When a crack is oriented by a magnetic field

Morphologies of electric-field-driven cracks in dried dispersions of ellipsoids

We report an experimental and theoretical study of the morphology of desiccation cracks formed in deposits of hematite ellipsoids dried in an externally applied alternating current (ac) electric field. A series of transitions in the crack morphology is observed by modulating the frequency and the strength of the applied field. We also found a clear transition in the morphology of cracks as a function of the aspect ratio of the ellipsoid. We show that these transitions in the crack morphology can be explained by a linear stability analysis of the equation describing the effective dynamics of an ellipsoid placed in an externally applied ac electric field.

Assisting and eliminating memory effects of paste by adding polysaccharides

A densely packed colloidal suspension, called a paste, is known to remember the direction of its motion because of its plasticity. Because the memory in the paste determines the preferential direction for crack propagation, the desiccation crack pattern morphology depends on memory of its motions (memory effect of paste). Two types of memory effects are memory of vibration and memory of flow. When a paste is dried, it usually shows an "isotropic and random cellular" desiccation crack pattern. However, when a paste is vibrated before drying and it remembers the direction of its vibrational motion, primary desiccation cracks propagate in a direction perpendicular to its vibrational motion before drying (memory of vibration). Once it flows and remembers the direction of its flow motion, primary desiccation cracks propagate in the direction parallel to its flow motion (memory of flow). Anisotropic network formation via interparticle attraction among colloidal particles in a suspension is the dominant factor affecting a paste's memory of its motion. Calcium carbonate (CaCO_{3}) paste remembers the direction of its vibrational motion, but not its own flow direction because Coulombic repulsion among charged CaCO_{3} colloidal particles prevents the formation of a network structure in a flow. For this study, we strove to assist and eliminate CaCO_{3} paste memory effects by adding polysaccharides. First, to characterize memory in paste, we propose a method of image analysis to quantify the strength and the direction of the anisotropy of desiccation crack patterns using Shannon's information entropy. Next, we conduct experiments to add polysaccharide to CaCO_{3} paste, revealing that the addition of a small amount of polysaccharide to CaCO_{3} paste assists the paste in remembering its own flow motion. Findings also indicate that the addition of a large amount of polysaccharide prevents the formation of both memories of its flow and vibrational motion and eliminates the memory effects of paste. We then perform "flocculation and sedimentation" experiments to investigate the interaction among CaCO_{3} colloidal particles in a solution. Results show that, in an aqueous solution with low polysaccharide concentration, CaCO_{3} colloidal particles flocculate each other and quickly form a sediment in a short time, whereas, in an aqueous solution with high polysaccharide concentration, a longer time is necessary for flocculation and sedimentation. Because the addition of small amounts of polysaccharides to CaCO_{3} paste induces polymer bridging between colloidal particles as interparticle attraction, it helps to produce a macroscopic network structure which retains memory of its flow motion and thereby assists the formation of memory of flow, whereas the addition of large amounts of polysaccharides induces interparticle repulsion, which prevents the formation of memory effects of all types.

Scaling mechanical instabilities in drying micellar droplets

Drying-induced mechanical instabilities in aqueous solution droplets occur primarily because, during evaporation, the central liquid minimizes the surface tension by pulling the packed gel-like region, leading to a stretching effect of the liquid region at the receding wet front. Under an appropriate scenario, it finally perturbs the gel-like zone at the droplet periphery, generating cracks, wrinkles, folds, cavities, buckles, etc. Here we report unique wrinkling patterns from evaporating sessile micellar aqueous droplets on rigid and soft substrates kept at temperatures well above the ambient. The wrinkling patterns remarkably vary depending on the material's elastic modulus and substrate, the concentration of the micellar solution (C_CTAB), and the substrate temperature (T_S). In the low concentration regime (C_CTAB ≤ 0.0364 wt%), coffee-ring-like morphologies are observed devoid of any wrinkling morphology irrespective of T_S and the substrate's elastic modulus. In the high initial concentration regime (C_CTAB ≥ 0.0364 wt%), for droplets deposited at T_S ≥ 85 °C, wrinkle formation starts at the droplet peripheral zone, radial on the stiff glass substrate, and annular on the soft cross-linked PDMS substrate. At C_CTAB ≥ 2.73 wt%, radial wrinkles on the glass substrate and annular wrinkles on the cross-linked PDMS substrate nucleate from the edges connecting to the central region of the deposit. The ratio between the width of the gel-like deposit (or wrinkle length) and the droplet's radius scales with the initial concentration of the surfactant and depends on the initial equilibrium contact angle of the micellar droplets. Our results support existing understandings of mechanical instabilities of dried deposits, which satisfies interdependent scaling relationships among their number, lengthscale (dried deposit radius, the wavelength of the wrinkles, and peripheral undulations from Rayleigh-Bénard instability), thickness, and elastic modulus. Interestingly, we found substrate-dependent antagonistic interdependence of the elastic modulus of the dried deposit with the initial surfactant concentration.

