arXiv subjects

Dario Vincenzi

Publications and source records attributed to Dario Vincenzi.

At least 37 records · Page 2Linked to original sources

arXiv2020

Polymer scission in turbulent flows

Polymers in a turbulent flow are subject to intense strain, which can cause their scission and thereby limit the experimental study and application of phenomena such as turbulent drag reduction and elastic turbulence. In this paper, we study polymer scission in homogeneous isotropic turbulence, through a combination of stochastic modelling, based on a Gaussian time-decorrelated random flow, and direct numerical simulations (DNSs) with both one-way (passive) and two-way (active) coupling of the polymers and the flow. For the first scission of passive polymers, the stochastic model yields analytical predictions which are found to be in good agreement with results from the DNSs, for the temporal evolution of the fraction of unbroken polymers and the statistics of the survival of polymers. The impact of scission on the dynamics of a turbulent polymer solution is investigated through DNSs with two-way coupling (active polymers). Our results indicate that the reduction of kinetic energy dissipation due to feedback from stretched polymers is an inherently transient effect, which is lost as the polymers breakup. Thus, the overall dissipation-reduction is maximised by an intermediate polymer relaxation time, for which polymers stretch significantly but without breaking too quickly. We also study the dynamics of the polymer fragments which form after scission; these daughter polymers can themselves undergo subsequent, repeated, breakups to produce a hierarchical population of polymers with a range of relaxation times and scission rates.

physics.flu-dyn↗

arXiv2019

Elasto-inertial Chains in a Two-dimensional Turbulent Flow

The interplay of inertia and elasticity is shown to have a significant impact on the transport of filamentary objects, modelled by bead-spring chains, in a two-dimensional turbulent flow. We show how elastic interactions amongst inertial beads result in a non-trivial sampling of the flow, ranging from entrapment within vortices to preferential sampling of straining regions. This behavior is quantified as a function of inertia and elasticity and is shown to be very different from free, non-interacting heavy particles, as well as inertialess chains [Picardo et al., Phys. Rev. Lett. 121, 244501 (2018)]. In addition, by considering two limiting cases, of a heavy-headed and a uniformly-inertial chain, we illustrate the critical role played by the mass distribution of such extended objects in their turbulent transport.

physics.flu-dyn↗

arXiv2019

Effect of polymer-stress diffusion in the numerical simulation of elastic turbulence

Elastic turbulence is a chaotic regime that emerges in polymer solutions at low Reynolds numbers. A common way to ensure stability in numerical simulations of polymer solutions is to add artificially large polymer-stress diffusion. In order to assess the accuracy of this approach in the elastic-turbulence regime, we compare numerical simulations of the two-dimensional Oldroyd-B and FENE-P models sustained by a cellular force with and without artificial diffusion. We find that artificial diffusion can have a dramatic effect even on the large-scale properties of the flow and we show some of the spurious phenomena that may arise when artificial diffusion is used.

physics.flu-dyn↗

arXiv2019

Kazantsev dynamo in turbulent compressible flows

We consider the kinematic fluctuation dynamo problem in a flow that is random, white-in-time, with both solenoidal and potential components. This model is a generalization of the well-studied Kazantsev model. If both the solenoidal and potential parts have the same scaling exponent, then, as the compressibility of the flow increases, the growth rate decreases but remains positive. If the scaling exponents for the solenoidal and potential parts differ, in particular if they correspond to typical Kolmogorov and Burgers values, we again find that an increase in compressibility slows down the growth rate but does not turn it off. The slow down is, however, weaker and the critical magnetic Reynolds number is lower than when both the solenoidal and potential components display the Kolmogorov scaling. Intriguingly, we find that there exist cases, when the potential part is smoother than the solenoidal part, for which an increase in compressibility increases the growth rate. We also find that the critical value of the scaling exponent above which a dynamo is seen is unity irrespective of the compressibility. Finally, we realize that the dimension $d = 3$ is special, since for all other values of $d$ the critical exponent is higher and depends on the compressibility.

physics.flu-dyn↗

arXiv2019

Preferential Sampling of Elastic Chains in Turbulent Flows

A string of tracers, interacting elastically, in a turbulent flow is shown to have a dramatically different behaviour when compared to the non-interacting case. In particular, such an elastic chain shows strong preferential sampling of the turbulent flow unlike the usual tracer limit: an elastic chain is trapped in the vortical regions and not the straining ones. The degree of preferential sampling and its dependence on the elasticity of the chain is quantified via the Okubo-Weiss parameter. The effect of modifying the deformability of the chain, via the number of links that form it, is also examined.

