is larger for a softer medium (smaller G). We construct a theory of this super-linear behavior by modelling the channels between the solid cylinders as elastic channels whose walls are made of material with a linear constitutive relation but can undergo large deformation. Our theory further predicts that the flow permeability is an universal function of ΔP/G, which is confirmed by the present simulations.

We study the dynamics of a flexible fiber freely moving in a three-dimensional fully developed turbulent field and present a phenomenological theory to describe the interaction between the fiber elasticity and the turbulent flow. This theory leads to the identification of two distinct regimes of flapping, which we validate against direct numerical simulations fully resolving the fiber dynamics. The main result of our analysis is the identification of a flapping regime where the fiber, despite its elasticity, is slaved to the turbulent fluctuations. In this regime the fiber can be used to measure two-point statistical observables of turbulence, including scaling exponents of velocity structure functions, the sign of the energy cascade and the energy flux of turbulence, as well as the characteristic times of the eddies within the inertial range of scales. Our results are expected to have a deep impact on the experimental turbulence research as a new way, accurate and efficient, to measure two-point, and more generally multipoint, statistics of turbulence.

Self-activated feathers are used by almost all birds to adapt their wing characteristics to delay stall or to moderate its adverse effects (e.g., during landing or sudden increase in angle of attack due to gusts). Some of the feathers are believed to pop up as a consequence of flow separation and to interact with the flow and produce beneficial modifications of the unsteady vorticity field. The use of self adaptive flaplets in aircrafts, inspired by birds feathers, requires the understanding of the physical mechanisms leading to the mentioned aerodynamic benefits and the determination of the characteristics of optimal flaps including their size, positioning and ideal fabrication material. In this framework, this numerical study is divided in two parts. Firstly, in a simplified scenario, we determine the main characteristics that render a flap mounted on an aerofoil at high angle of attack able to deliver increased lift and improved aerodynamic efficiency, by varying its length, position and its natural frequency. Later on, a detailed direct numerical simulation analysis is used to understand the origin of the aerodynamic benefits introduced by the flaplet movement induced by the interaction with the flow field. The parametric study that has been carried out, reveals that an optimal flap can deliver a mean lift increase of about 20 % on a NACA0020 aerofoil at an incidence of 20 o degrees. The results obtained from the direct numerical simulation of the flow field around the aerofoil equipped with the optimal flap at a chord Reynolds number of 2 × 10 4 shows that the flaplet movement is mainly induced by a cyclic passage of a large recirculation bubble on the aerofoil suction side. In turns, when the flap is pushed downward, the induced plane jet displaces the trailing edge vortices further downstream, away from the wing, moderating the downforce generated by those vortices and regularising the shedding cycle that appears to be much more organised when the optimal flaplet configuration is selected., Competing Interests: Compliance with Ethical StandardsThe authors declare that they have no conflict of interest.

During the flight of birds, it is often possible to notice that some of the primaries and covert feathers on the upper side of the wing pop-up under critical flight conditions, such as the landing approach or when stalking their prey (see Fig. 1) . It is often conjectured that the feathers pop up plays an aerodynamic role by limiting the spread of flow separation . A combined experimental and numerical study was conducted to shed some light on the physical mechanism determining the feathers self actuation and their effective role in controlling the flow field in nominally stalled conditions. In particular, we have considered a NACA0020 aerofoil, equipped with a flexible flap at low chord Reynolds numbers. A parametric study has been conducted on the effects of the length, natural frequency, and position of the flap. A configuration with a single flap hinged on the suction side at 70 % of the chord size c (from the leading edge), with a length of [Formula: see text] matching the shedding frequency of vortices at stall condition has been found to be optimum in delivering maximum aerodynamic efficiency and lift gains. Flow evolution both during a ramp-up motion (incidence angle from [Formula: see text] to [Formula: see text] with a reduced frequency of [Formula: see text], [Formula: see text] being the free stream velocity magnitude), and at a static stalled condition ([Formula: see text]) were analysed with and without the flap. A significant increase of the mean lift after a ramp-up manoeuvre is observed in presence of the flap. Stall dynamics (i.e., lift overshoot and oscillations) are altered and the simulations reveal a periodic re-generation cycle composed of a leading edge vortex that lift the flap during his passage, and an ejection generated by the relaxing of the flap in its equilibrium position. The flap movement in turns avoid the interaction between leading and trailing edge vortices when lift up and push the trailing edge vortex downstream when relaxing back. This cyclic behaviour is clearly shown by the periodic variation of the lift about the average value, and also from the periodic motion of the flap. A comparison with the experiments shows a similar but somewhat higher non-dimensional frequency of the flap oscillation. By assuming that the cycle frequency scales inversely with the boundary layer thickness, one can explain the higher frequencies observed in the experiments which were run at a Reynolds number about one order of magnitude higher than in the simulations. In addition, in experiments the periodic re-generation cycle decays after 3-4 periods ultimately leading to the full stall of the aerofoil. In contrast, the 2D simulations show that the cycle can become self-sustained without any decay when the flap parameters are accurately tuned.