arXiv subjects

Sujata Tarafdar

Publications and source records attributed to Sujata Tarafdar.

At least 19 recordsLinked to original sources

arXiv2023

Evolution of polygonal crack patterns in mud when subjected to repeated wetting-drying cycles

The present paper demonstrates how a natural crack mosaic resembling a random tessellation evolves with repeated 'wetting followed by drying' cycles. The natural system here is a crack network in a drying colloidal material, for example, a layer of mud. A spring network model is used to simulate consecutive wetting and drying cycles in mud layers until the crack mosaic matures. The simulated results compare favourably with reported experimental findings. The evolution of these crack mosaics has been mapped as a trajectory of a 4-vector tuple in a geometry-topology domain. A phenomenological relation between energy and crack geometry as functions of time cycles is proposed based on principles of crack mechanics. We follow the crack pattern evolution to find that the pattern veers towards a Voronoi mosaic in order to minimize the system energy. Some examples of static crack mosaics in nature have also been explored to verify if nature prefers Voronoi patterns. In this context, the authors define new geometric measures of Voronoi-ness of crack mosaics to quantify how close a tessellation is to a Voronoi tessellation, or even, to a Centroidal Voronoi tessellation.

cond-mat.soft↗

arXiv2019

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 $χ(p) \ [=N_B(p)-N_W(p)]$ 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.

cond-mat.stat-mech↗

arXiv2018

Evaluation of Porosity for Gamma Irradiated Poly(ethylene oxide): A New Approach Using Microscopic Image Aided with Computer Programming

Porous polymer films of Poly(ethylene oxide)(PEO) are synthesized by solution casting technique using gamma irradiated: (a) PEO powder (S-series) and (b) PEO - methanol solution (L-series). Pore phase forms instantaneously during preparation. Optimization of the pore content and distribution enables tailoring of associated properties for multifaceted applications. This method could be analyzed for mapping of porosity and average pore size. Practicability and repeatability of the developed programme has been established for monophasic system using backscattered imaging mode of SEM. This program is underdevelopment, but PROGIMAGE-POR bears the novelty of using image from either 2D-or 3D imaging system and could be applied for intricate composite/layered system.

physics.app-ph↗

arXiv2018

Monitoring of Wild Pseudomonas Biofilm Strain Conditions Using Statistical Characterisation of Scanning Electron Microscopy Images

The present paper proposes a novel method of quantification of the variation in biofilm architecture, in correlation with the alteration of growth conditions that include, variations of substrate and conditioning layer. The polymeric biomaterial serving as substrates are widely used in implants and indwelling medical devices, while the plasma proteins serve as the conditioning layer. The present method uses descriptive statistics of FESEM images of biofilms obtained during a variety of growth conditions. We aim to explore here the texture and fractal analysis techniques, to identify the most discriminatory features which are capable of predicting the difference in biofilm growth conditions. We initially extract some statistical features of biofilm images on bare polymer surfaces, followed by those on the same substrates adsorbed with two different types of plasma proteins, viz. Bovine serum albumin (BSA) and Fibronectin (FN), for two different adsorption times. The present analysis has the potential to act as a futuristic technology for developing a computerized monitoring system in hospitals with automated image analysis and feature extraction, which may be used to predict the growth profile of an emerging biofilm on surgical implants or similar medical applications.

physics.bio-ph↗

arXiv2017

Identifying 'Island-Mainland' phase transition using the Euler number

In the present communication we describe the Island-Mainland transition, occurring in a square lattice, when black squares are randomly dropped on a white background. Initially clusters of black squares are observed on the connected white background. But as concentration of black sites increases, at some point the black squares join to form a single continuous black background with white clusters randomly scattered in it. We show that the minimum in the Euler number, defined as the difference between number of white clusters and number of black clusters, reaches a minimum at this point. This occurs at a concentration higher than the well-known percolation phase transition and we show that the phenomenon can be related to experimental observations in several physical systems.

cond-mat.stat-mech↗

arXiv2016

Pattern formation in desiccated sessile colloidal droplets with salt admixture: Short review

