Condensation and evaporation on a randomly occupied square lattice

We study the evolution of an initially random distribution of particles on a square lattice, under certain rules for `growing' and `culling' of particles. In one version we allow the particles to move laterally along the surface (mobile layer) and in the other version this motion is not allowed (immobile case). In the former case both analytical and computer simulation results are presented, while in the latter only simulation is possible. We introduce growth and culling probabilities appropriate for condensation and evaporation on a two-dimensional surface, and compare results with existing models for this problem. Our results show very interesting behaviour, under certain conditions quite different from earlier models. We find a possibility of hysteresis not reported earlier for such models. ~Comment: 13 pages, 10 figure

Spreading of Fluids on Solids Under Pressure: Effect of Slip

Spreading of different types of fluid on substrates under an impressed force is an interesting problem. Here we study spreading of four fluids, having different hydrophilicity and viscosity on two substrates - glass and perspex, under an external force. The area of contact of fluid and solid is video-photographed and its increase with time is measured. The results for different external forces can be scaled onto a common curve. We try to explain the nature of this curve on the basis of existing theoretical treatment where either the no-slip condition is used or slip between fluid and substrate is introduced. We find that of the eight cases under study, in five cases quantitative agreement is obtained using a slip coefficient.Comment: 6 figure

Euler Number and Percolation Threshold on a Square Lattice with Diagonal Connection Probability and Revisiting the Island-Mainland Transition

We report some novel properties of a square lattice filled with white sites, randomly occupied by black sites (with probability $p$). We consider connections up to second nearest neighbours, according to the following rule. Edge-sharing sites, i.e. nearest neighbours of similar type are always considered to belong to the same cluster. A pair of black corner-sharing sites, i.e. second nearest neighbours may form a 'cross-connection' with a pair of white corner-sharing sites. In this case assigning connected status to both pairs simultaneously, makes the system quasi-three dimensional, with intertwined black and white clusters. The two-dimensional character of the system is preserved by considering the black diagonal pair to be connected with a probability $q$, in which case the crossing white pair of sites are deemed disjoint. If the black pair is disjoint, the white pair is considered connected. In this scenario we investigate (i) the variation of the Euler number $\chi(p) \ [=N_B(p)-N_W(p)]$ versus $p$ graph for varying $q$, (ii) variation of the site percolation threshold with $q$ and (iii) size distribution of the black clusters for varying $p$, when $q=0.5$. Here $N_B$ is the number of black clusters and $N_W$ is the number of white clusters, at a certain probability $p$. We also discuss the earlier proposed 'Island-Mainland' transition (Khatun, T., Dutta, T. & Tarafdar, S. Eur. Phys. J. B (2017) 90: 213) and show mathematically that the proposed transition is not, in fact, a critical phase transition and does not survive finite size scaling. It is also explained mathematically why clusters of size 1 are always the most numerous

Radially Interrupted Viscous Fingers in a Lifting Hele-Shaw Cell

Viscous fingers have been produced in the lifting Hele-Shaw cell, with concentric circular grooves etched onto the lower plate. The invading fluid (air) enters the defending newtonian fluid - olive oil as fingers proceeding radially inwards towards the centre. The fingers are interrupted at the circular groove, and reform as secondary fingers. The effect of the grooves is to speed up the fingering process considerably and the fingers now reach the centre much faster. We explain this by comparing the variation in velocity of the fingers in the normal HS cell and the grooved cells with time. In the normal HS cell the fingers move fastest on initial formation and slow down later. Since in case of the grooved plate, the fingers reform and receive a boost in their speed each time they encounter a groove, the fingers proceed to the centre faster. PACS nos. 47.20.Gv, 47.54.+r, 68.03.-gComment: 4 pg. 2 fi