Flows Of Particle-laden Bingham Fluids In A Hele-Shaw Cell
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S. Boronin, A. Osiptsov & J. Desroches
We consider the multiphase flow of immiscible particle-laden Bingham fluids in a Hele-Shaw cell. The flow is described within the framework of interpenetrating-continua model with account for particle velocity slip. Using lubrication approximation, a system of governing equations is reduced to a quasilinear equation in terms of pressure and transport equations for volume concentrations of fluids and particles. The numerical solution is obtained on a rectangular mesh using a finite-difference method. The pressure equation is solved using an iterative algorithm and preconditioned Bi-Conjugated Gradient- Stabilized method, while transport equations are solved using a second-order TVD flux-limiting scheme with the Superbee limiter. The model and numerical algorithm are validated against experiments on particle-free gravitational slumping and viscous fingering, as well as against experiments of particle-laden suspension flow with sediment layer growth. In particular, particle transport and settling are validated against experimental data and an analytical formula for the height of a packed bed. Numerical simulations show that the slumping rate of Bingham fluid is significantly less pronounced than that of a Newtonian fluid with the same density and viscosity. If a low viscosity fluid is injected after the Bingham one, the Saffman-Taylor instability at the interface leads to the development of fingers and origination of unyielded zones. Keywords: Bingham rheology, viscous fingering, gravitational slumping, particles, Hele-Shaw cell.
Keywords: Bingham rheology, viscous fingering, gravitational slumping, particles, Hele-Shaw cell.