This short review is devoted to the simple process of drying a multi-component droplet consisting of a complex fluid containing a salt. These processes provide a fascinating subject for study. The explanation of the rich variety of patterns formed is not only an academic challenge, but a problem of practical importance, as applications are growing in medical diagnosis and improvement of coating/printing technology. The fundamental scientific problem is the study of the mechanism of micro- and nanoparticle self-organization in open systems. The specific fundamental problem to be solved, related to this system is - the investigation of the mass transfer processes, the formation and evolution of phase fronts and the identification of mechanisms of pattern formation. The drops of liquid containing dissolved substances and suspended particles are assumed to be drying on a horizontal solid substrate. The chemical composition and macroscopic properties of the complex fluid, the concentration and nature of the salt, the surface energy of the substrate and the interaction between the fluid and substrate which determines the wetting, all affect the final morphology of the dried film.

cond-mat.soft↗

arXiv2016

Relation between Lacunarity, Correlation dimension and Euclidean dimension of Systems

Lacunarity is a measure often used to quantify the lack of translational invariance present in fractals and multifractal systems. The generalised dimensions, specially the first three, are also often used to describe various aspects of mass distribution in such systems. In this work we establish that the graph (\textit{lacunarity curve}) depicting the variation of lacunarity with scaling size, is non-linear in multifractal systems. We propose a generalised relation between the Euclidean dimension, the Correlation Dimension and the lacunarity of a system that lacks translational invariance, through the slope of the lacunarity curve. Starting from the basic definitions of these measures and using statistical mechanics, we track the standard algorithms- the box counting algorithm for the determination of the generalised dimensions, and the gliding box algorithm for lacunarity, to establish this relation. We go on to validate the relation on six systems, three of which are deterministically determined, while three others are real. Our examples span 2- and 3- dimensional systems, and euclidean, monofractal and multifractal geometries. We first determine the lacunarity of these systems using the gliding box algorithm. In each of the six cases studied, the euclidean dimension, the correlation dimension in case of multifractals, and the lacunarity of the system, together, yield a value of the slope $S$ of the lacunarity curve at any length scale. The predicted $S$ value matches the slope as determined from the actual plot of the lacunarity curves at the corresponding length scales. This establishes that the relation holds for systems of any geometry or dimension.

cond-mat.soft↗

arXiv2015

Growth kinetics of NaCl crystals in a drying drop of gelatin: transition from faceted to dendritic growth

We report a study on the kinetics of drying of a droplet of aqueous gelatin containing sodium chloride. The process of drying recorded on video, clearly shows different regimes of growth leading to a variety of crystalline patterns. Large faceted crystals of $\sim$mm size form in the early stages of evaporation, followed by highly branched multi-fractal patterns with micron sized features. We simulate the growth using a simple algorithm incorporating aggregation and evaporation, which reproduces the cross-over between the two growth regimes. As evaporation proceeds, voids form in the gel film. The time development of the fluid-void system can be characterized by an Euler number. A minimum in the Euler number marks the transition between the two regimes of growth.

cond-mat.soft↗

arXiv2015

Multi-scale Patterns formed by Sodium Sulphate in a Drying Droplet of Gelatin

We present a study of patterns, formed in drying drops of aqueous gelatin solution containing sodium sulphate. The patterns are highly complex, consisting of a hierarchical sequence of rings which form concentric bands as well as dendritic crystalline aggregates. When the preparation of the complex fluid is done by mixing an aqueous solution of the salt with an aqueous solution of gelatin prepared separately, another feature is observed in the pattern on the dried out drop. This is a viscous fingering pattern, superposed on the series of rings. We try to explain the origin of these two features from a simple physical approach.

cond-mat.soft↗

arXiv2015

Squeeze flow of potato starch gel: effect of loading history on visco-elastic properties

In this work gelatinized potato starch is shown to retain the memory of past loading history. It exhibits a visco-elastic response which does not depend solely on instantaneous conditions. A simple squeeze flow experiment is performed, where loading is done in two steps with a time lag $τ\sim$ seconds between the steps. The effect on the strain, of varying $τ$ is reproduced by a three element visco-elastic solid model. Non-linearity is introduced through a generalized calculus approach by incorporating a non-integer order time derivative in the viscosity equation. A strain hardening proportional to the time lag between the two loading steps is also incorporated. This model reproduces the three salient features observed in the experiment, namely - the memory effect, slight initial oscillations in the strain as well as the long-time solid-like response. Dynamic visco-elasticity of the sample is also reported.

