arXiv subjects

Roberto Benzi

Publications and source records attributed to Roberto Benzi.

At least 37 records · Page 2Linked to original sources

arXiv2022

Continuum modeling of Soft Glassy Materials under shear

Soft Glassy Materials (SGM) consist in dense amorphous assemblies of colloidal particles of multiple shapes, elasticity, and interactions, which confer upon them solid-like properties at rest. They are ubiquitously encountered in modern engineering, including additive manufacturing, semi-solid flow cells, dip-coating, adhesive locomotion, where they are subjected to complex mechanical histories. Such processes often include a solid-to-liquid transition induced by large enough shear, which results in complex transient phenomena such as non-monotonic stress responses, i.e., stress overshoot, and spatially heterogeneous flows, e.g., shear-banding or brittle failure. In the present article, we propose a pedagogical introduction to a continuum model based on a spatially-resolved fluidity approach that we recently introduced to rationalize shear-induced yielding in SGMs. Our model, which relies upon non-local effects, quantitatively captures salient features associated with such complex flows, including the rate dependence of the stress overshoot, as well as transient shear-banded flows together with nontrivial scaling laws for fluidization times. This approach offers a versatile framework to account for subtle effects, such as avalanche-like phenomena, or the impact of boundary conditions, which we illustrate by including in our model the elasto-hydrodynamic slippage of soft particles compressed against solid surfaces.

cond-mat.soft↗

arXiv2022

Spatial population genetics with fluid flow

The growth and evolution of microbial populations is often subjected to advection by fluid flows in spatially extended environments, with immediate consequences for questions of spatial population genetics in marine ecology, planktonic diversity and origin of life scenarios. Here, we review recent progress made in understanding this rich problem in the simplified setting of two competing genetic microbial strains subjected to fluid flows. As a pedagogical example we focus on antagonsim, i.e., two killer microorganism strains, each secreting toxins that impede the growth of their competitors (competitive exclusion), in the presence of stationary fluid flows. By solving two coupled reaction-diffusion equations that include advection by simple steady cellular flows composed of characteristic flow motifs in two dimensions (2d), we show how local flow shear and compressibility effects can interact with selective advantage to have a dramatic influence on genetic competition and fixation in spatially distributed populations. We analyze several 1d and 2d flow geometries including sources, sinks, vortices and saddles, and show how simple analytical models of the dynamics of the genetic interface can be used to shed light on the nucleation, coexistence and flow-driven instabilities of genetic drops. By exploiting an analogy with phase separation with nonconserved order parameters, we uncover how these genetic drops harness fluid flows for novel evolutionary strategies, even in the presence of number fluctuations, as confirmed by agent-based simulations as well.

q-bio.PE↗

arXiv2021

Self-consistent stochastic dynamics for finite-size networks of spiking neurons

Despite the huge number of neurons composing a brain network, ongoing activity of local cell assemblies composing cortical columns is intrinsically stochastic. Fluctuations in their instantaneous rate of spike firing $ν(t)$ scale with the size of the assembly and persist in isolated network, i.e., in absence of external source of noise. Although deterministic chaos due to the quenched disorder of the synaptic couplings likely underlies this seemingly stochastic dynamics, an effective theory for the network dynamics of a finite ensemble of spiking neurons is lacking. Here, we fill this gap by extending the so-called population density approach including an activity- and size-dependent stochastic source in the Fokker-Planck equation for the membrane potential density. The finite-size noise embedded in this stochastic partial derivative equation is analytically characterized leading to a self-consistent and non-perturbative description of $ν(t)$ valid for a wide class of spiking neuron networks. Its power spectra of $ν(t)$ are found in excellent agreement with those from detailed simulations both in the linear regime and across a synchronization phase transition, when a size-dependent smearing of the critical dynamics emerges.

q-bio.NC↗

arXiv2021

Build up of yield stress fluids via chaotic emulsification

Stabilized dense emulsions display a rich phenomenology connecting microstructure and rheology. In this work we study how an emulsion with a finite yield stress can be built via large-scale stirring. By gradually increasing the volume fraction of the dispersed minority phase, under the constant action of a stirring force, we are able to achieve volume fractions close to $80\%$. Despite the fact that our system is highly concentrated and not yet turbulent we observe a droplet size distribution consistent with the $-10/3$ scaling, often associated to inertial range droplets breakup. We report that the polydispersity of droplet sizes correlates with the dynamics of the emulsion formation process. Additionally we quantify the visco-elastic properties of the dense emulsion finally obtained and we demonstrate the presence of a finite yield stress. The approach reported can pave the way to a quantitative understanding of the complex interplay between the dynamics of mesoscale constituents and the large scale flow properties yield-stress fluids.

cond-mat.soft↗

arXiv2021

The collective effect of finite-sized inhomogeneities on the spatial spread of populations in two dimensions

