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

TL;DR

This study investigates the topology and invariant properties of crack patterns in desiccating clay films, revealing a critical thickness for network connectivity and constant crack interface areas beyond this threshold, supported by energy conservation principles.

Contribution

It introduces the concept of a critical thickness for crack network formation and demonstrates invariance of crack interface areas in desiccating clay films, supported by topological and energy analyses.

Findings

Identification of a critical thickness $h_c$ for crack network connectivity.

Invariance of total crack interface area and exposed substrate area for $h \,\geq\, h_c$.

Scaling of cumulative crack area with layer thickness at finer resolutions.

Abstract

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 $h_{c}$, 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 $h_{c}$. (ii) We find further, that the total vertical surface area of the clay $A_v$, which has opened up due to cracking, is a constant independent of the layer thickness for $h \geq h_c$. (iii) The total area of the glass substrate $A_s$, exposed by the hierarchical sequence of cracks is also a constant for $h \geq h_c$. 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.