cond-mat.soft↗

arXiv2015

Electrical Impedance Response of Gamma Irradiated Gelatin based Solid Polymer Electrolytes Analyzed Using a Generalized Calculus Formalism

The electrical impedance response of Gelatin based solid polymer electrolyte to gamma irradiation is investigated by impedance spectroscopy. An analysis based on Poisson-Nernst-Plank model, incorporating fractional time derivatives is carried out. A detailed derivation for anomalous impedance function is given.The model involves boundary conditions with convolution of the fractional time derivative of ion density and adsorption desorption relaxation kinetics. A fractional diffusion-drift equation is used to solve the bulk behavior of the mobile charges in the electrolyte. The complex adsorption-desorption process at the electrode-electrolyte interface produces an anomalous effect in the system. The model gives a very good fit for the observed impedance data for this biopolymer based solid electrolyte in wide range of frequencies. We have compared different parameters based upon this model for both irradiated and unirradiated samples.

cond-mat.mtrl-sci↗

arXiv2014

Topology of desiccation crack patterns in clay and invariance of crack interface area with thickness

We study the crack patterns developed on desiccating films of an aqueous colloidal suspension of bentonite on a glass substrate. Varying the thickness of the layer $h$ gives the following new and interesting results: (i)We identify a critical thickness $h_{c}$, above which isolated cracks join each other to form a fully connected network. A topological analysis of the crack network shows that the Euler number falls to a minimum at $h_{c}$. (ii) We find further, that the total vertical surface area of the clay $A_v$, which has opened up due to cracking, is a constant independent of the layer thickness for $h \geq h_c$. (iii) The total area of the glass substrate $A_s$, exposed by the hierarchical sequence of cracks is also a constant for $h \geq h_c$. These results are shown to be consistent with a simple energy conservation argument, neglecting dissipative losses. (iv) Finally we show that if the crack pattern is viewed at successively finer resolution, the total cumulative area of cracks visible at a certain resolution, scales with the layer thickness. A suspension of Laponite in methanol is found to exhibit similar salient features (i)-(iv), though in this case the crack initiation process for very thin layers is quite different.

cond-mat.soft↗

arXiv2014

Structural Modificationand Variation in the Kinetics of Isoconversional Phenomena: A Study on the Effect of Gamma Irradiation on Poly (Ethylene Oxide)

Interactions of Poly (Ethylene Oxide) [PEO] and gamma irradiation of variable doses (1-30 kGy) on the thermal, crystalline and structural properties are investigated using DSC and FTIR technique. Two states of PEO, viz. powder (P-S-series) and solution (P-L-series) are subjected to irradiationand are castinto uniform film.DSC results revealed steady increment of crystallinity upto 20 kGy for P-S-series after which amorphous region increases till 30 kGy. Conversely, P-L-series shows much enhanced crystallinity retained within low regime of 7 kGy, followed by sharp declining trend till 30 kGy. DSC is also used to determine the multiple kinetic processes in an isoconversional PEO melting using Friedman differential analysis. Gamma irradiation is found to generate newer functional groups established from FTIR study. FTIR spectra of generated peaks viz. -C=O, -C=C- exhibit scission dominated irradiation induced in presence of air. Contribution of cross-linkage which is higher in liquid irradiation is also proved from FTIR. The studied observations of DSC and FTIR are correlated with polymer microstructures. Hence, selective irradiation dose could be determined with respect to the exposed state (solid or solution) of polymer and utilized to tailor the properties of PEO.

cond-mat.mtrl-sci↗

arXiv2014

Impact of Tailored Gamma Irradiation on Pore Size and Particle Size of Poly[Ethylene Oxide]Films: Correlation with Molecular Weight Distribution andMicrostructural Study