The dynamics of a population expanding into unoccupied habitat has been primarily studied for situations in which growth and dispersal parameters are uniform in space or vary in one dimension. Here we study the influence of finite-sized individual inhomogeneities and their collective effect on front speed if randomly placed in a two-dimensional habitat. We use an individual-based model to investigate the front dynamics for a region in which dispersal or growth of individuals is reduced to zero (obstacles) or increased above the background (hotspots), respectively. In a regime where front dynamics is determined by a local front speed only, a principle of least time can be employed to predict front speed and shape. The resulting analytical solutions motivate an event-based algorithm illustrating the effects of several obstacles or hotspots. We finally apply the principle of least time to large heterogeneous environments by solving the Eikonal equation numerically. Obstacles lead to a slow-down that is dominated by the number density and width of obstacles, but not by their precise shape. Hotspots result in a speedup, which we characterise as function of hotspot strength and density. Our findings emphasise the importance of taking the dimensionality of the environment into account.

q-bio.PE↗

arXiv2021

Stress Overshoots in Simple Yield Stress Fluids

Soft glassy materials such as mayonnaise, wet clays, or dense microgels display under external shear a solid-to-liquid transition. Such a shear-induced transition is often associated with a non-monotonic stress response, in the form of a stress maximum referred to as "stress overshoot". This ubiquitous phenomenon is characterized by the coordinates of the maximum in terms of stress $σ_\text{M}$ and strain $γ_\text{M}$ that both increase as weak power laws of the applied shear rate. Here we rationalize such power-law scalings using a continuum model that predicts two different regimes in the limit of low and high applied shear rates. The corresponding exponents are directly linked to the steady-state rheology and are both associated with the nucleation and growth dynamics of a fluidized region. Our work offers a consistent framework for predicting the transient response of soft glassy materials upon start-up of shear from the local flow behavior to the global rheological observables.

cond-mat.soft↗

arXiv2021

Continuum modelling of shear start-up in soft glassy materials

Yield stress fluids (YSFs) display a dual nature highlighted by the existence of a yield stress such that YSFs are solid below the yield stress, whereas they flow like liquids above it. Under an applied shear rate $\dotγ$, the solid-to-liquid transition is associated with a complex spatiotemporal scenario. Still, the general phenomenology reported in the literature boils down to a simple sequence that can be divided into a short-time response characterized by the so-called "stress overshoot", followed by stress relaxation towards a steady state. Such relaxation can be either long-lasting, which usually involves the growth of a shear band that can be only transient or that may persist at steady-state, or abrupt, in which case the solid-to-liquid transition resembles the failure of a brittle material, involving avalanches. Here we use a continuum model based on a spatially-resolved fluidity approach to rationalize the complete scenario associated with the shear-induced yielding of YSFs. Our model provides a scaling for the coordinates of the stress maximum as a function of $\dotγ$, which shows excellent agreement with experimental and numerical data extracted from the literature. Moreover, our approach shows that such a scaling is intimately linked to the growth dynamics of a fluidized boundary layer in the vicinity of the moving boundary. Yet, such scaling is independent of the fate of that layer, and of the long-term behavior of the YSF. Finally, when including the presence of "long-range" correlations, we show that our model displays a ductile to brittle transition, i.e., the stress overshoot reduces into a sharp stress drop associated with avalanches, which impacts the scaling of the stress maximum with $\dotγ$. Our work offers a unified picture of shear-induced yielding in YSFs, whose complex spatiotemporal dynamics are deeply connected to non-local effects.

cond-mat.soft↗

arXiv2021

Self Similar Properties of Avalanche Statistics in a Simple Turbulent Model

In this paper, we consider a simplified model of turbulence for large Reynolds numbers driven by a constant power energy input on large scales. In the statistical stationary regime, the behaviour of the kinetic energy is characterised by two well defined phases: a laminar phase where the kinetic energy grows linearly for a (random) time $t_w$ followed by abrupt avalanche-like energy drops of sizes $S$ due to strong intermittent fluctuations of energy dissipation. We study the probability distribution $P[t_w]$ and $P[S]$ which both exhibit a quite well defined scaling behaviour. Although $t_w$ and $S$ are not statistically correlated, we suggest and numerically checked that their scaling properties are related based on a simple, but non trivial, scaling argument. We propose that the same approach can be used for other systems showing avalanche-like behaviour such as amorphous solids and seismic events.

cond-mat.soft↗

arXiv2021

Effective modelling of the Rayleigh-Bénard convection of concentrated emulsions with finite-size droplets

