Tree-like crack patterns in clay dried in a uniform DC electric field

We report desiccation crack formation on a layer of aqueous Laponite$^{\textregistered}$ RD gel, exposed to a uniform static electric field varying from 357 to 928 V/m. The cracks formed exhibit an interesting tree-like pattern. A large number of cracks $(\sim70)$ appear initially at the positive end of the sample. Several neighbouring cracks merge with each other, while proceeding towards the negative end leading to a smaller number of cracks. This process is repeated a few times before the hierarchical pattern thus formed reaches the negative end of the sample. The number of cracks is finally reduced to $\sim10$. The initial number of cracks increases with increasing field strength. The disc-like Laponite$^{\textregistered}$ RD clay particles behave as negatively charged in an aqueous medium, because of the diffusion of positive counterions into the solvent, which form a double layer. The external field causes gradual build up of density of positive counterions towards the negative electrode. The bare Laponite$^{\textregistered}$ discs which are negatively charged repel each other to create the cracks at the positive end. We develop a simple model to calculate the charge distribution of counterions along the sample. We offer an explanation for the structure of the anisotropic tree-like crack patterns observed on the basis of this model.