Constitutive laws in liquid-fluidized beds

The objective of the present work is to test experimentally the two-phase modelling approach which is widely used in fluidization. A difficulty of this way of modelling fluidized beds is the use of empirical relations in order to close the system of equations describing the fluidized bed as a two-phase continuum, especially concerning the description of the solid phase. We performed an experimental investigation of the primary wavy instability of liquid-fluidized beds. Experiments demonstrate that the wave amplitude saturates up the bed and we were able to measure the precise shape of this voidage wave. We then related this shape to the unknown solid phase viscosity and pressure functions of a simple two-phase model with a Newtonian stress-tensor for the solid phase. We found the scaling laws and the particle concentration dependence for these two quantities. It appears that this simplest model is quite satisfactory to describe the one-dimensional voidage waves in the limited range of parameters that we have studied. In our experimental conditions, the drag on the particles nearly balances their weight corrected for buoyancy, the small imbalance being mostly accounted for by solid phase viscous stress with a much smaller contribution from the solid phase pressure.