Structure of force networks in tapped particulate systems of disks and pentagons. I. Clusters and loops.

The force network of a granular assembly, defined by the contact network and the corresponding contact forces, carries valuable information about the state of the packing. Simple analysis of these networks based on the distribution of force strengths is rather insensitive to the changes in preparation protocols or to the types of particles. In this and the companion paper [Kondic et al., Phys. Rev. E 93, 062903 (2016)10.1103/PhysRevE.93.062903], we consider two-dimensional simulations of tapped systems built from frictional disks and pentagons, and study the structure of the force networks of granular packings by considering network's topology as force thresholds are varied. We show that the number of clusters and loops observed in the force networks as a function of the force threshold are markedly different for disks and pentagons if the tangential contact forces are considered, whereas they are surprisingly similar for the network defined by the normal forces. In particular, the results indicate that, overall, the force network is more heterogeneous for disks than for pentagons. Such differences in network properties are expected to lead to different macroscale response of the considered systems, despite the fact that averaged measures (such as force probability density function) do not show any obvious differences. Additionally, we show that the states obtained by tapping with different intensities that display similar packing fraction are difficult to distinguish based on simple topological invariants.

Stability study of a constant-volume thin film flow.

We study the stability of a constant volume of fluid spreading down an incline. In contrast to the commonly considered flow characterized by constant fluid flux, in the present problem the base flow is time dependent. We present a method to carry out consistently linear stability analysis, based on simultaneously solving the time evolution of the base flow and of the perturbations. The analysis is performed numerically by using a finite-difference method supplemented with an integral method developed here. The computations show that, after a short transient stage, imposed perturbations travel with the same velocity as the leading contact line. The spectral analysis of the modes evolution shows that their growth rates are, in general, time dependent. The wavelength of maximum amplitude, lambda_{max} , decreases with time until it reaches an asymptotic value which is in good agreement with experimental results. We also explore the dependence of lambda_{max} on the cross sectional fluid area A , and on the inclination angle alpha of the substrate. For considered small A 's, corresponding to small Bond numbers, we find that the dependence of lambda_{max} on A is in good agreement with experimental data. This dependence differs significantly from the one observed for the films characterized by much larger A 's and Bond numbers. We also predict the dependence of lambda_{max} on the inclination angle alpha .

Spreading of a thin two-dimensional strip of fluid on a vertical plane: experiments and modeling.

We study the thin-film flow of a constant volume of silicon oil (polydymethilsiloxane) spreading down a vertical glass plate. The initial condition is generated from a horizontal fluid filament of typical diameter 0.4 mm. Two optical diagnostic methods are used: One based on an anamorphic system, and the other on the Schlieren method. The first one allows for a detailed characterization of the early stable stage of the spreading which is used to estimate the thickness of the precursor film needed to model the flow. The second one captures the bidimensional pattern of the transversal film instability. We use these techniques to determine the film thickness profiles, and the evolution of the moving contact line, including its shape and Fourier spectra. The numerical simulations of the stable stage of spreading are in good quantitative agreement with the experimental results. We develop a model based on linear stability theory that predicts the evolution of the modes present in the linear stage of the instability.

Contact line instabilities of thin liquid films.

We present results of fully nonlinear time-dependent simulations of a thin liquid film flowing down an inclined plane. Within the lubrication approximation, and assuming complete wetting, we find that varying the inclination angle considerably modifies the shape of the emerging patterns (fingers versus sawtooth). Our results strongly suggest that the shape of the patterns is not necessarily related to either partial or complete coverage of the substrate, a technologically important feature of the flow. We find quantitative agreement with reported experiments and suggest new ones.