Evolution of Tiling-like Crack Patterns in Maturing Columnar Joints.

Fracture or cracking essentially involves the formation of new interfaces. These patterns are usually studied as two-dimensional mosaics. The new surface that opens up is in the third dimension, along the thickness of the sample. The thickness is usually very small compared to the lateral dimensions of the pattern. A spectacular and distinctive departure from these everyday examples of cracks are columnar joints. Here, molten volcanic lava, by the sea, cools and cracks under appropriate thermal and elastic conditions, causing the crack system to grow downward, creating long, vertical columns with polygonal cross-section. The focus of this paper is the study of the elongated interfaces of these columns: how the cross-section of their outlines gradually undergoes a metamorphosis from a disordered-looking Gilbert tessellation to a well-ordered hexagonal Voronoi pattern. As the columns grow downward to lengths of several meters (in natural systems), their outline continuously changes, the center may shift, causing the column to twist. For the first time, the evolution of these crack mosaics has been simulated and mapped as a trajectory of a 4-vector tuple in a geometry-topology domain. The trajectory of the columnar joint systems is found to depend on the crack seed distribution and crack orientation. An empirical relationship between the system energy and the crack mosaic shape parameter λ has been proposed on the basis of principles of fracture mechanics. The total system energy shows a power-law dependence on λ with the exponent ß âˆ¼ 0.3 and λ ≈ 0.75 at crack maturation. The parameter values are validated by matching the proposed relation with energy estimates existing in the literature. The relation not only matches the visible changes in geometry but also provides a feasible measure of the energy of the system. The geometric energy for the polygonal mosaics in the transverse section has also been estimated as a function of time. The geometric energy moves toward a minimum as the mosaic becomes more Voronoi-like at maturation.

Branched crack patterns in layers of Laponite® dried under electric fields: Evidence of power-laws and fractal scalin>.

In the present work we report crack patterns formed in aqueous Laponite® gel in a rectangular box, while exposed to a uniform static electric field. The crack pattern shows a very interesting tree-like geometry extending from the positive to the negative electrode. At the positive electrode a large number of cracks appear at first and merge with each other in stages thus forming tree-like fractal structures. These structures are reminiscent of the Bethe lattice or Cayley tree. The "trees" divide the system into peds of varying size, with numerous smaller ones on the positively charged end, gradually increasing in size, and decreasing in number towards the negative end. If the cumulative distribution of the number of peds exceeding a certain area in size, is plotted against that area, a power-law relation is obtained. This implies a scale-invariant fractal character of the pattern. For a given system size, the exponent of the power-law has a nearly constant value for different applied voltages. We present an experimental study demonstrating this behaviour and discuss how it compares with similar distributions of river-basin areas and viscous fingers in a Hele-Shaw cell.

Narrowing Desiccating Crack Patterns by an Azeotropic Solvent for the Fabrication of Nanomesh Electrodes.

Desiccation of a colloidal layer produces crack patterns because of stress arising out of solvent evaporation. Associated with it is the rearrangement of particles, while adhesion to the substrate resists such movements. The nature of solvent, which is often overlooked, plays a key role in the process as it dictates evaporation and wetting properties of the colloidal film. Herein, we study the crack formation process by using a mixture of solvents, water, and isopropyl alcohol (IPA). Among the various ratios, a water/IPA mixture (15:85 by volume) close to the azeotropic composition possesses unusual evaporation and wetting properties, leading to narrower cracks with widths down to ∼162 nm, uncommon among the known crackle patterns. The dense and narrow crack patterns have been used as sacrificial templates to obtain metal meshes on transparent substrates for optoelectronic applications.

Formation of desiccation crack patterns in electric fields: a review.

Desiccation crack formation is an important and interesting part of the broad area of fracture mechanics. Generation of cracks due to drying depends on ambient conditions, which may include externally applied fields. In this review, we discuss the effect of both direct and alternating electrical fields on desiccation crack formation. After a brief introduction to materials which crack on drying, e.g. colloids, clay and ceramics we discuss how they respond to an electric field. Following that, we present an account of experiments and modelling studies performed on granular pastes or clays drying while exposed to an electric field. Specific patterns formed under different geometries, strengths and frequencies of the electric field are described and explained. The review includes work on cracks formed in clay droplets, where a memory effect has been observed and analysed using a generalized calculus formalism.This article is part of the theme issue 'Statistical physics of fracture and earthquakes'.