We present mesoscale numerical simulations of Rayleigh-Bénard convection in a two-dimensional concentrated emulsion, confined between two parallel walls, heated from below and cooled from above, under the effect of buoyancy forces. The systems under study comprise finite-size droplets, whose concentration $Φ_0$ is varied, ranging from the dilute limit up to the point where the emulsion starts to be packed and exhibits non-Newtonian rheology. We focus on the characterisation of the convective heat transfer properties close to the transition from conductive to convective states. The convective flow is confined and heterogeneous, which causes the emulsion to exhibit concentration heterogeneities in space $ϕ_0(y)$, depending on the location in the wall-to-wall direction ($y$). With the aim of assessing quantitatively the heat transfer efficiency of such heterogeneous systems, we resort to a side-by-side comparison between the concentrated emulsion system and a single-phase (SP) system, whose local viscosity $η^{\mbox{SP}}(y)$ is suitably constructed from the shear rheology of the emulsion. Such comparison highlights that a suitable degree $Λ$ of coarse-graining needs to be introduced in the local viscosity $η_Λ^{\mbox{SP}}(y)$, in order for the single-phase system to attain the same heat transfer efficiency of the emulsion. Specifically, it is shown that a quantitative matching between the two systems is possible whenever the coarse-graining is performed over a scale of the order of the droplet size.

physics.flu-dyn↗

arXiv2021

Convective heat transfer of a model emulsion at the droplet scale

We numerically study the Rayleigh-Bénard (RB) convection in two-dimensional model emulsions confined between two parallel walls at fixed temperatures. The systems under study are heterogeneous, with finite-size droplets dispersed in a continuous phase. The droplet concentration is chosen to explore the convective heat transfer of both Newtonian (low droplet concentration) and non-Newtonian (high droplet concentration) emulsions, the latter exhibiting shear-thinning rheology, with a noticeable increase of viscosity at low shear rates. It is well known that the transition to convection of a homogeneous Newtonian system is accompanied by the onset of steady flow and time-independent heat flux; in marked contrast, the heterogeneity of emulsions brings in an additional and previously unexplored phenomenology. As a matter of fact, when the droplet concentration increases, we observe that the heat transfer process is mediated by a non-steady flow, with neat heat-flux fluctuations, obeying a non-Gaussian statistics. The observed findings are ascribed to the emergence of space correlations among distant droplets, which we highlight via direct measurements of the droplets displacement and the characterisation of the associated correlation functions.

physics.flu-dyn↗

arXiv2021

Rayleigh-Bénard convection of a model emulsion: anomalous heat-flux fluctuations and finite-size droplets effects

We present mesoscale numerical simulations of Rayleigh-Bénard (RB) convection in a two-dimensional model emulsion. The systems under study are constituted of finite-size droplets, whose concentration Phi_0 is systematically varied from small (Newtonian emulsions) to large values (non-Newtonian emulsions). We focus on the characterisation of the heat transfer properties close to the transition from conductive to convective states, where it is known that a homogeneous Newtonian system exhibits a steady flow and a time-independent heat flux. In marked contrast, emulsions exhibit a non-steady dynamics with fluctuations in the heat flux. In this paper, we aim at the characterisation of such non-steady dynamics via detailed studies on the time-averaged heat flux and its fluctuations. To understand the time-averaged heat flux, we propose a side-by-side comparison between the emulsion system and a single-phase (SP) system, whose viscosity is constructed from the shear rheology of the emulsion. We show that such local closure works well only when a suitable degree of coarse-graining (at the droplet scale) is introduced in the local viscosity. To delve deeper into the fluctuations in the heat flux, we propose a side-by-side comparison between a Newtonian emulsion and a non-Newtonian emulsion, at fixed time-averaged heat flux. This comparison elucidates that finite-size droplets and the non-Newtonian rheology cooperate to trigger enhanced heat-flux fluctuations at the droplet scales. These enhanced fluctuations are rooted in the emergence of space correlations among distant droplets, which we highlight via direct measurements of the droplets displacement and the characterisation of the associated correlation function. The observed findings offer insights on heat transfer properties for confined systems possessing finite-size constituents.

physics.flu-dyn↗

arXiv2020

A free boundary problem for binary fluids

A free boundary problem for the dynamics of a glasslike binary fluid naturally leads to a singular perturbation problem for a strongly degenerate parabolic partial differential equation in 1D. We present a conjecture for an asymptotic formula for the velocity of the free boundary and prove a weak version of the conjecture. The results are based on the analysis of a family of local travelling wave solutions.

math.AP↗

arXiv2019

Discrete Eulerian model for population genetics and dynamics under flow

Marine species reproduce and compete while being advected by turbulent flows. It is largely unknown, both theoretically and experimentally, how population dynamics and genetics are changed by the presence of fluid flows. Discrete agent-based simulations in continuous space allow for accurate treatment of advection and number fluctuations, but can be computationally expensive for even modest organism densities. In this report, we propose an algorithm to overcome some of these challenges. We first provide a thorough validation of the algorithm in one and two dimensions without flow. Next, we focus on the case of weakly compressible flows in two dimensions. This models organisms such as phytoplankton living at a specific depth in the three-dimensional, incompressible ocean experiencing upwelling and/or downwelling events. We show that organisms born at sources in a two-dimensional time-independent flow experience an increase in fixation probability.

