Complex interactions of fluids and granular media 

Marc A. Habisreutinger1  and Ivan Lunati1

1University of Lausanne – Institute of geophysics, Lausanne, Vaud, Switzerland

ABSTRACT:  

In this study, we focus on the interaction between a Newtonian fluid and a granular medium. In the framework of the Jackson equations, we describe the system as a double continuum, in which the fluid and the solid phase interpenetrate and interact.

If the granular skeleton is static, the closure of these equations is quite straightforward and the fluid momentum equation reduces to the Brinkman equation, which allows coupling flow in porous media and free fluid flow. If the solid skeleton is deformable, more complex phenomena arise from the interaction between fluid and solid phase. This requires explicit modeling of momentum transfer in the solid, which is considered as a viscoelastic medium. 

 In the general case, in which the granular medium can behave as a solid or as fluid, describing the transition between a solid-like dense packing and a fluidized granular medium is a challenge. The difficulty originates from fundamental characteristics of granular matter such as negligible thermal fluctuations, highly dissipative interactions, and a lack of separation between the microscopic grain scale and the macroscopic scale of the flow.

Using a unified rheology for suspensions and granular fluids proposed by Boyer et al. (PRL 107, 188301, 2011), we numerically investigate processes like sedimentation of a granular suspension, granular Rayleigh-Taylor instability, or decompaction waves in granular media.