Polydisperse granular flows over inclined channels

This thesis focuses on modelling the dynamics of dense granular materials flowing over an inclined channel, utilising a continuum description. In the process of understanding and developing this, besides continuum modelling, the thesis also exhibits the utility of discrete particle simulations (DPMs), and the need for developing an accurate micro-macro mapping technique. As most of these dense gravity-driven flows are shallow in nature, for monodisperse mixtures, Chapter 2 illustrates the formulation of a novel one -- dimensional (width- and depth-averaged) shallow granular model. Using this model, we not only predict the flow dynamics -- flow height, velocity and granular jumps or shocks -- but also shows that one can forecast the existence of multiple steady states for a given a range of channel inclinations. However, in reality, the majority of flowing particulate mixtures are known to comprise of particles with varied physical attributes, i.e. they are bidisperse or polydisperse. Thereby, as a step towards understanding the associated flow dynamics, and developing improved continuum models, several studies presented in this thesis have utilised discrete particle method. DPMs provide a plethora of information at a particle scale, such as particle position, velocity, interaction forces or stresses. In order to accurately map the particle scale mechanics onto a macroscopic continuum scale, Chapter 3 comprehensively presents a generic framework for an efficient and accurate micro-macro mapping technique for polydisperse mixtures comprising of convex shaped particles, e.g. spheres. More importantly, the method presented is valid for any discrete data, e.g. particle simulations, molecular dynamics and experimental data, for both steady and unsteady configurations. Before employing the efficient mapping technique of Chapter 3 to its full capacity, based on the current understanding of bidisperse segregation dynamics, we formulate in Chapter 4 a mixture theory segregation model for bidisperse mixtures varying both in size and density. The developed formulation is an extension to an already existing size-segregation model, and is applicable to both shallow (linear velocity profile) and thick (Bagnold profile) flows. Besides predicting the extent of segregation, the theory also predicts zero or weak segregation for a range of size and density ratios, which was further benchmarked using DPMs. Although, we developed an efficient continuum size- and density-segregation model, a detailed study is to be implemented in order to determine more accurate pressure scalings and further extend it to polydisperse mixtures. As a stepping stone, towards determining these pressure scalings, in Chapter 5 we give an example application of the micro-macro mapping technique (illustrated in Chapter 3). For simplicity, we consider a purely size-based segregation model, which was built upon a pressure scaling function containing an unknown parameter. Not only did we determine this unknown material parameter but, more importantly, we also found out that the complete size- and density-based segregation in any flowing particulate mixture is an effect of the generated kinetic stress, rather than the contact stress. The current form of the existing scaling functions is, however, still an active area of research, which definitely needs further attention and care. Chapters 3, 4 and 5, show how one can mix and match continuum models with DPMs using an efficient coarse-graining method. However, it is still vital to see if the DPMs can actually emulate reality. As a consequence, we illustrate in Chapter 6, how DPMs can be used as a suitable alternative to experiments using two commonly used DPM experiments.