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

摘要

We study the crack patterns developed on desiccating films of an aqueouscolloidal suspension of bentonite on a glass substrate. Varying the thicknessof the layer $h$ gives the following new and interesting results: (i)Weidentify a critical thickness $h_{c}$, above which isolated cracks join eachother to form a fully connected network. A topological analysis of the cracknetwork shows that the Euler number falls to a minimum at $h_{c}$. (ii) We findfurther, that the total vertical surface area of the clay $A_v$, which hasopened 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 thehierarchical sequence of cracks is also a constant for $h \geq h_c$. Theseresults are shown to be consistent with a simple energy conservation argument,neglecting dissipative losses. (iv) Finally we show that if the crack patternis viewed at successively finer resolution, the total cumulative area of cracksvisible at a certain resolution, scales with the layer thickness. A suspensionof 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 quitedifferent.