Sujata Tarafdar

Desiccation cracks and their patterns: Formation and modelling in science and nature

The ideal team of authors, combining experimental and theoretical backgrounds, and with experience in both physical and earth sciences, discuss how the study of cracks can lead to the design of crack-resistant materials, as well as how cracks can be grown to generate patterned surfaces at the nanoand micro-scales. Important research and recent developments on tailoring desiccation cracks by different methods are covered, supported by straightforward, yet deep theoretical models.

Modelling porous structures by repeated Sierpinski carpets

Porous materials such as sedimentary rocks often show a fractal character at certain length scales. Deterministic fractal generators, iterated upto several stages and then repeated periodically, provide a realistic model for such systems. On the fractal, diffusion is anomalous, and obeys the law 〈r2〉∼t2/dw, where 〈r2〉 is the mean square distance covered in time t and dw>2 is the random walk dimension. The question is: How is the macroscopic diffusivity related to the characteristics of the small scale fractal structure, which is hidden in the large-scale homogeneous material? In particular, do structures with same dw necessarily lead to the same diffusion coefficient at the same iteration stage? The present paper tries to shed some light on these questions.

Pore morphology and pore surface roughening in rocks: a small-angle neutron scattering investigation

Pore morphology and pore-matrix interface roughening in some metamorphosed sedimentary rocks, sandstones and igneous rocks have been investigated using small-angle neutron scattering (SANS), in the length scales of ∼20–1000 nm., which reveal the fractal nature of the rock-pore interfaces. Surface fractal dimension of the metamorphosed rocks and the sandstones has been estimated to be ∼2.8 while, that for the igneous rocks has been found to be ∼2.3. An attempt has been made to explain the relatively high surface fractal nature of the former rocks with the help of a computer simulation model based on the formation mechanisms of these rocks. SANS data indicate some ideas about the upper cut-off of the fractal geometry for the igneous rocks as well as for the sandstone, but no unambiguous cut-off value has been obtained for the metamorphosed rocks in the accessible length scale. The multiple scattering effect in these rock specimens has also been looked into by performing the SANS experiments for the two thicknesses on each specimen.

A growth model for porous sedimentary rocks

A growth model for porous sedimentary rocks is proposed, using a simple computer simulation algorithm. We generate the structure by ballistic deposition of particles with a bimodal size distribution. Porosity and specific surface area are calculated varying the proportion of small and larger particles. Permeability and its variation with porosity are studied, and the percolation threshold for connectivity is determined. The fractal nature of the pore space is also discussed.

Crack Formation under an Electric Field in Droplets of Laponite Gel: Memory Effect and Scaling Relations

When a colloidal gel dries through evaporation, cracks are usually formed, which often reveal underlying processes at work during desiccation. Desiccating colloid droplets of a few hundred microliters size show interesting effects of pattern formation and cracking which makes this an active subject of current research. Because 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. Scanning electron microscopy (SEM) images of the surface between the macroscopic cracks show the presence of microcracks, which are wider and more numerous when no electric field is applied. The microcracks are reduced in the presence of stronger fields.

Correlation between porosity, conductivity and permeability of sedimentary rocks — a ballistic deposition model

We contruct a porous rock structure by ballistic deposition of grains of two different sizes. The conductivity (σ) of the rock with brine-filled pores is calculated using a simple parallel resistor model, taking the tortuosity of the pore channels into account. The results are used to calculate the permeability (K) from an equivalent channel model. Variation of σ and K with porosity are compared with geological field data. The agreement is quite satisfactory.

Crack patterns in desiccating clay–polymer mixtures with varying composition

Crack patterns in desiccating clay suspensions are drastically altered by the addition of polymers. In this paper we report a systematic study of the effect of varying the composition of a clay-polymer composite on the formation of crack patterns. Experiments as well as computer simulations have been done. Details of the morphology and fractal dimension of the experimental patterns are observed and the simulation is done on a two-dimensional spring network model. We find a transition from a completely fragmented fractal pattern at high clay content to a continuous film at about 50% clay content. The results of the simulation are in good qualitative agreement with the experiments. The study is expected to be of importance for clay-polymer composites. These can be designed to give improved mechanical and electrical properties for practical applications.

Formation of crack patterns in clay films : Desiccation and relaxation

A study of crack patterns in laponite films of different thickness is presented. Two cracking regimes are observed. The earlier, with a higher rate of desiccation and shrinking, has predominantly 4-fold vertices in the crack network, while the later regime has less volume shrinking and forms mainly 3-fold vertices. The pattern shows a self-similarity under coarse-graining. The graph of the area covered by cracks versus minimum crack-width resolved, scales with the film thickness. Curves representing crack area for different thickness thus collapse onto a single curve.

Adhesion and fingering in the lifting Hele-Shaw cell: Role of the substrate

Abstract.The lifting Hele-Shaw cell (LHSC) is used to study adhesion as well as viscous fingering. In the present paper we report a series of observations of development of the interface for different viscous fluids, both Newtonian and non-Newtonian, in a LHSC operated at a constant lifting force. Glass and perspex are used as the plates in two different sets of experiments. The objectives are 1) to measure the time required to separate the plates as a function of the lifting force and 2) to note the force above which viscous fingering appears. We find that for the Newtonian fluids, the plate separation time follows a universal power law with the lifting force, irrespective of fluid and substrate. The non-Newtonian fluids too, with proper scaling obey the same power law. The appearance of fingering, however, depends on the properties of the fluid as well as the substrate. We suggest a modified form of the capillary number which controls the onset of fingering; this new quantity, termed the “fingering parameter” involves the dielectric constants of the substrate and fluid in addition to the viscosity and surface tension.

Morphology and Ion-Conductivity of Gelatin–LiClO4 Films: Fractional Diffusion Analysis

Biopolymers are expected to replace synthetic polymers in the quest for cost-effective, environment friendly, and pollution free technology. We report here a study on gelatin films with different concentrations of lithium perchlorate, which may be a candidate for electrolyte material in solid polymer batteries. Morphology studies and impedance spectroscopy both are done on the same set of samples. We study the microstructure of the film by SEM and try to see if a correlation between impedance spectroscopy results and features of gel morphology can be identified. A network structure is revealed in the SEM images where details of the network parameters appear to depend on the salt fraction. Analysis of the impedance measurements is done using a physically meaningful model based on material properties instead of the usual equivalent circuit formalism, where circuit elements are difficult to interpret. We find that anomalous diffusion of charge carriers plays an important role; this is incorporated through a fractional calculus approach.