THE production of many goods, ranging from pharmaceuticals and foods to polymers and semiconductors, depends on reliable, uniform mixing of solids. Although there have been several notable recent advances1-6, solid mixing processes are still poorly understood. We can neither qualitatively nor quantitively determine the effectiveness of any given mixing process in advance. In contrast to the case of liquid mixing7, we do not have a widely accepted theoretical basis that describes the mixing of solids. Moreover, we cannot determine whether a given set of solids will mix or separate during a specified stirring process8-23. As a step towards uncovering the basic physical principles, it is helpful to analyse systems that are both experimentally and theoretically tractable. Here we describe a geometric technique for the analysis of slow granular mixing processes, as are commonly encountered in industry. By comparing our calculations with experiments on thin rotating containers partially filled with coloured particles, we demonstrate that the mixing behaviour of powders in slow flows can be divided into geometric and dynamic parts. For monodisperse, weakly cohesive particles, geometric aspects dominate.
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