Immiscible Rayleigh-Taylor turbulence: Implications for bacterial degradation in oil spills.

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.

Chemotactic Interactions Drive Migration of Membraneless Active Droplets.

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.

Anisotropic Mean Flow Enhancement and Anomalous Transport of Finite-Size Spherical Particles in Turbulent Flows.

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.

Puff turbulence in the limit of strong buoyancy.

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)'.

Unraveling the Secrets of Turbulence in a Fluid Puff.

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 breakdown of Darcy's law in a soft porous material.

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.

Numerical simulations of vorticity banding of emulsions in shear flows.

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.

Flexible Fiber Reveals the Two-Point Statistical Properties of Turbulence.

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.

Dense bidisperse suspensions under non-homogeneous shear.

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.