Angular circulation speed of tablets in a vibratory tablet coating pan.

In this work, a single tablet model and a discrete element method (DEM) computer simulation are developed to obtain the angular circulation speed of tablets in a vibratory tablet coating pan for range of vibration frequencies and amplitudes. The models identify three important dimensionless parameters that influence the speed of the tablets: the dimensionless amplitude ratio (a/R), the Froude number (aω2/g), and the tablet-wall friction coefficient, where a is the peak vibration amplitude at the drum center, ω is the vibration angular frequency, R is the drum radius, and g is the acceleration due to gravity. The models predict that the angular circulation speed of tablets increases with an increase in each of these parameters. The rate of increase in the angular circulation speed is observed to decrease for larger values of a/R. The angular circulation speed reaches an asymptote beyond a tablet-wall friction coefficient value of about 0.4. Furthermore, it is found that the Froude number should be greater than one for the tablets to start circulating. The angular circulation speed increases as Froude number increases but then does not change significantly at larger values of the Froude number. Period doubling, where the motion of the bed is repeated every two cycles, occurs at a Froude number larger than five. The single tablet model, although much simpler than the DEM model, is able to predict the maximum circulation speed (the limiting case for a large value of tablet-wall friction coefficient) as well as the transition to period doubling.