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Connectedness percolation phenomena in two-dimensional packings of elongated particles (discorectangles) were studied numerically. The packings were produced using random sequential adsorption (RSA) off-lattice model with preferential orientations of particles along a given direction. The partial ordering was characterized by order parameter $S$, with $S=0$ for completely disordered films (random orientation of particles) and $S=1$ for completely aligned particles along the horizontal direction $x$. The aspect ratio (length-to-width ratio) for the particles was varied within the range $\varepsilon \in [1;100]$. Analysis of connectivity was performed assuming a core-shell structure of particles. The value of $S$ affected the structure of packings, formation of long-range connectivity and electrical conductivity behavior. The effects were explained accounting for the competition between the particles' orientational degrees of freedom and the excluded volume effects. For aligned deposition, the anisotropy in electrical conductivity was observed and the values along alignment direction, $\sigma_x$, were larger than the values in perpendicular direction, $\sigma_y$. The anisotropy in localization of percolation threshold was also observed in finite sized packings, but it disappeared in the limit of infinitely large systems., Comment: 13 pages, 14 figures, 75 references

Using Monte Carlo simulation, we studied the percolation of sticks, i.e. zero-width rods, on a plane paying special attention to the effects of stick alignment and their length dispersity. The stick lengths were distributed in accordance with log-normal distributions, providing a constant mean length with different widths of distribution. Scaling analysis was performed to obtain the percolation thresholds in the thermodynamic limits for all values of the parameters. Greater alignment of the sticks led to increases in the percolation threshold while an increase in length dispersity decreased the percolation threshold. A fitting formula has been proposed for the dependency of the percolation threshold both on stick alignment and on length dispersity., Comment: 6 pages, 6 figures, 2 tables, 36 references

Numerical simulations by means of the Monte Carlo method have been performed to study the electrical properties of a two-dimensional composite filled with rodlike particles. The main goal was to study the effect of the alignment of such rods on the anisotropy of its electrical conductivity. A continuous model was used. In this model, the rods have zero-width (i.e., infinite aspect ratio) and they may intersect each other. To involve both the low conductive host matrix and highly conductive fillers (rods) in the consideration, a discretization algorithm based on the use of a supporting mesh was applied. The discretization is equivalent to the substitution of rods with the polyominoes. Once discretized, the Frank-Lobb algorithm was applied to evaluate the electrical conductivity. Our main findings are (i) the alignment of the rods essentially affects the electrical conductivity and its anisotropy, (ii) the discrete nature of computer simulations is crucial. For slightly disordered system, high electrical anisotropy was observed at small filler content, suggesting a method to enable the production of optically transparent and highly anisotropic conducting films.

The electrical conductivity of two-dimensional films filled with rodlike particles (rods) was simulated by the Monte Carlo method. The main attention has been paid to the investigation of the effect of the rod alignment on the electrical properties of the films. Both continuous and lattice approaches were used. Intersections of particles were forbidden. Our main findings are (i) both models demonstrate similar behaviors, (ii) at low concentration of rods, both approaches lead to the same dependencies of the electrical conductivity on the concentration of the rods, (iii) the alignment of the rods essentially affects the electrical conductivity, (iv) at some concentrations of partially aligned rods, the films may be conducting only in one direction, and (v) the films may simultaneously be both highly transparent and electrically anisotropic.

An analytical expression of hydrodynamic potential inside an evaporating sessile drop with pinned contact line is found. The problem is considered for a hemispherical drop (with the contact angle of 90\ifmmode^\circ\else\textdegree\fi{}) at the very early stages of the evaporation process when the shape of the drop is still a hemisphere and the evaporation field is uniform. The capillary flow carries a fluid from the drop apex to the contact line. Comparison with the published calculations performed using lubrication approximation (very thin drop) suggests that qualitative picture of the capillary flow is insensitive to the ratio of initial drop height to the drop radius.