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arXiv · 2505.24114

The 'Brazil-nut effect' in bidisperse particle laden flow on an incline

Jack Luong·Sarah Cassie Burnett·Andrea L. Bertozzi
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Abstract

We study bidisperse suspensions -- suspensions where there are two particle species of the same density but different sizes -- of a viscous fluid on an incline. We use a lubrication theory/thin film model to form a hyperbolic system of three conservation laws for the height and particle volume fractions. The model predicts, over a range of parameters, that the larger particles rise to the top of the layer, consistent with the well-known `Brazil-nut effect' for granular media. The model predicts well-separated fronts of the two species of particles, behind a clear fluid front, at lower inclination angles and volume fractions. This corresponds to a triple shock structure in the system of conservations. At higher inclination angles and volume fractions the particles congregate at a high concentration at the leading front corresponding to a singular shock in the model. We find excellent agreement between theory and experiments in terms of the overall dynamic structures as the parameters vary.

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Jack Luong, Sarah Cassie Burnett, Andrea L. Bertozzi. 2025-05-30. The 'Brazil-nut effect' in bidisperse particle laden flow on an incline. https://arxiv.org/abs/2505.24114

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