physics.flu-dyn↗

arXiv2018

Droplets in isotropic turbulence: deformation and breakup statistics

The statistics of the deformation and breakup of neutrally buoyant sub-Kolmogorov ellipsoidal drops is investigated via Lagrangian simulations of homogeneous isotropic turbulence. The mean lifetime of a drop is also studied as a function of the initial drop size and the capillary number. A vector model of drop previously introduced by Olbricht, Rallison and Leal [J. Non-Newtonian Fluid Mech. $\mathbf{10}$, 291 (1982)] is used to predict the behaviour of the above quantities analytically.

physics.flu-dyn↗

arXiv2017

Emergence of chaos in a viscous solution of rods

It is shown that the addition of small amounts of microscopic rods in a viscous fluid at low Reynolds number causes a significant increase of the flow resistance. Numerical simulations of the dynamics of the solution reveal that this phenomenon is associated to a transition from laminar to chaotic flow. Polymer stresses give rise to flow instabilities which, in turn, perturb the alignment of the rods. This coupled dynamics results in the activation of a wide range of scales, which enhances the mixing efficiency of viscous flows.

physics.flu-dyn↗

arXiv2017

Lyapunov dimension of elastic turbulence

Low-Reynolds-number polymer solutions exhibit a chaotic behaviour known as 'elastic turbulence' when the Weissenberg number exceeds a critical value. The two-dimensional Oldroyd-B model is the simplest constitutive model that reproduces this phenomenon. To make a practical estimate of the resolution scale of the dynamics requires an assumption that an attractor of the Oldroyd-B model exists : numerical simulations show that the quantities on which this assumption is based are bounded. We estimate the Lyapunov dimension of this assumed attractor as a function of the Weissenberg number by combining a mathematical analysis of the model with direct numerical simulations.

physics.flu-dyn↗

arXiv2016

Bead-rod-spring models in random flows

Bead-rod-spring models are the foundation of the kinetic theory of polymer solutions. We derive the diffusion equation for the probability density function of the configuration of a general bead-rod-spring model in short-correlated Gaussian random flows. Under isotropic conditions, we solve this equation analytically for the elastic rhombus model introduced by Curtiss, Bird, and Hassager [Adv. Chem. Phys. 35 (1976), pp. 31-117].

cond-mat.stat-mech↗

arXiv2016

Tumbling of a Brownian particle in an extensional flow

The phenomenon of tumbling of microscopic objects is commonly associated with shear flows. We address the question of whether tumbling can also occur in stretching-dominated flows. To answer this, we study the dynamics of a semi-flexible trumbbell in a planar extensional velocity field. We show that the trumbbell undergoes a random tumbling-through-folding motion. The probability distribution of long tumbling times is exponential with a time scale exponentially increasing with the Weissenberg number.

physics.flu-dyn↗

arXiv2016

Elastic turbulence in a shell model of polymer solution

We show that, at low inertia and large elasticity, shell models of viscoelastic fluids develop a chaotic behaviour with properties similar to those of elastic turbulence. The low dimensionality of shell models allows us to explore a wide range both in polymer concentration and in Weissenberg number. Our results demonstrate that the physical mechanisms at the origin of elastic turbulence do not rely on the boundary conditions or on the geometry of the mean flow.

physics.flu-dyn↗

arXiv2015

On the Peterlin approximation for turbulent flows of polymer solutions

We study the impact of the Peterlin approximation on the statistics of the end-to-end separation of poly- mers in a turbulent flow. The FENE and FENE-P models are numerically integrated along a large number of Lagrangian trajectories resulting from a direct numerical simulation of three-dimensional homogeneous isotropic turbulence. Although the FENE-P model yields results in qualitative agreement with those of the FENE model, quantitative differences emerge. The steady-state probability of large extensions is overesti- mated by the FENE-P model. The alignment of polymers with the eigenvectors of the rate-of-strain tensor and with the direction of vorticity is weaker when the Peterlin approximation is used. At large Weissenberg numbers, both the correlation times of the extension and of the orientation of polymers are underestimated by the FENE-P model.

