Topology of desiccation crack patterns in clay and invariance of crack interface area with thickness

Original · EN

We study the crack patterns developed on desiccating films of an aqueous colloidal suspension of bentonite on a glass substrate. Varying the thickness of the layer h gives the following new and interesting results: (i)We identify a critical thickness hc, above which isolated cracks join each other to form a fully connected network. A topological analysis of the crack network shows that the Euler number falls to a minimum at hc. (ii) We find further, that the total vertical surface area of the clay Aᵥ, which has opened up due to cracking, is a constant independent of the layer thickness for h ≥ hc. (iii) The total area of the glass substrate Aₛ, exposed by the hierarchical sequence of cracks is also a constant for h ≥ hc. These results are shown to be consistent with a simple energy conservation argument, neglecting dissipative losses. (iv) 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. A suspension of Laponite in methanol is found to exhibit similar salient features (i)-(iv), though in this case the crack initiation process for very thin layers is quite different.