Measurement of fluctuating velocities and dispersion behaviour of particles in a solid-liquid fluidised bed

Dispersion coefficient is essential to characterise the complex hydrodynamics of liquid-solid fluidised bed such as phase segregation and mixing which is often determined empirically. In this study, a more theoretical approach was utilized to estimate dispersion coefficient in a liquid solid fluidised bed system comprising glass particles (dS = 8 mm, ρS = 2230 kg m-3) and water as fluidizing medium (VL = 0.184 m s-1). The trajectory of a coloured tracer particle was tracked in time by high speed imaging and particle velocity was computed in vertical (y) and horizontal directions (x) from the particle centroids data while the z-velocity was obtained by the change in particle diameter due to its movement towards or away from the camera focal plane. The particle velocity was noted to follow a normal distribution pattern. From the velocity data, particle acceleration (-26 to 28 m s-2) was computed which revealed numerous peaks due to the contact force resulted from collisions with the neighbouring particles and column wall. The average distance between the two successive peaks were then computed to determine the mean free path (MFP) which was estimated to be 3.10-4 m and was comparable with the theoretical estimations within the order of magnitude. Finally, the solid dispersion coefficient was determined as the product of MFP and fluctuating velocity component in each direction which was obtained in the range 10-5 to 10-9 m2 s-1