Crack Patterns in Drying Laponite-NaCl Suspension: Role of the Substrate and a Static Electric Field.

We report the formation of crack patterns in drying films of Laponite-NaCl solution. Crack patterns that develop upon drying aqueous Laponite-NaCl solution change drastically as the amount of NaCl is varied in the solution. In this work, we have investigated the effect of NaCl on drying films of aqueous solution of Laponite under two conditions: (i) when the film is bounded by a wall, as in Petri dish experiments and (ii) when the film does not have any boundary, as in experiments with droplets. In order to obtain insights into the effect of the substrate, the experiments have been done with two different substrates of different hydrophobicities, polypropylene and glass. The formation of crack patterns has been explained on the basis of the wetting and spreading properties of the solution on these substrates and the effect of salt on colloidal aggregation. In this work, we have shown that the presence of salt in aqueous Laponite solution can induce crack patterns depending on the nature of the substrate. Another important aspect of this work is the role of NaCl in crack inhibition in desiccating films of aqueous Laponite, in the presence of static electric field. This effect can be utilized to suppress undesirable crack formation in many applications.

Memory of Electric Field in Laponite and How It Affects Crack Formation: Modeling through Generalized Calculus.

Desiccation crack formation is affected by the presence of electric fields. We show here that the field effect not only is at work while the power supply is on but also leaves a memory even after switching off. The time required for the first appearance of cracks is shown to depend on the voltage of the field as well as the time duration of exposure. We model the system as a leaky capacitor described by a fractional order derivative in the constitutive equation. This gives a good fit to experimental data and explains the memory effect.

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 as a video clearly shows different regimes of growth leading to a variety of crystalline patterns. Large faceted crystals of ∼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 the Euler number. A minimum in the Euler number marks the transition between the two regimes of growth.

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 suspensions of three different clays-bentonite, halloysite nanoclay and laponite on a glass substrate. Varying the thickness of the layer, h gives the following new and interesting results: i) We can identify a critical thickness h c for bentonite and halloysite, above which isolated cracks join each other to form a fully connected network. ii) A topological analysis involving the Euler number is shown to be useful for characterising the patterns. iii) We find, further, that the total vertical surface area of the clay A v, which has opened up due to cracking, and the total area of the glass substrate A s, exposed by the hierarchical sequence of cracks are constant, independent of the layer thickness for a certain range of h. These results are shown to be consistent with a simple energy conservation argument, neglecting dissipative losses. 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.

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.

Electric-field-induced crack patterns: experiments and simulation.

We report a study of crack patterns formed in laponite gel drying in an electric field. The sample dries in a circular petri dish and the field is radial, acting inward or outward. A system of radial cracks forms in the setup with the center terminal positive, while predominantly cross-radial cracks form when the center is at a negative potential. The laponite accumulates near the negative terminal making the layer thicker at this end. A spring model on a square lattice is used to simulate the desiccation crack formation, with an additional radial force acting due to the electric field. With the radial force acting outward, radial cracks form and for the reversed field cross-radial cracks form. This conforms to the observation that laponite platelets become effectively positive due to overcharging and are attracted towards the negative terminal.

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.

Spreading of fluids on solids under pressure: slip and stick effects.

Spreading of different types of fluid on solids 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 positive slip coefficient. The remaining three can be explained with a negative slip coefficient, equivalent to a sticking effect.

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.

Fingering and pressure distribution in lifting Hele-Shaw cells with grooves: A computer simulation study.

We report a computer simulation study of viscous fingering patterns in a lifting Hele-Shaw cell with grooves. Here circular or square grooves concentric to the plates are etched on the lower plate. Experiments show that the presence of such grooves affect formation of viscous fingers quite strongly. We report a simulated pressure map generated in such grooved cells, when the two plates are separated with a constant force and compare the patterns with experiments. Variation in the simulated patterns for different fluid viscosity and lifting force is also studied.