Memory effect of external oscillation on residual stress in a paste

We numerically investigate the stress distribution of a paste when an external oscillation is applied. The paste memorizes the oscillation through plastic deformation. Due to the plastic deformation, the residual stress remains after the oscillation, where the residual stress distribution depends on the number of cycles in the oscillation. As this number increases, the symmetry of the stress distribution is enhanced, which is consistent with the crack patterns observed in the experiments using a drying paste.

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.

The solute mechanical properties impact on the drying of dairy and model colloidal systems

The evaporation of colloidal solutions is frequently observed in nature and in everyday life. The investigation of the mechanisms taking place during the desiccation of biological fluids is currently a scientific challenge with potential biomedical and industrial applications. In the last few decades, seminal works have been performed mostly on dried droplets of saliva, urine and plasma. However, the full understanding of the drying process in biocolloids is far from being achieved and, notably, the impact of solute properties on the morphological characteristics of the evaporating droplets, such as colloid segregation, skin formation and crack pattern development, is still to be elucidated. For this purpose, the use of model colloidal solutions, whose rheological behavior is more easily deducible, could represent a significant boost. In this work, we compare the drying of droplets of whey proteins and casein micelles, the two main milk protein classes, to that of dispersions of silica particles and polymer-coated silica particles, respectively. The mechanical behavior of such biological colloids and model silica dispersions was investigated through the analysis of crack formation, and the measurements of their mechanical properties using indentation testing. The study reveals numerous analogies between dairy and the corresponding model systems, thus confirming the latter as a plausible powerful tool to highlight the signature of the matter at the molecular scale during the drying process.

Universal scaling of polygonal desiccation crack patterns

Polygonal desiccation crack patterns are commonly observed in natural systems. Despite their quotidian nature, it is unclear whether similar crack patterns which span orders of magnitude in length scales share the same underlying physics. In thin films, the characteristic length of polygonal cracks is known to monotonically increase with the film thickness; however, existing theories that consider the mechanical, thermodynamic, hydrodynamic, and statistical properties of cracking often lead to contradictory predictions. Here we experimentally investigate polygonal cracks in drying suspensions of micron-sized particles by varying film thickness, boundary adhesion, packing fraction, and solvent. Although polygonal cracks were observed in most systems above a critical film thickness, in cornstarch-water mixtures, multiscale crack patterns were observed due to two distinct desiccation mechanisms. Large-scale, primary polygons initially form due to capillary-induced film shrinkage, whereas small-scale, secondary polygons appear later due to the deswelling of the hygroscopic particles. In addition, we find that the characteristic area of the polygonal cracks, A_{p}, obeys a universal power law, A_{p}=αh^{4/3}, where h is the film thickness. By quantitatively linking α with the material properties during crack formation, we provide a robust framework for understanding multiscale polygonal crack patterns from microscopic to geologic scales.

Mechanism of memory effect of paste which dominates desiccation crack patterns

When a densely packed colloidal suspension, called a paste, behaves as plastic fluid, it can remember the direction of its motion it has experienced, such as vibrational motion and flow. These memories kept in paste can be visualized as the morphology of crack patterns that appear when the paste is dried. For example, when a paste remembers the direction of vibrational motion, all primary desiccation cracks propagate in the direction perpendicular to the direction of the vibrational motion that the paste has experienced. On the other hand, when a paste remembers the direction of flow motion, all primary cracks propagate along the flow direction. To find out the mechanism of memory effect of vibration, we perform experiments to rewrite memory in paste by applying additional vibration to the paste along a different direction before the paste is dried. By investigating the process of rewriting memory in paste, we find the competitive phenomena between quasi-linear effect and nonlinear effect, which were studied in each theoretical model based on residual tension theories. That is, at the initial stage of the memory-imprinting process of the vibrational motion, the mechanism predicted by the quasi-linear analysis based on residual tension theory holds, but, as the paste is vibrated repeatedly, the mechanism shown by the nonlinear analysis gradually come to play a dominant role in the memory effect.This article is part of the theme issue 'Statistical physics of fracture and earthquakes'.

