Abstract
Segregation is common in granular flows consisting of mixtures of particles differing in size or density. In gravity-driven flows, both gradients in total pressure (induced by gravity) and gradients in velocity fluctuation fields (often associated with shear rate gradients) work together to govern the evolution of segregation. Since the local shear rate and velocity fluctuations are dependent on the local concentration of the components, understanding the co-evolution of segregation and flow is critical for understanding and predicting flows where there can be a variety of particle sizes and densities, such as in nature and industry. Kinetic theory has proven to be a robust framework for predicting this simultaneous evolution but has a limit in its applicability to dense systems where collisions are highly correlated. In this paper, we introduce a model that captures the coevolution of these evolving dynamics for high density gravity driven granular mixtures. For the segregation dynamics we use a recently developed mixture theory (Fan & Hill 2011, New J. Phys; Hill & Tan 2014, J. Fluid Mech.) which captures the combined effects of gravity and fluctuation fields on segregation evolution in high density granular flows. For the mixture flow dynamics, we use a recently proposed viscous-elastic-plastic constitutive model, which can describe the multi-state behaviors of granular materials, i.e. the granular solid, granular liquid and granular gas mechanical states (Fei et al. 2016, Powder Technol.). The platform we use for implementing this model is a modified Material Point Method (MPM), and we use discrete element method simulations of gravity-driven flow in an inclined channel to demonstrate that this new MPM model can predict the final segregation distribution as well as flow velocity profile well. We then discuss ongoing work where we are using this platform to test the effectiveness of particular segregation models under different boundary conditions.
Highlights
Granular materials may behave like solid, liquid or gas when they are under different load and/or dense conditions [8, 9], a unified constitutive model that can represent the mechanical behaviors of granular materials in different states is of importance in simulating granular flow segregation
The internal energy of particles inside granular materials can be divided as elastic energy and irreversible heat, the elastic energy comes from the reversible elastic contacts between particles, while the later one represents the irreversible dissipation that accompany particle interactions, such as irreversible deformation of a single particle, frictional sliding and structure rearrangement between particles
The Lagrangian material points make it simpler to trace the deformation and movement of materials when compared to traditional Eulerian method; in the end of each calculation circle, Euler background grids would be reset, accuracy loss caused by large mesh deformation in Lagrangian method is avoid [18]
Summary
Granular materials may behave like solid, liquid or gas when they are under different load and/or dense conditions [8, 9], a unified constitutive model that can represent the mechanical behaviors of granular materials in different states is of importance in simulating granular flow segregation. Material information is transferred between Lagrangian material points and Euler background gird nodes with the help of shape function. The Lagrangian material points make it simpler to trace the deformation and movement of materials when compared to traditional Eulerian method; in the end of each calculation circle, Euler background grids would be reset, accuracy loss caused by large mesh deformation in Lagrangian method is avoid [18]. MPM has the benefit of flexibility in tracking evolution of densities, velocities, and stress fields for different mechanical states of granular materials
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