Reaction Spreading on Graphs

We study reaction-diffusion processes on graphs through an extension of the standard reaction-diffusion equation starting from first principles. We focus on reaction spreading, i.e. on the time evolution of the reaction product, M(t). At variance with pure diffusive processes, characterized by the spectral dimension, d_s, for reaction spreading the important quantity is found to be the connectivity dimension, d_l. Numerical data, in agreement with analytical estimates based on the features of n independent random walkers on the graph, show that M(t) ~ t^{d_l}. In the case of Erdos-Renyi random graphs, the reaction-product is characterized by an exponential growth M(t) ~ e^{a t} with a proportional to ln, where is the average degree of the graph.Comment: 4 pages, 3 figure

The FDF or LES/PDF method for turbulent two-phase flows

In this paper, a new formalism for the filtered density function (FDF) approach is developed for the treatment of turbulent polydispersed two-phase flows in LES simulations. Contrary to the FDF used for turbulent reactive single-phase flows, the present formalislm is based on Lagrangian quantities and, in particular, on the Lagrangian filtered mass density function (LFMDF) as the central concept. This framework allows modeling and simulation of particle flows for LES to be set in a rigorous context and various links with other approaches to be made. In particular, the relation between LES for particle simulations of single-phase flows and Smoothed Particle Hydrodynamics (SPH) is put forward. Then, the discussion and derivation of possible subgrid stochastic models used for Lagrangian models in two-phase flows can set in a clear probabilistic equivalence with the corresponding LFMDF.Comment: 11 pages, proceedings of the 13 europena turbulence conference, submitted to JPC

Mesoscopic lattice Boltzmann modeling of soft-glassy systems: theory and simulations

A multi-component lattice Boltzmann model recently introduced (R. Benzi et al. Phys. Rev. Lett 102, 026002 (2009)) to describe some dynamical behaviors of soft-flowing materials is theoretically analyzed. Equilibrium and transport properties are derived within the framework of a continuum free-energy formulation, and checked against numerical simulations. Due to the competition between short-range inter-species repulsion and mid-range intra-species attraction, the model is shown to give rise to a very rich configurational dynamics of the density field, exhibiting numerous features of soft-flowing materials, such as long-time relaxation due to caging effects, enhanced viscosity and structural arrest, ageing under moderate shear and shear-thinning flow above a critical shear threshold.Comment: 25 pages, 17 figures, submitted to Journal of chemical physics

Capillary filling using Lattice Boltzmann Equations: the case of multi-phase flows

We present a systematic study of capillary filling for multi-phase flows by using mesoscopic lattice Boltzmann models describing a diffusive interface moving at a given contact angle with respect to the walls. We compare the numerical results at changing the density ratio between liquid and gas phases and the ratio between the typical size of the capillary and the interface width. It is shown that numerical results yield quantitative agreement with the Washburn law when both ratios are large, i.e. as the hydrodynamic limit of a infinitely thin interface is approached. We also show that in the initial stage of the filling process, transient behaviour induced by inertial effects and ``vena contracta'' mechanisms, may induce significant departure from the Washburn law. Both effects are under control in our lattice Boltzmann equation and in good agreement with the phenomenology of capillary filling

LES and RANS calculations of particle dispersion behind a wall-mounted cubic obstacle

In the present paper, we evaluate the performances of three stochastic models for particle dispersion in the case of a three-dimensional turbulent flow. We consider the flow in a channel with a cubic wall-mounted obstacle, and perform large-eddy simulations (LESs) including passive particles injected behind the obstacle, for cases of low and strong inertial effects. We also perform Reynolds-averaged simulations of the same case, using standard turbulence models, and employ the two discrete stochastic models for particle dispersion implemented in the open-source code OpenFOAM and the continuous Lagrangian stochastic model proposed by Minier et al. (2004). The Lagrangian model is consistent with a Probability Density Function (PDF) model of the exact particle equations, and is based on the modelling of the fluid velocity seen by particles. This approach allows a consistent formulation which eliminates the spurious drifts flawing discrete models and to have the drag force in a closed form. The LES results are used as reference data both for the fluid RANS simulations and particle simulations with dispersion models. The present test case allows to evaluate the performance of dispersion models in highly non-homogeneous flow, and it used in this context for the first time. The continuous stochastic model generally shows a better agreement with the LES than the discrete stochastic models, in particular in the case of particles with higher inertia

Lagrangian stochastic modelling of acceleration in turbulent wall-bounded flows

The Lagrangian approach is natural for studying issues of turbulent dispersion and mixing. We propose in this work a general Lagrangian stochastic model for inhomogeneous turbulent flows, using velocity and acceleration as dynamical variables. The model takes the form of a diffusion process, and the coefficients of the model are determined via Kolmogorov theory and the requirement of consistency with velocity-based models. We show that this model generalises both the acceleration-based models for homogeneous flows as well as velocity-based generalised Langevin models. The resulting closed model is applied to a channel flow at high Reynolds number, and compared to experiments as well as direct numerical simulations. A hybrid approach coupling the stochastic model with a Reynolds-averaged Navier-Stokes model is used to obtain a self-consistent model, as is commonly used in probability density function methods. Results highlight that most of the acceleration features are well represented, notably the anisotropy between streamwise and wall-normal components and the strong intermittency. These results are valuable, since the model improves on velocity-based models for boundary layers while remaining relatively simple. Our model also sheds some light on the statistical mechanisms at play in the near-wall region

Lattice Boltzmann models for non-ideal fluids with arrested phase-separation

The effects of mid-range repulsion in Lattice Boltzmann models on the coalescence/breakup behaviour of single-component, non-ideal fluids are investigated. It is found that mid-range repulsive interactions allow the formation of spray-like, multi-droplet configurations, with droplet size directly related to the strength of the repulsive interaction. The simulations show that just a tiny ten-percent of mid-range repulsive pseudo-energy can boost the surface/volume ratio of the phase- separated fluid by nearly two orders of magnitude. Drawing upon a formal analogy with magnetic Ising systems, a pseudo-potential energy is defined, which is found to behave like a quasi-conserved quantity for most of the time-evolution. This offers a useful quantitative indicator of the stability of the various configurations, thus helping the task of their interpretation and classification. The present approach appears to be a promising tool for the computational modelling of complex flow phenomena, such as atomization, spray formation and micro-emulsions, break-up phenomena and possibly glassy-like systems as well.Comment: 12 pages, 9 figure

Statistical properties of an ideal subgrid-scale correction for Lagrangian particle tracking in turbulent channel flow

One issue associated with the use of Large-Eddy Simulation (LES) to investigate the dispersion of small inertial particles in turbulent flows is the accuracy with which particle statistics and concentration can be reproduced. The motion of particles in LES fields may differ significantly from that observed in experiments or direct numerical simulation (DNS) because the force acting on the particles is not accurately estimated, due to the availability of the only filtered fluid velocity, and because errors accumulate in time leading to a progressive divergence of the trajectories. This may lead to different degrees of inaccuracy in the prediction of statistics and concentration. We identify herein an ideal subgrid correction of the a-priori LES fluid velocity seen by the particles in turbulent channel flow. This correction is computed by imposing that the trajectories of individual particles moving in filtered DNS fields exactly coincide with the particle trajectories in a DNS. In this way the errors introduced by filtering into the particle motion equations can be singled out and analyzed separately from those due to the progressive divergence of the trajectories. The subgrid correction term, and therefore the filtering error, is characterized in the present paper in terms of statistical moments. The effects of the particle inertia and of the filter type and width on the properties of the correction term are investigated.Comment: 15 pages,24 figures. Submitted to Journal of Physics: Conference Serie