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'.

Drying drops : Drying drops containing solutes: From hydrodynamical to mechanical instabilities

The drying of complex fluids involves a large number of microscopic phenomena (transport and organization of non-volatile solutes) as well as hydrodynamic and mechanical instabilities. These phenomena can be captured in drying sessile drops where different domains can be identified: strong concentration gradients, formation of a glassy or porous envelope that withstands mechanical stress, and consolidation of a layer strongly adhering to the substrate at the drop edge. In colloidal systems, we quantify the evolution of the particle volume fraction at a nanometric scale and microscopic scale and identify the conditions for the envelope formation at the free surface by balancing the effect of diffusion and evaporation. When a solid envelope is formed at a drop surface, the mechanical instabilities induced by the drying result in different drop shapes. Finally, large drying stresses build up in the solid layer adhering on the substrate, and possibly cause crack formation. In particular, we study how crack patterns are affected by the contact angle of drops and the drying conditions. A particular interest of the review is devoted to drying pattern of solutes.

Memory effect and anisotropy of particle arrangements in granular paste

It is known that pastes of fine powder, for example those of clay, retain memory of shaking applied early in a drying process. This memory results in the appearance of anisotropic patterns of desiccation cracks after drying. In this work, we find a similar behavior in pastes consisting of large granular particles, specifically cornstarch and Lycopodium spores. Because of the large particle size, we were able to observe particle arrangements in Lycopodium paste with micro-focus X-ray computerized tomography ( μ CT). We prepared pastes consisting of Lycopodium particles and water. Agar was added to the paste in order to allow for solidification during a drying process. In these samples, we found statistical anisotropy induced by shaking applied early in the drying process. This anisotropy possesses a feature that was predicted on the basis of results obtained in previous experimental and theoretical studies.

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.

Tailoring crack morphology in coffee-ring deposits via substrate heating

The drying of a sessile drop consisting of colloidal particles and the formation of particulate deposits with spatially periodic cracks were ubiquitous. The drying induced stress, which is generated during the evaporation of a colloidal drop, is released by the formation of cracks. We find that the morphology of cracks formed in particulate films dried at substrate temperature, T_sub = 25 °C is markedly different from that of cracks formed at T_sub > 45 °C. The cracks are disordered in the former case, but ordered and periodic in the latter. The disorderedness of cracks observed at T_sub = 25 °C is mainly due to the formation of a coffee-ring like particle deposit that exhibits a larger height gradient. The ultimate deposit pattern after complete drying is observed to be different for colloidal dispersion drops evaporated at different substrate temperatures. This is attributed to temperature-dependent solvent flow mechanisms and capillary-driven flow, which occur inside the colloidal drop during the course of drying. In addition, for the coffee-ring-like particulate deposit obtained at T_sub ≤ 45 °C, the ratio between the width of the deposit w and the radius of the ring R scales with the volume fraction of the colloids φ, w/R ∼ φ^0.5, in the range of volume fractions studied in this work. The deposited patterns obtained at temperature T_sub > 45 °C are largely dominated by the capture of particles by the receding liquid-vapor interface. This is due to the faster rate of decrease of the liquid-vapor interface position with an increase in substrate temperature.

Ordered fragmentation of oxide thin films at submicron scale

Crack formation is typically undesirable as it represents mechanical failure that compromises strength and integrity. Recently, there have also been numerous attempts to control crack formation in materials with the aim to prevent or isolate crack propagation. In this work, we utilize fragmentation, at submicron and nanometre scales, to create ordered metal oxide film coatings. We introduce a simple method to create modified films using electroplating on a prepatterned substrate. The modified films undergo preferential fragmentation at locations defined by the initial structures on the substrate, yielding ordered structures. In thicker films, some randomness in the characteristic sizes of the fragments is introduced due to competition between crack propagation and crack creation. The method presented allows patterning of metal oxide films over relatively large areas by controlling the fragmentation process. We demonstrate use of the method to fabricate high-performance electrochromic structures, yielding good coloration contrast and high coloration efficiency.

