Cohesion mediated layering in sheared grains

We consider pattern formation in a sheared dense mixture of cohesive and non-cohesive grains. Our findings show that cohesive grains, which would typically form distributed agglomerates, instead segregate into percolating stripes or layers when the cohesive grain concentration ($c_o$) and cohesion strength ($C$) increase -- in a way that the average agglomerate size and the average normal stress collapse onto a single curve when plotted against $c_oC$. Our central proposal is that the development of interfaces between cohesive and non-cohesive grains is akin to phase separation in binary molecular mixtures driven by an effective free energy, although we are dealing with a non-equilibrium system; we setup the segregation flux such that the effect of this free energy is activated only upon application of the external driving. By constructing the segregation flux proportional to the gradient of the variational derivative of the free energy, we closely reproduce the layering in the steady-state limit. We find a robust correspondence between the parameter $c_o C$ in the discrete simulations and the parameters in the free energy.