Pattern formation in the geosciences

Pattern formation is a natural property of nonlinear and non-equilibrium dynamical systems. Geophysical examples of such systems span practically all observable length scales, from rhythmic banding of chemical species within a single mineral crystal, to the morphology of cusps and spits along hundreds of kilometres of coastlines. This article briefly introduces the general principles of pattern formation and argues how they can be applied to open problems in the Earth sciences. Particular examples are then discussed, which summarize the contents of the rest of this Theme Issue

Plasticity and fracture in drying colloidal films

Cracks in drying colloidal dispersions are typically modeled by elastic fracture mechanics, which assumes that all strains are linear, elastic, and reversible. We tested this assumption in films of a hard latex, by intermittently blocking evaporation over a drying film, thereby relieving the film stress. Here we show that although the deformation around a crack tip has some features of brittle fracture, only 20%-30% of the crack opening is relieved when it is unloaded. Atomic force micrographs of crack tips also show evidence of plastic deformation, such as microcracks and particle rearrangement. Finally, we present a simple scaling argument showing that the yield stress of a drying colloidal film is generally comparable to its maximum capillary pressure, and thus that the plastic strain around a crack will normally be significant. This also suggests that a film’s fracture toughness may be increased by decreasing the interparticle adhesion

Fracture of a model cohesive granular material

We study experimentally the fracture mechanisms of a model cohesive granular medium consisting of glass beads held together by solidified polymer bridges. The elastic response of this material can be controlled by changing the cross-linking of the polymer phase, for example. Here we show that its fracture toughness can be tuned over an order of magnitude by adjusting the stiffness and size of the polymer bridges. We extract a well-defined fracture energy from fracture testing under a range of material preparations. This energy is found to scale linearly with the cross-sectional area of the bridges. Finally, X-ray microcomputed tomography shows that crack propagation is driven by adhesive failure of about one polymer bridge per bead located at the interface, along with microcracks in the vicinity of the failure plane. Our findings provide insight into the fracture mechanisms of this model material, and the mechanical properties of disordered cohesive granular media in general

A cohesive granular material with tunable elasticity

By mixing glass beads with a curable polymer we create a well-defined cohesive granular medium, held together by solidified, and hence elastic, capillary bridges. This material has a geometry similar to a wet packing of beads, but with an additional control over the elasticity of the bonds holding the particles together. We show that its mechanical response can be varied over several orders of magnitude by adjusting the size and stiffness of the bridges, and the size of the particles. We also investigate its mechanism of failure under unconfined uniaxial compression in combination with in situ x-ray microtomography. We show that a broad linear-elastic regime ends at a limiting strain of about 8%, whatever the stiffness of the agglomerate, which corresponds to the beginning of shear failure. The possibility to finely tune the stiffness, size and shape of this simple material makes it an ideal model system for investigations on, for example, fracturing of porous rocks, seismology, or root growth in cohesive porous media

The HI content of extremely metal-deficient blue compact dwarf galaxies

We have obtained new HI observations with the 100m Green Bank Telescope (GBT) for a sample of 29 extremely metal-deficient star-forming Blue Compact Dwarf (BCD) galaxies, selected from the Sloan Digital Sky Survey spectral data base to be extremely metal-deficient (12+logO/H<7.6). Neutral hydrogen was detected in 28 galaxies, a 97% detection rate. Combining the HI data with SDSS optical spectra for the BCD sample and adding complementary galaxy samples from the literature to extend the metallicity and mass ranges, we have studied how the HI content of a galaxy varies with various global galaxian properties. There is a clear trend of increasing gas mass fraction with decreasing metallicity, mass and luminosity. We obtain the relation M(HI)/L(g)~L(g)^{-0.3}, in agreement with previous studies based on samples with a smaller luminosity range. The median gas mass fraction f(gas) for the GBT sample is equal to 0.94 while the mean gas mass fraction is 0.90+/-0.15, with a lower limit of ~0.65. The HI depletion time is independent of metallicity, with a large scatter around the median value of 3.4 Gyr. The ratio of the baryonic mass to the dynamical mass of the metal-deficient BCDs varies from 0.05 to 0.80, with a median value of ~0.2. About 65% of the BCDs in our sample have an effective yield larger than the true yield, implying that the neutral gas envelope in BCDs is more metal-deficient by a factor of 1.5-20, as compared to the ionized gas.Comment: 21 pages, 13 figures, accepted for publication in MNRA

