Abstract

We introduce a continuum framework for the energetics of particle-size segregation in bidisperse granular flows. Building on continuum segregation equations and a recent segregation flux model, the proposed framework offers general analytical expressions to study the physics of granular flows from a mechanical energy perspective. To demonstrate the framework's applicability, we examined the energetics in shear-driven granular flows. Numerical experiments with varying frictional coefficients and particle-size ratios reveal two distinct phases in the energetics, marked by the separate onset of particle segregation and diffusive remixing. Furthermore, our numerical simulations alongside previous experimental results show that the bulk Richardson number Ri, defined as the potential energy to kinetic energy ratio at steady state, follows the scaling relationship Ri equivalent to E<^>((s))(gp)/E<^>((s))(k)proportional to Pe(sr)(-1/2) for 0.1 <= Ri <= 10(3)and 10(-4) <= Pe(sr)<= 300, the segregation-rheology Peclet number. Finally, we present a Peclet-number-dependent theoretical expression for the degree of mixing (or segregation), validated by the compiled numerical and experimental dataset. Our findings hint that the bulk segregation-mixing state can be predicted and controlled using the segregation Peclet number Pe and Pe(sr), both determined from known system parameters, providing an instrumental tool for engineering and geophysical applications.