Nina Pesheva

Contact angle hysteresis and meniscus corrugation on randomly heterogeneous surfaces with mesa-type defects.

The results of a numerical study of the various characteristics of the static contact of a liquid meniscus with a flat but heterogeneous surface, consisting of two types of homogeneous materials, forming regularly and randomly distributed microscopic defects are presented. The solutions for the meniscus shape are obtained numerically using the full expression of the system free energy functional. The goal is to establish how the magnitude and the limits of the hysteresis interval of the equilibrium contact angle, the Cassies angle, and the contact line (CL) roughness exponent are related to the parameters, characterizing the heterogeneous surface-the equilibrium contact angles on the two materials and their fractions. We compare the results of different ways of determining the averaged contact angle on heterogeneous surfaces. We study the spread of the CL corrugation along the liquid meniscus. We compare our results with the numerical results, obtained using linearized energy functional, and also with experimental results for the CL roughness exponent. The obtained results support the conclusion that some characteristics depends on the type (regular or random) of the heterogeneity pattern.

Quasistatic relaxation of arbitrarily shaped sessile drops.

We study a spontaneous relaxation dynamics of arbitrarily shaped liquid drops on solid surfaces in the partial wetting regime. It is assumed that the energy dissipated near the contact line is much larger than that in the bulk of the fluid. We have shown rigorously in the case of quasi-static relaxation using the standard mechanical description of dissipative system dynamics that the introduction of a dissipation term proportional to the contact line length leads to the well-known local relation between the contact line velocity and the dynamic contact angle at every point of an arbitrary contact line shape. A numerical code is developed for three-dimensional drops to study the dependence of the relaxation dynamics on the initial drop shape. The available asymptotic solutions are tested against the obtained numerical data. We show how the relaxation at a given point of the contact line is influenced by the dynamics of the whole drop which is a manifestation of the nonlocal character of the contact line relaxation.

4D imaging through spray-on optics

Light fields are a powerful concept in computational imaging and a mainstay in image-based rendering; however, so far their acquisition required either carefully designed and calibrated optical systems (micro-lens arrays), or multi-camera/multi-shot settings. Here, we show that fully calibrated light field data can be obtained from a single ordinary photograph taken through a partially wetted window. Each drop of water produces a distorted view on the scene, and the challenge of recovering the unknown mapping from pixel coordinates to refracted rays in space is a severely underconstrained problem. The key idea behind our solution is to combine ray tracing and low-level image analysis techniques (extraction of 2D drop contours and locations of scene features seen through drops) with state-of-the-art drop shape simulation and an iterative refinement scheme to enforce photo-consistency across features that are seen in multiple views. This novel approach not only recovers a dense pixel-to-ray mapping, but also the refractive geometry through which the scene is observed, to high accuracy. We therefore anticipate that our inherently self-calibrating scheme might also find applications in other fields, for instance in materials science where the wetting properties of liquids on surfaces are investigated.

Position dependence of the particle density in a double-chain section of a linear network in a totally asymmetric simple exclusion process.

We report here results on the study of the totally asymmetric simple exclusion processes (TASEP), defined on an open network, consisting of head and tail simple chain segments with a double-chain section inserted in-between. Results of numerical simulations for relatively short chains reveal an interesting new feature of the network. When the current through the system takes its maximum value, a simple translation of the double-chain section forward or backward along the network, leads to a sharp change in the shape of the density profiles in the parallel chains, thus affecting the total number of cars in that part of the network. In the symmetric case of equal injection and ejection rates α = β > 1/2 and equal lengths of the head and tail sections, the density profiles in the two parallel chains are almost linear, characteristic for the coexistence line (shock phase). Upon moving the section forward (backward), their shape changes to the one typical for the high (low) density phases of a simple chain. The total bulk density of cars in a section with a large number of parallel chains is evaluated too. The observed effect might have interesting implications for the traffic flow control as well as for biological transport processes in living cells. An explanation of this phenomenon is offered in terms of finite-size dependence of the effective injection and ejection rates at the ends of the double-chain section.

Exact density profiles for the fully asymmetric exclusion process with discrete-time dynamics on semi-infinite chains.

Exact density profiles in the steady state of the one-dimensional fully asymmetric simple-exclusion process on a semi-infinite chain are obtained in the case of forward-ordered sequential dynamics by taking the thermodynamic limit in our recent exact results for a finite chain with open boundaries. The corresponding results for sublattice-parallel dynamics follow from the relationship obtained by Rajewsky and Schreckenberg [Physica A 245, 139 (1997)], and for parallel dynamics from the mapping found by Evans, Rajewsky, and Speer [J. Stat. Phys. 95, 45 (1999)]. Our analytical expressions involve Laplace-type integrals, rather than complicated combinatorial expressions, which makes them convenient for taking the limit of a semi-infinite chain, and for deriving the asymptotic behavior of the density profiles at large distances from its end. By comparing the asymptotic results appropriate for parallel update with those published in the above cited paper by Evans, Rajewsky, and Speer, we find complete agreement except in two cases, in which we correct technical errors in the final results given there.