Application of ERTS-1 data to integrated state planning in the state of Maryland

There are no author-identified significant results in this report

Solidification and ordering during directional drying of a colloidal dispersion

During drying, colloidal dispersions undergo processes such as solidi cation, cracking, and the raining f interstitial pores. Here we show that the solidication of polystyrene and silica dispersions, during directional drying, occurs in two separate stages. These correspond to the initial ordering, and subsequent aggregation, of the colloidal particles. Transitions between these stages are observed as changes in transparency and color that propagate as distinct fronts along the drying layer. The dynamics of these fronts are shown to arise from a balance between compressive capillary forces, and the electrostatic and van der Waals forces described by DLVO theory. This suggests a simple method by which the maximum inter-particle repulsion between particles can be measured through the optical inspection of the dynamics of a drying dispersion, under a microscope

Wavy cracks in drying colloidal films

Fracture mechanics successfully predicts when cracks will grow. Describing the path that cracks follow, however, has remained difficult. The study of crack paths has recently focused on a single experimental system, that of thermally quenched glass, where straight, wavy, helical, and branched cracks appear under different conditions. Several models of crack path prediction have been developed but none is generally accepted. Here we show that slowly oscillating wavy cracks can form during the drying of a colloidal dispersion. These drying films are subject to large stress gradients perpendicular to the mean direction of crack growth. Under these conditions existing models do not predict periodic paths. We show, instead, how to model crack paths by allowing a growing crack to curve towards the direction of maximum energy release rate. Not only does this explain wavy cracks in drying films, and correctly describe the wavelength dependence of our experiments, but it is generally applicable to predicting crack paths in spatially varying stress fields

Drying and percolation in spatially correlated porous media

We study how the dynamics of a drying front propagating through a porous medium are affected by small-scale correlations in material properties. For this, we first present drying experiments in micro-fluidic micro-models of porous media. Here, the fluid pressures develop more intermittent dynamics as local correlations are added to the structure of the pore spaces. We also consider this problem numerically, using a model of invasion percolation with trapping, and find that there is a crossover in invasion behaviour associated with the length-scale of the disorder in the system. The critical exponents that describe large enough events are similar to the classic invasion percolation problem, while the addition of a finite correlation length significantly affects the exponent values of avalanches and bursts, up to some characteristic size. We thus find that even a weak local structure can interfere with the universality of invasion percolation phenomena. This has implications for a variety of multi-phase flow problems, such as drying, drainage, and fluid invasion

Drying dip-coated colloidal films

We present the results from a small-angle X-ray scattering (SAXS) study of lateral drying in thin films. The films, initially 10 μm thick, are cast by dip-coating a mica sheet in an aqueous silica dispersion (particle radius 8 nm, volume fraction ϕs = 0.14). During evaporation, a drying front sweeps across the film. An X-ray beam is focused on a selected spot of the film, and SAXS patterns are recorded at regular time intervals. As the film evaporates, SAXS spectra measure the ordering of particles, their volume fraction, the film thickness, and the water content, and a video camera images the solid regions of the film, recognized through their scattering of light. We find that the colloidal dispersion is first concentrated to ϕs = 0.3, where the silica particles begin to jam under the effect of their repulsive interactions. Then the particles aggregate until they form a cohesive wet solid at ϕs = 0.68 ± 0.02. Further evaporation from the wet solid leads to evacuation of water from pores of the film but leaves a residual water fraction ϕw = 0.16. The whole drying process is completed within 3 min. An important finding is that, in any spot (away from boundaries), the number of particles is conserved throughout this drying process, leading to the formation of a homogeneous deposit. This implies that no flow of particles occurs in our films during drying, a behavior distinct to that encountered in the iconic coffee-stain drying. It is argued that this type of evolution is associated with the formation of a transition region that propagates ahead of the drying front. In this region the gradient of osmotic pressure balances the drag force exerted on the particles by capillary flow toward the liquid–solid front