Fracture and related processes are typically considered detrimental, but have also attracted interest in more constructive roles. Here authors demonstrate ordered fragmentation at submicron scales of a metal oxide/hydroxide thin film by introducing preferential sites for fracture on the underlying substrate.

Magnetic-field-driven crack formation in an evaporated anisotropic colloidal assembly

We report the effect of applied magnetic field on the morphology of cracks formed after evaporation of a colloidal suspension consisting of shape-anisotropic ellipsoidal particles on a glass substrate. The evaporation experiments are performed in sessile drop configuration, which usually leads to accumulation of particles at the drop boundaries, commonly known as the "coffee-ring effect." The coffee-ring-like deposits that accompany cracks are formed in the presence as well as in the absence of magnetic field. However, the crack patterns formed in both cases are found to differ markedly. The direction of cracks in the presence of the magnetic field is found to be governed by the orientation of particles and not solely by the magnetic field direction. Our experimental results show that at the vicinity of cracks the particles are ordered and oriented with their long-axis parallel to crack direction. In addition, we observe that the crack spacing in general increases with the height of the particulate film.

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.

Surface wrinkling and cracking dynamics in the drying of colloidal droplets

The cracking behavior accompanied with the drying of colloidal droplets containing polytetrafluoroethylene (PTFE) nanoparticles was studied. During evaporation, due to the stretching effect of the liquid zone, the receding wet front leads to the formation of radialized surface wrinkling in the gel zone. This indicates the building of a macroscopic stress field with a similar distribution. As a result, the cracks in the deposited films are in a radial arrangement. The propagation velocity of the cracks depends on the thickness of the film, ∼ H (3/5). In addition, sodium dodecylsulfate (SDS) additives can be used to tune crack behavior by causing a reduction of the capillary force between particles. The results highlight the significance of the receding wet front in building the drying deposition stress field and may be helpful in other fields related to drying and cracking processes.

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.

Position control of desiccation cracks by memory effect and Faraday waves

Pattern formation of desiccation cracks on a layer of a calcium carbonate paste is studied experimentally. This paste is known to exhibit a memory effect, which means that a short-time application of horizontal vibration to the fresh paste predetermines the direction of the cracks that are formed after the paste is dried. While the position of the cracks (as opposed to their direction) is still stochastic in the case of horizontal vibration, the present work reports that their positioning is also controllable, at least to some extent, by applying vertical vibration to the paste and imprinting the pattern of Faraday waves, thus breaking the translational symmetry of the system. The experiments show that the cracks tend to appear in the node zones of the Faraday waves: in the case of stripe-patterned Faraday waves, the cracks are formed twice more frequently in the node zones than in the anti-node zones, presumably due to the localized horizontal motion. As a result of this preference of the cracks to the node zones, the memory of the square lattice pattern of Faraday waves makes the cracks run in the oblique direction differing by 45 degrees from the intuitive lattice direction of the Faraday waves.

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.

Modeling the properties of ferrogels in uniform magnetic fields

The properties of ferrogels in homogeneous magnetic fields are studied using a simple microscopic model and Monte Carlo simulations. The main phenomena of interest concern the anisotropy and enhancement of the elastic moduli that result from applying uniform magnetic fields before and after the magnetic grains are locked in to the polymer-gel matrix by cross-linking reactions. The positional organization of the magnetic grains is influenced by the application of a magnetic field during gel formation, leading to a pronounced anisotropy in the mechanical response of the ferrogel to an applied magnetic field. In particular, the elastic moduli can be enhanced to different degrees depending on the mutual orientation of the fields during and after ferrogel formation. The model represents ferrogels by ensembles of dipolar spheres dispersed in elastic matrices. Experimental trends are shown to be reflected accurately in the simulations of the microscopic model. In addition, the simulations yield microscopic insights on the organization of the magnetic grains. Finally, simple relationships between the elastic moduli and the magnetization are proposed. If supplemented by the magnetization curve, these relationships yield the dependencies of the elastic moduli on the applied magnetic field, which are often measured directly in experiments.