Self-organized criticality in 1D stochastic traffic flow model

Abstract Results of computer simulations of a 1D particle hopping model of traffic flow are presented. The model is characterized by parallel update and fully asymmetric stochastic hopping dynamics which allows unbounded series of jumps to empty neighbour sites on the right. The considered case of open boundary conditions can be used to model a “bottleneck” situation in traffic. Evidence for self-organized criticality is found in two aspects: the presence of long-range spatial correlations manifested in the shape of density profiles, and long-time temporal correlations showing up in the low-frequency behaviour of the spectral density of the total particle number and flow. A plausible conjecture is to interpret the observed qualitative changes in these features, as a function of the injection rate and the hopping probability, in terms of a nonequilibrium phase transition between a low-density phase and a maximal current phase. This conjecture is supported by the phase diagram obtained in mean-field approximation.

Self-organized criticality in 1D stochastic traffic flow model with a speed limit

The aim of the present work is to investigate the effect of a speed limit 1 ≤ vmax < ∞ on the phase diagram of the model with vmax = ∞ considered in [1], as well as on the features of self-organized criticality (SOC) which have been observed there. Results of computer simulations and mean-field calculations of a 1D particle hopping model of traffic flow with a speed limit and open boundary conditions are presented here. The results are compared with the corresponding ones for the model without a speed limit. Evidence for SOC is found both in space and in time.

One-dimensional irreversible aggregation with dynamics of a totally asymmetric simple exclusion process

We define and study one-dimensional model of irreversible aggregation of particles obeying a discrete-time kinetics, which is a special limit of the generalized Totally Asymmetric Simple Exclusion Process (gTASEP) on open chains. The model allows for clusters of particles to translate as a whole entity one site to the right with the same probability as single particles do. A particle and a cluster, as well as two clusters, irreversibly aggregate whenever they become nearest neighbors. Nonequilibrium stationary phases appear under the balance of injection and ejection of particles. By extensive Monte Carlo simulations it is established that the phase diagram in the plane of the injection-ejection probabilities consists of three stationary phases: a multi-particle (MP) one, a completely filled (CF) phase and a ’mixed’ (MP+CF) one. The transitions between these phases are: an unusual transition between MP and CF with jump discontinuity in both the bulk density and the current, a conventional first-order transition with a jump in the bulk density between MP and MP+CF, and a continuous clustering-type transition from MP to CF, which takes place throughout the MP+CF phase between them. By the data collapse method a finite-size scaling function for the current and bulk density is obtained near the unusual phase transition line. A diverging correlation length, associated with that transition, is identified and interpreted as the size of the largest cluster. The model allows for a future extension to account for possible cluster fragmentation.

Contact-angle hysteresis on periodic microtextured surfaces: Strongly corrugated liquid interfaces.

We study numerically the shapes of a liquid meniscus in contact with ultrahydrophobic pillar surfaces in Cassies wetting regime, when the surface is covered with identical and periodically distributed micropillars. Using the full capillary model we obtain the advancing and the receding equilibrium meniscus shapes when the cross-sections of the pillars are both of square and circular shapes, for a broad interval of pillar concentrations. The bending of the liquid interface in the area between the pillars is studied in the framework of the full capillary model and compared to the results of the heterogeneous approximation model. The contact angle hysteresis is obtained when the three-phase contact line is located on one row (block case) or several rows (kink case) of pillars. It is found that the contact angle hysteresis is proportional to the line fraction of the contact line on pillars tops in the block case and to the surface fraction for pillar concentrations 0.1-0.5 in the kink case. The contact angle hysteresis does not depend on the shape (circular or square) of the pillars cross-section. The expression for the proportionality of the receding contact angle to the line fraction [Raj et al., Langmuir 28, 15777 (2012)LANGD50743-746310.1021/la303070s] in the case of block depinning is theoretically substantiated through the capillary force, acting on the solid plate at the meniscus contact line.

Monolayer spreading on a chemically heterogeneous substrate

Abstract We study the spreading kinetics of a monolayer of hard-core particles on a semi-infinite, chemically heterogeneous solid substrate, one side of which is coupled to a particle reservoir. The substrate is modeled as a square lattice containing two types of sites—ordinary ones and special, chemically active sites placed at random positions with mean concentration α. These special sites temporarily immobilize particles of the monolayer which then serve as impenetrable obstacles for the other particles. In terms of a mean-field-type theory, we show that the mean displacement X0(t) of the monolayer edge grows with time t as X 0 (t)= 2D α t ln (4D α t/πa 2 ) , (a being the lattice spacing). This time dependence is confirmed by numerical simulations; Dα is obtained numerically for a wide range of values of the parameter α and trapping times of the chemically active sites. We also study numerically the behavior of a stationary particle current in finite samples. The question of the influence of attractive particle–particle interactions on the spreading kinetics is also addressed.