physics.flu-dyn↗

arXiv2014

Weak-strong clustering transition in renewing compressible flows

We investigate the statistical properties of Lagrangian tracers transported by a time-correlated compressible renewing flow. We show that the preferential sampling of the phase space performed by tracers yields significant differences between the Lagrangian statistics and its Eulerian counterpart. In particular, the effective compressibility experienced by tracers has a non-trivial dependence on the time correlation of the flow. We examine the consequence of this phenomenon on the clustering of tracers, focusing on the transition from the weak- to the strong-clustering regime. We find that the critical compressibility at which the transition occurs is minimum when the time correlation of the flow is of the order of the typical eddy turnover time. Further, we demonstrate that the clustering properties in time-correlated compressible flows are non-universal and are strongly influenced by the spatio-temporal structure of the velocity field.

physics.flu-dyn↗

arXiv2014

Regimes of nonlinear depletion and regularity in the 3D Navier-Stokes equations

The periodic $3D$ Navier-Stokes equations are analyzed in terms of dimensionless, scaled, $L^{2m}$-norms of vorticity $D_{m}$ ($1 \leq m < \infty$). The first in this hierarchy, $D_{1}$, is the global enstrophy. Three regimes naturally occur in the $D_{1}-D_{m}$ plane. Solutions in the first regime, which lie between two concave curves, are shown to be regular, owing to strong nonlinear depletion. Moreover, numerical experiments have suggested, so far, that all dynamics lie in this heavily depleted regime \cite{DGGKPV13}\,; new numerical evidence for this is presented. Estimates for the dimension of a global attractor and a corresponding inertial range are given for this regime. However, two more regimes can theoretically exist. In the second, which lies between the upper concave curve and a line, the depletion is insufficient to regularize solutions, so no more than Leray's weak solutions exist. In the third, which lies above this line, solutions are regular, but correspond to extreme initial conditions. The paper ends with a discussion on the possibility of transition between these regimes.

nlin.CD↗

arXiv2014

Bending dynamics of semi-flexible macromolecules in isotropic turbulence

We study the Lagrangian dynamics of semi-flexible macromolecules in laminar as well as in homogeneous and isotropic turbulent flows by means of analytically solvable stochastic models and direct numerical simulations. The statistics of the bending angle is qualitatively different in laminar and turbulent flows and exhibits a strong dependence on the topology of the velocity field. In particular, in two-dimensional turbulence, particles are either found in a fully extended or in a fully folded configuration; in three dimensions, the predominant configuration is the fully extended one.

physics.flu-dyn↗

arXiv2014

Elliptical Tracers in Two-dimensional, Homogeneous, Isotropic Fluid Turbulence: the Statistics of Alignment, Rotation, and Nematic Order

We study the statistical properties of orientation and rotation dynamics of elliptical tracer particles in two-dimensional, homogeneous and isotropic turbulence by direct numerical simulations. We consider both the cases in which the turbulent flow is generated by forcing at large and intermediate length scales. We show that the two cases are qualitatively different. For large-scale forcing, the spatial distribution of particle orientations forms large-scale structures, which are absent for intermediate-scale forcing. The alignment with the local directions of the flow is much weaker in the latter case than in the former. For intermediate-scale forcing, the statistics of rotation rates depends weakly on the Reynolds number and on the aspect ratio of particles. In contrast with what is observed in three-dimensional turbulence, in two dimensions the mean-square rotation rate decreases as the aspect ratio increases.

physics.flu-dyn↗

arXiv2012

Orientation of non-spherical particles in an axisymmetric random flow

The dynamics of non-spherical rigid particles immersed in an axisymmetric random flow is studied analytically. The motion of the particles is described by Jeffery's equation; the random flow is Gaussian and has short correlation time.The stationary probability density function of orientations is calculated exactly. Four regimes are identified depending on the statistical anisotropy of the flow and on the geometrical shape of the particle. If λ is the axis of symmetry of the flow, the four regimes are: rotation about λ, tumbling motion between λ and -λ, combination of rotation and tumbling, and preferential alignment with a direction oblique to λ.

nlin.CD↗

arXiv2010

Deformation of a flexible polymer in a random flow with long correlation time

The effects induced by long temporal correlations of the velocity gradients on the dynamics of a flexible polymer are investigated by means of theoretical and numerical analysis of the Hookean and FENE dumbbell models in a random renewing flow. For Hookean dumbbells, we show that long temporal correlations strongly suppress the Weissenberg-number dependence of the power-law tail characterising the probability density function (PDF) of the elongation. For the FENE model, the PDF becomes bimodal, and the coil-stretch transition occurs through the simultaneous drop and rise of the two peaks associated with the coiled and stretched configurations, respectively.

nlin.CD↗