Eur. Phys. J. E (2015) 38: 83
https://doi.org/10.1140/epje/i2015-15083-6

Regular Article

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

¹ Condensed Matter Physics Research Centre, Physics Department, Jadavpur University, 700032, Kolkata, India
² Physics Department, Charuchandra College, 700029, Kolkata, India
³ Physics Department, St. Xavier’s College, 700016, Kolkata, India

^* e-mail: tajkerakhatun88@gmail.com
^** e-mail: tapati_mithu@yahoo.com
^*** e-mail: sujata_tarafdar@hotmail.com

Received: 5 January 2015
Revised: 16 May 2015
Accepted: 25 June 2015
Published online: 10 August 2015

Abstract

We study the crack patterns developed on desiccating films of suspensions of three different clays—bentonite, halloysite nanoclay and laponite on a glass substrate. Varying the thickness of the layer, h gives the following new and interesting results: i) We can identify a critical thickness h _c for bentonite and halloysite, above which isolated cracks join each other to form a fully connected network. ii) A topological analysis involving the Euler number is shown to be useful for characterising the patterns. iii) We find, further, that the total vertical surface area of the clay A _v, which has opened up due to cracking, and the total area of the glass substrate A _s, exposed by the hierarchical sequence of cracks are constant, independent of the layer thickness for a certain range of h. These results are shown to be consistent with a simple energy conservation argument, neglecting dissipative losses. 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.