The structure and morphology of polymers are significantly altered upon exposure to high energy gamma irradiation. The present investigation reports the influence of such irradiation of doses in the range of 1 - 30 kGy on the particle size of Poly (Ethylene Oxide) [PEO] powder along with its correlation with molecular weight distribution. Pore-size distribution and overall porosity of the synthesized films prepared with irradiated and unirradiated PEO powder is also reported. The particle size of both unirradiated and irradiated PEO powders is found be in the range of 0.01 - 1000 micrometer. It is known that, variation in irradiation dose either generates particles of lower dimension through bond breakage i.e scission or higher dimension through cross-linkage. PEO films exhibit strong dependence of irradiation effect on pore size distribution and porosity. PEO films synthesized using both unirradiated and irradiated powders exhibit pore dimension in the range of 20 - 500 nm. The overall porosity of PEO films studied through BET adsorption technique initially increases with dose upto 3 kGy followed by linear decrease upto 30 kGy. Films cast with unirradiated PEO powder show multimodal pore size distribution, but perturbation with irradiation changes the modality to uni-or bimodal nature. The mentioned outcome of irradiation viz. particle and pore size variation is also correlated with PEO microstructures.The article demonstrates that, selective irradiation is capable of tailoring the pore-size within a definite regime thereby reducing the multimodal trait. The reported study may be relevant towards applications such as catalysis, sensing and filtration, where pore size distribution plays a crucial role.

cond-mat.mtrl-sci↗

arXiv2013

Crack Formation in the Presence of an Electric Field in Droplets of Laponite Gel

When a colloidal gel dries through evaporation, cracks are usually formed, which often reveal underlying processes at work during desiccation. Desiccating colloid droplets of few hundred $μl$ size show interesting effects of pattern formation and cracking which makes this an active subject of current research. Since aqueous gels of clay are known to be strongly affected by an electric field, one may expect crack patterns to exhibit a field effect. In the present study we allow droplets of laponite gel to dry under a radial electric field. This gives rise to highly reproducible patterns of cracks, which depend on the strength, direction and time of exposure to the electric field. For a continuously applied DC voltage, cracks always appear on dissipation of a certain constant amount of energy. If the field is switched off before cracks appear, the observed results are shown to obey a number of empirical scaling relations, which enable us to predict the time of appearance and the number of cracks under specified conditions.

cond-mat.soft↗

arXiv2013

Crack Formation in Laponite Gel under AC Fields

Crack formation patterns in laponite gel are known to be strongly affected by DC electric fields. We show that AC fields produce equally remarkable patterns in a radially symmetric set-up. The character of the pattern depends crucially on the field strength. A significant feature observed is the bending of radial cracks, with the curvature increasing as field strength is increased. Fields of 20 to 70 V have been applied and several features of the resulting patterns quantified. Striations on the fracture surfaces and crack speeds are also studied.

cond-mat.soft↗

arXiv2013

Multifractal analysis of the pore space of real and simulated sedimentary rocks

It is well known that sedimentary rocks having same porosity can have very different pore size distribution. The pore distribution determines many characteristics of the rock among which, its transport property is often the most useful. Multifractal analysis is a powerful tool that is increasingly used to characterize the pore space. In this study we have done multifractal analysis of pore distribution on sedimentary rocks simulated using the Relaxed Bidisperse Ballistic Model (RBBDM). The RBBDM can generate a $3-D$ structure of sedimentary rocks of variable porosity by tuning the fraction $p$ of particles of two different sizes. We have also done multifractal analysis on two samples of real sedimentary rock to compare with the simulation studies. One sample, an oolitic limestone is of high porosity (40%)while the other is a reefal carbonate of low porosity around 7%. $2-D$ sections of X-ray micro-tomographs of the real rocks were stacked sequentially to reconstruct the real rock specimens. Both samples show a multifractal character, but we show that RBBDM gives a very realistic representation of a typical high porosity sedimentary rock.

cond-mat.dis-nn↗

arXiv2012

Aggregation Patterns of Salt Crystalizing in Drying Colloidal Solvents

We report a study of the structure of droplets of colloidal gels containing dissolved sodium chloride. The components segregate and form intricate patterns. The salt crystalizes in fractal and multi-fractal dendritic forms which are determined by the material which forms the colloidal gel. Here potato starch, gelatine and carboxymethyl cellulose have been used. The substrate also plays a role in some cases. Photographs and micrographs at different level of magnification are shown.

cond-mat.soft↗