The Apparent Viscosity of the Particulate Phase of Bubbling Gas-Fluidized Beds: A Comparison of the Falling or Rising Sphere Technique with Other Methods

Literature concerned with measuring the apparent viscosity of the particulate phase, μfluid(mf), of a bubbling, gas-fluidized bed is reviewed. It is demonstrated that values of μfluid(mf) derived from measurements using a falling or rising sphere compare favourably with results from other techniques. The measurements of Daniels (1959) for the terminal velocities of descent of various metallic spheres in incipiently fluidized beds have been analysed to obtain values for μfluid(mf). For the systems considered here: (1) the terminal velocity for each sphere was proportional to its diameter squared, and (2) each value derived for μfluid(mf) was independent of the rate of shear. This allowed the sphere‘s movement to be analysed using a modified form of Stokes’ law in the same manner as Rees et al. (2005); their analysis allowed for a defluidized hood of bed-particles resting on top of the sphere.Comparison of values of μfluid(mf) in the literature for bed-materials with diameters of 60–550 μm (mostly sand or glass ballotini) demonstrate that μfluid(mf) increases with the size of the bed-particles. A value of μfluid(mf) = 1 kg m−1 s−1 appears appropriate for a Group B solid [from the classification of Geldart (1973)], if no better information is available.