q-bio.PE↗

arXiv2019

Deep learning velocity signals allows to quantify turbulence intensity

Turbulence, the ubiquitous and chaotic state of fluid motions, is characterized by strong and statistically non-trivial fluctuations of the velocity field, over a wide range of length- and time-scales, and it can be quantitatively described only in terms of statistical averages. Strong non-stationarities hinder the possibility to achieve statistical convergence, making it impossible to define the turbulence intensity and, in particular, its basic dimensionless estimator, the Reynolds number. Here we show that by employing Deep Neural Networks (DNN) we can accurately estimate the Reynolds number within $15\%$ accuracy, from a statistical sample as small as two large-scale eddy-turnover times. In contrast, physics-based statistical estimators are limited by the rate of convergence of the central limit theorem, and provide, for the same statistical sample, an error at least $100$ times larger. Our findings open up new perspectives in the possibility to quantitatively define and, therefore, study highly non-stationary turbulent flows as ordinarily found in nature as well as in industrial processes.

physics.flu-dyn↗

arXiv2019

Unified theoretical and experimental view on transient shear banding

Dense emulsions, colloidal gels, microgels, and foams all display a solid-like behavior at rest characterized by a yield stress, above which the material flows like a liquid. Such a fluidization transition often consists of long-lasting transient flows that involve shear-banded velocity profiles. The characteristic time for full fluidization, $τ_\text{f}$, has been reported to decay as a power-law of the shear rate $\dot γ$ and of the shear stress $σ$ with respective exponents $α$ and $β$. Strikingly, the ratio of these exponents was empirically observed to coincide with the exponent of the Herschel-Bulkley law that describes the steady-state flow behavior of these complex fluids. Here we introduce a continuum model, based on the minimization of a "free energy", that captures quantitatively all the salient features associated with such \textit{transient} shear-banding. More generally, our results provide a unified theoretical framework for describing the yielding transition and the steady-state flow properties of yield stress fluids.

cond-mat.soft↗

arXiv2019

Interevent time distributions of avalanche dynamics

Physical systems characterized by stick-slip dynamics often display avalanches. Regardless of the diversity of their microscopic structure, these systems are governed by a power-law distribution of avalanche size and duration. Here we focus on the interevent times between avalanches and show that, unlike their distributions of size and duration, the interevent time distributions are able to distinguish different mechanical states of the system, characterized by different volume fractions or confining pressures. We use experiments on granular systems and numerical simulations of emulsions to show that systems having the same probability distribution for avalanche size and duration can have different interevent time distributions. Remarkably, for large packing ratios, these interevent time distributions look similar to those for earthquakes and are indirect evidence of large space-time correlations in the system. Our results therefore indicate that interevent time statistics are more informative to characterize the dynamics of avalanches.

cond-mat.soft↗

arXiv2019

Avalanche statistics during coarsening dynamics

We study the coarsening dynamics of a two dimensional system via lattice Boltzmann numerical simulations. The system under consideration is a biphasic system consisting of domains of a dispersed phase closely packed together in a continuous phase and separated by thin interfaces. Such system is elastic and typically out of equilibrium. The equilibrium state is attained via the coarsening dynamics, wherein the dispersed phase slowly diffuses through the interfaces, causing domains to change in size and eventually rearrange abruptly. The effect of rearrangements is propagated throughout the system via the intrinsic elastic interactions and may cause rearrangements elsewhere, resulting in intermittent bursts of activity and avalanche behaviour. Here we aim at quantitatively characterizing the corresponding avalanche statistics (i.e. size, duration, inter-avalanche time). Despite the coarsening dynamics is triggered by an internal driving mechanism, we find quantitative indications that such avalanche statistics displays scaling-laws very similar to those observed in the response of disordered materials to external loads.

cond-mat.soft↗

arXiv2019

Fixation Probabilities in Weakly Compressible Fluid Flows

Competition between biological species in marine environments is affected by the motion of the surrounding fluid. An effective 2D compressibility can arise, for example, from the convergence and divergence of water masses at the depth at which passively traveling photosynthetic organisms are restricted to live. In this report, we seek to quantitatively study genetics under flow. To this end, we couple an off-lattice agent-based simulation of two populations in 1D to a weakly compressible velocity field--first a sine wave and then a shell model of turbulence. We find for both cases that even in a regime where the overall population structure is approximately unaltered, the flow can significantly diminish the effect of a selective advantage on fixation probabilities. We understand this effect in terms of the enhanced survival of organisms born at sources in the flow and the influence of Fisher genetic waves.

q-bio.PE↗