Hydrodynamic instabilities in shear flows of dry cohesive granular particles

Abstract

We extend the dynamic van der Waals model introduced by A. Onuki [Phys. Rev. Lett., 2005, 94, 054501] to the description of cohesive granular flows under a plane shear to study their hydrodynamic instabilities. By numerically solving the dynamic van der Waals model, we observed various heterogeneous structures of density fields in steady states, where the viscous heating is balanced with the energy dissipation caused by inelastic collisions. Based on the linear stability analysis, we found that the spatial structures are determined by the mean volume fraction, the applied shear rate, and the inelasticity, where the instability is triggered if the system is thermodynamically unstable, i.e. the pressure, p, and the volume fraction, ϕ, satisfy ∂p/∂ϕ < 0.

Kinetic theory for dilute cohesive granular gases with a square well potential

“…In our previous paper, we have demonstrated the existence of various phases for fine powders in the presence of a plane shear, which cannot be observed in granular gases under the shear [42]. We have also developed the dynamic van der Waals model in describing such a system [33] and obtain qualitatively consistent results with those in Ref. [42].…”

“…The origins of such cohesive force are, respectively, van der Waals force for fine powders and capillary force for wet granular particles [30][31][32]. Such cohesive forces can cause the liquid-gas phase transition [33], the variations of cluster formation of freely falling granular particles [34][35][36][37][38][39], and the enhancement of the jamming transition [40,41]. Thus, the study of cohesive granular materials is important for both physics and industry to treat real granular materials.…”

“…Needless to say, the kinetic theory is important to give us the microscopic basis of the macroscopic phenomenology such as Ref. [33] and the simulation results such as Ref. [42].…”

Rheological transition in simple shear of moderately dense assemblies of dry cohesive granules

“…Recent simulations [20] and theory [43] for sheared systems of cohesive frictionless particles, modeled through a Lennard-Jones potential, also reveal a transition in the rheological behavior. When cohesion is below some threshold value, dispersed particle assemblies were obtained [20].…”

“…When cohesion is below some threshold value, dispersed particle assemblies were obtained [20]. However, when the shear rate became small enough or cohesion large enough, particle assemblies became thermodynamically unstable [43] and formed various patterns.…”