This paper is devoted to an unresolved model for the simulation of air invasion in immersed granular flows without interface reconstruction between the liquid and the gas. Experiments of air invading a granular bed immersed in ethanol were achieved in a Hele-Shaw cell to observe the gas invasion paths and to calibrate the numerical multiscale model. The grains movements are computed at a fine scale using the non-smooth contact dynamics method, a time-stepping method considering impenetrable grains. The fluid flow is modelled by equations averaged using the volume fraction of fluid and computed at a coarse scale with the finite element method. A phase indicator function is used to dissociate the gas and the liquid constituting the fluid and to compute the density and viscosity of the fluid at each position. It is moved using a convection equation at each time step. The fluid, solid and phase indicator function computations are validated on simple cases before being used to reproduce experiments of air invasion in immersed granular flows. The experiments are supported by simulations in two dimensions to refine the study and the understanding of the invasion dynamics at short times.

The drag exerted on an object moving in a granular medium is subject to many studies: in dry grains, it depends on the stress -often due to gravity -inside the grains. For Froude numbers less than 10, the drag is independent of the velocity. In immersed grains, it is proportional to the apparent weight of the grains and it depends on both velocity and fluid viscosity. In this paper, the drag on a cylinder in dry and immersed granular flow is simulated with a multi-scale FEM-DEM model. The Janssen stress saturation effect before the flow and velocity independence of the drag are both reproduced. The semi-circular orientation of the stress field supports the hypothesis of a spherical zone of influence of the cylinder. This orientation does not significantly change upon flowing. The results show the velocity independence of the drag is due to particle friction. In the immersed case, the fluid contribution is negligible on its own. A dimensional analysis suggests that shear thickening should be taken into account. The transition between the quasi-static and the fluidized regime is accompanied by a decrease of the stress field downstream of the cylinder and a change in the shape of the shear zone. KeywordsGranular drag • Janssen effect • Nonsmooth contact dynamics • Unresolved model • MigFlow B Nathan Coppin

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