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 wit
h 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<k>, where <k> is the average degree of the graph.
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-dro
plet 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.
We study the impact of wall corrugations in microchannels on the process of capillary filling by means of three broadly used methods - Computational Fluid Dynamics (CFD), Lattice-Boltzmann Equations (LBE) and Molecular Dynamics (MD). The numerical re
sults of these approaches are compared and tested against the Concus-Finn (CF) criterion, which predicts pinning of the contact line at rectangular ridges perpendicular to flow for contact angles theta > 45. While for theta = 30, theta = 40 (no flow) and theta = 60 (flow) all methods are found to produce data consistent with the CF criterion, at theta = 50 the numerical experiments provide different results. Whilst pinning of the liquid front is observed both in the LB and CFD simulations, MD simulations show that molecular fluctuations allow front propagation even above the critical value predicted by the deterministic CF criterion, thereby introducing a sensitivity to the obstacle heigth.
We report on simulations of capillary filling of high-wetting fluids in nano-channels with and without obstacles. We use atomistic (molecular dynamics) and hydrokinetic (lattice-Boltzmann) approaches which point out clear evidence of the formation of
thin precursor films, moving ahead of the main capillary front. The dynamics of the precursor films is found to obey a square-root law as the main capillary front, z^2(t) ~ t, although with a larger prefactor, which we find to take the same value for the different geometries (2D-3D) under inspection. The two methods show a quantitative agreement which indicates that the formation and propagation of thin precursors can be handled at a mesoscopic/hydrokinetic level. This can be considered as a validation of the Lattice-Boltzmann (LB) method and opens the possibility of using hydrokinetic methods to explore space-time scales and complex geometries of direct experimental relevance. Then, LB approach is used to study the fluid behaviour in a nano-channel when the precursor film encounters a square obstacle. A complete parametric analysis is performed which suggests that thin-film precursors may have an important influence on the efficiency of nanochannel-coating strategies.
We present hydrokinetic Lattice Boltzmann and Molecular Dynamics simulations of capillary filling of high-wetting fluids in nano-channels, which provide clear evidence of the formation of thin precursor films, moving ahead of the main capillary front
. The dynamics of the precursor films is found to obey the Lucas-Washburn law as the main capillary front, z2(t) proportional to t, although with a larger prefactor, which we find to take the same value for both geometries under inspection. Both hydrokinetic and Molecular Dynamics approaches indicate a precursor film thickness of the order of one tenth of the capillary diameter. The quantitative agreement between the hydrokinetic and atomistic methods indicates that the formation and propagation of thin precursors can be handled at a mesoscopic/hydrokinetic level, thereby opening the possibility of using hydrokinetic methods to space-time scales and complex geometries of direct experimental relevance.
The dynamics of capillary filling in the presence of chemically coated heterogeneous boundaries is investigated, both theoretically and numerically. In particular, by mapping the equations of front motion onto the dynamics of a dissipative driven osc
illator, an analytical criterion for front pinning is derived, under the condition of diluteness of the coating spots. The criterion is tested against two dimensional Lattice Boltzmann simulations, and found to provide satisfactory agreement as long as the width of the front interface remains much thinner than the typical heterogeneity scale of the chemical coating.
We present a systematic study of capillary filling for a binary fluid by using mesoscopic a lattice Boltzmann model describing a diffusive interface moving at a given contact angle with respect to the walls. We compare the numerical results at changi
ng the ratio the typical size of the capillary, H, and the wettability of walls. Numerical results yield quantitative agreement with the Washburn law in all cases, provided the channel lenght is sufficiently larger then the interface width. We also show that in the initial stage of the filling process, transient behaviour induced by inertial effects are under control in our lattice Boltzmann equation and in good agreement with the phenomenology of capillary filling. Finally, at variance with multiphase LB simulations, velocity and pressure profiles evolve under the sole effect of capillary drive all along the channel.
Numerical simulations of two-dimensional capillary filling using the pseudo-potential lattice Boltzmann model for multiphase fluids are presented, with special emphasis on the role of finite-vapour density effects. It is shown that whenever the densi
ty of the light-phase exceeds about ten percent of the dense phase, the front motion proceeds through a combined effect of capillary advection and condensation. As a result, under these conditions, the front proceeds at a higher speed as compared to the Washburn prediction. It is suggested that such an acceleration effect might be observed in experiments performed sufficiently close to critical conditions
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 chan
ging 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.
