From discrete particles to continuum fields in mixtures

We present a novel way to extract continuum fields from discrete particle systems that is applicable to flowing mixtures as well as boundaries and interfaces. The mass and momentum balance equations for mixed flows are expressed in terms of the partial densities, velocities, stresses and interaction terms for each constituent. Expressions for these variables in terms of the microscopic quantities are derived by coarse-graining the balance equations, and thus satisfy them exactly. A simple physical argument is used to apportion the interaction forces to the constituents. Discrete element simulations of granular chute flows are presented to illustrate the strengths of the new boundary/mixture treatment. We apply the mixture formulation to confirm two assumptions on the segregation dynamics in particle simulations of bidispersed chute flows: Firstly, the large constituent supports a fraction of the stress that is higher than their volume fraction. Secondly, the interaction force between the constituents follows a drag law that causes the large particles to segregate to the surface. Furthermore, smaller particles support disproportionally high kinetic stress, which is a prediction of the theory on shear-induced segregation.