A.M. Vidales

Pore-level modelling of wetting on correlated porous media

The displacement of a non-wetting fluid by a wetting one in a porous medium is influenced, among other things, by two competing mechanisms: the flow of the wetting phase along crevices, giving the possibility of snapping off in throats; and its advance through the centres of the pore space under various pore- and throat-filling conditions, leading to a cooperative filling. The percolation process associated with these two mechanisms on porous networks in two and three dimensions is well understood; it is a classic bond percolation problem competing with an invasion percolation one. We present a three-dimensional pore-level model that describes these effects on a site and bond network representing pores and throats, respectively. The network elements may have various degrees of correlation among their sizes. Site and bond-size distributions may be any kind of function representing a real pore space. In this work, we are able to predict various kinds of patterns that arise when the two aforementioned mechanisms compete and to study the effect of the correlations strength on the onset of each pattern, revealing the strong influence of the topology of the network in determining which process will dominate. Buoyancy forces are not taken into account in the present work.

Effect of the Drug-Excipient Ratio in Matrix-Type-Controlled Release Systems: Computer Simulation Study

The main objective of this work is to study the drug release behavior from inert matrix systems by using computer simulation. This study allowed us to propose a new statistical method to evaluate the drug percolation threshold as a function of the exposed surface area of the device. The matrix system was simulated as a simple cubic lattice. The sites of the lattice were randomly occupied at various drug–excipient ratios. By simulating a diffusive process, the drug was delivered from the matrix system. The obtained release profiles were fitted to two different models: near the excipient percolation threshold, the square root of the time was well fitted, whereas close to (but above) the drug percolation threshold, the power law described accurately the release data. A relationship between the initial drug load and the amount of drug trapped inside the matrix system at infinite time was found. This relationship was conveniently described by an error function. Percolation thresholds in the matrix systems were determined from the latter relationship by using a nonlinear regression method. The assessment of percolation thresholds depends on the exposed surface area of the matrix systems. Moreover, estimated percolation thresholds were in agreement with the predicted values stated in the percolation theory.

Pore-blocking and pore-assisting factors during capillary condensation and evaporation

Abstract Thirty-four years ago Everett [The Solid–Gas Interface, Vol. 2, Marcel Dekker, New York, 1967, p. 1055] proposed a pore-blocking factor when establishing the foundations of a non-independent domain theory (IDT) of sorption hysteresis. Such pore-blocking factor was defined as the ratio between two desorbed volumes within the same pressure range. The first volume arose from a non-independent pore structure. The second quantity was a virtual one since it represented the volume desorbed if the pores of the substrate had acted as independent domains. In fact, Everett calculated the ratio between pore-blocking factors, while not their absolute values, from experimental data proceeding from sorption results on porous glasses. The astonishing conclusion of all this preliminary work, was that blocking factors depended upon the total amount of condensate at a certain stage of a desorption process rather than on the distribution of it within the porous network. In this way, a unique pore-blocking factor curve ensued from different sorption processes such as boundary and scanning curves. Now, through the aid of simulated heterogeneous 3-D porous networks and the sorption curves thereon developed, an assessment of the above mentioned important assertion has been undertaken. Besides, a pore-assisting factor that may arise during an ascending sorption process has been treated under a similar context.

CORRELATED SITE-BOND PERCOLATION ON A SQUARE LATTICE

A percolation model is studied, on a square lattice, with computer simulations. The sites and bonds distributions overlap and introduce correlations between sites and bonds. The percolation thresholds have been evaluated numerically. Percolation becomes easier as the correlation increases. The percolation probability (i.e. the percolating cluster mass) shows a change in its behaviour as the correlation changes. For low correlation it grows monotonically but for large correlations it shows a maximum. Similar characteristics have previously been found on a Bethe lattice.

The effect of the packing fraction on the jamming of granular flow through small apertures

We investigate the flow through and jamming of small apertures for a column of granular disks via a pseudo-dynamic model. We focus on the effect that the preparation of the granular assembly has on the size of the avalanches obtained. Ensembles of packings with different mean packing fractions are created by tapping the system at different intensities. Surprisingly, the packing fraction is not a good indicator of the ability of the deposit to jam a given orifice. Different mean avalanche sizes are obtained for deposits with the same mean packing fraction that were prepared with very different tap intensities. It has been speculated that the number and size of arches in the bulk of the granular column should be correlated with the ability of the system to jam a small opening. We show that this correlation, if it exists, is rather poor. A comparison between bulk arches and jamming arches (i.e., arches that block the opening) reveals that the aperture imposes a lower cutoff on the horizontal span of the arches which is greater than the actual size of the opening. This is related to the fact that blocking arches have to have the appropriate orientation to fit the gap between two piles of grains resting on each side of the aperture.

Fractal properties of correlated invasion percolation patterns

We present results on Monte Carlo simulations for invasion percolation with trapping considering the presence of spatial size correlations, a problem which is relevant to multiphase flow in field scale of porous media. The correlations are generated through the dual site bond model, characterized by a spatial correlation length r0, which depends on the overlap between site and bond distributions. Our results indicate that in two-dimensional lattices the fractal dimension of the sample-spanning cluster, is non-universal and vary with the correlation. Comparison with other authors recent findings is presented.

Arching during the segregation of two-dimensional tapped granular systems: Mixtures versus intruders

We present numerical simulations of binary mixtures of granular disks subjected to tapping. We consider the size segregation process in terms of the arches formed by small and big particles. Although arching has been proposed as one of the chief mechanisms that determines size segregation in non-convecting systems, there is no direct data on arching to support the existing proposals. The pseudo-dynamic approach chosen for this work allows for a straightforward identification of arches in the bulk of the column. We find that, indeed, arch formation and breakage are crucial to the segregation process. Our results show that the presence of large particles induce the formation of more arches than found in mono-sized samples. However, tapping leads to the progressive breakage of big arches where large particles are involved as the segregation process takes place. Interestingly, isolated intruders may or may not rise under tapping depending not only on the size ratio (as it is well known) but also on the degree of ordering of the environment.Graphical abstract

Pentagon deposits unpack under gentle tapping.

We present results from simulations of regular pentagons arranged in a rectangular box. The particles are subjected to vertical tapping. We study the packing fraction, number of contacts, and arch size distribution as a function of the tapping amplitude. Compared with disks, pentagons show peculiar features. As a general rule, pentagons tend to form fewer arches than do disks. Nevertheless, as the tapping amplitude is decreased, the typical size of the pentagon arches grows significantly. As a consequence, a pentagon packing reduces its packing fraction when tapped gently, in contrast with the behavior found in rounded particle deposits.

Difference percolation on a square lattice

Simulations of percolation processes on random site square lattices are performed implementing a different occupation algorithm for both ordinary percolation (OP) and invasion percolation (IP) problems. The main feature of the occupation process is the fact that it is performed in a locally restricted way by inspecting the difference between the measure assigned to neighboring sites. This restriction carries an intrinsic change in the distribution of invaded sites with a different percolation threshold and the same universality class. Conclusions are drawn concerning physical problems of propagation phenomena with local barriers where these simulations prove the possibility of controlling the wide spread of the invasor.

Force–displacement distributions and percolation properties in simulated 2-D packings

The first part of this paper studies the behavior of contact force distributions and displacement distributions in isostatic 2-D arrays of polydispersed grains as a function of force strength and displacement strength, respectively. The array is built by pouring disks, one by one, into a rectangular die. After the array is ready, force and displacement measurements are performed on it. We also introduce a relaxation procedure (rearrangements of disks) in order to study the behavior of the corresponding distributions as a function of the number of relaxations performed on the system.