Lucas Goehring

Solidification and Ordering during Directional Drying of a Colloidal Dispersion

During drying, colloidal dispersions undergo processes such as solidification, cracking, and the draining of interstitial pores. Here we show that the solidification 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 interparticle repulsion between particles can be measured through the optical inspection of the dynamics of a drying dispersion, under a microscope.

Nonequilibrium scale selection mechanism for columnar jointing

Crack patterns in laboratory experiments on thick samples of drying cornstarch are geometrically similar to columnar joints in cooling lava found at geological sites such as the Giants Causeway. We present measurements of the crack spacing from both laboratory and geological investigations of columnar jointing, and show how these data can be collapsed onto a single master scaling curve. This is due to the underlying mathematical similarity between theories for the cracking of solids induced by differential drying or by cooling. We use this theory to give a simple quantitative explanation of how these geometrically similar crack patterns arise from a single dynamical law rooted in the nonequilibrium nature of the phenomena. We also give scaling relations for the characteristic crack spacing in other limits consistent with our experiments and observations, and discuss the implications of our results for the control of crack patterns in thin and thick solid films.

Experimental investigation of the scaling of columnar joints

Columnar jointing is a fracture pattern common in igneous rocks in which cracks self-organize into a roughly hexagonal arrangement, leaving behind an ordered colonnade. We report observations of columnar jointing in a laboratory analog system, desiccated corn starch slurries. Using measurements of moisture density, evaporation rates, and fracture advance rates as evidence, we suggest that an advective-diffusive system is responsible for the rough scaling behavior of columnar joints. This theory explains the order of magnitude difference in scales between jointing in lavas and in starches. We investigated the scaling of average columnar cross-sectional areas due to the evaporation rate, the analog of the cooling rate of igneous columnar joints. We measured column areas in experiments where the evaporation rate depended on lamp height and time, in experiments where the evaporation rate was fixed using feedback methods, and in experiments where gelatin was added to vary the rheology of the starch. Our results suggest that the column area at a particular depth is related to both the current conditions, and hysteretically to the geometry of the pattern at previous depths. We argue that there exists a range of stable column scales allowed for any particular evaporation rate.

Evolution of mud-crack patterns during repeated drying cycles

In mud, crack patterns are frequently seen with either an approximately rectilinear or hexagonal tiling. Here we show, experimentally, how a desiccation crack pattern changes from being dominated by 90° joint angles, to 120° joint angles. Layers of bentonite clay, a few mm thick, were repeatedly wetted and dried. When dried, the layers crack. These cracks visibly close when rewetted, but a similar crack pattern forms when the layer is redried, with cracks forming along the lines of previously open cracks. Time-lapse photography was used to show how the sequence in which individual cracks open is different in each generation of drying. The geometry of the crack pattern was observed after each of 25 generations of wetting and drying. The angles between cracks were found to approach 120°, with a relaxation time of approximately 4 generations. This was accompanied by a gradual change in the position of the crack vertices, as the crack pattern evolved. A simple model of crack behavior in a layer where the positions of previously open cracks define lines of weakness is developed to explain these observations.

Order and disorder in columnar joints

Columnar joints are three-dimensional fracture networks that form in cooling basalt and several other media. The network organizes itself into ordered, mostly hexagonal columns. The same pattern can be observed on a smaller scale in desiccating starch. We show how surface boundary conditions in the desiccation of starch affect the formation of columnar joints. Under constant drying power conditions, we find a power law dependence of columnar cross-sectional area with depth, while under constant drying rate conditions this coarsening is eventually halted. Discontinuous transitions in pattern scale can be observed under constant external conditions, which may prompt a reinterpretation of similar transitions found in basalt. Starch patterns are statistically similar to those found in basalt, suggesting that mature columnar jointing patterns contain inherent residual disorder, but are statistically scale invariant.

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 ϕ(s) = 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 ϕ(s) = 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 ϕ(s) = 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 ϕ(w) = 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.

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.

Evolving fracture patterns: columnar joints, mud cracks and polygonal terrain.

When cracks form in a thin contracting layer, they sequentially break the layer into smaller and smaller pieces. A rectilinear crack pattern encodes information about the order of crack formation, as later cracks tend to intersect with earlier cracks at right angles. In a hexagonal pattern, in contrast, the angles between all cracks at a vertex are near 120°. Hexagonal crack patterns are typically seen when a crack network opens and heals repeatedly, in a thin layer, or advances by many intermittent steps into a thick layer. Here, it is shown how both types of pattern can arise from identical forces, and how a rectilinear crack pattern can evolve towards a hexagonal one. Such an evolution is expected when cracks undergo many opening cycles, where the cracks in any cycle are guided by the positions of cracks in the previous cycle but when they can slightly vary their position and order of opening. The general features of this evolution are outlined and compared with a review of the specific patterns of contraction cracks in dried mud, polygonal terrain, columnar joints and eroding gypsum–sand cements.

Effect of film thickness and particle size on cracking stresses in drying latex films.

The stress at which latex films crack during drying was investigated using beam bending. Two systems were investigated: (i) poly(methyl methacrylate/butyl acrylate) particles cast as thin films to examine the effect of film thickness on cracking film stress and (ii) polystyrene particles dried as drops to investigate the effect of particle size. Results indicated an inverse relationship between film thickness and film stress, whilst film stress was shown to be independent of the original particle size. These outcomes were in good agreement with Tirumkudulu and Russels theoretical analysis [M.S. Tirumkudulu and W.B. Russel, Langmuir 21 (2005) 4938], albeit the measured stress values were almost twice the theoretical estimation.

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.