Investigation of an intensifier-bar tumble bin scale-up model

Abstract

In recent years, more and more powder blending operations have been augmented with the addition of an intensifier bar (I-bar) in a tumble bin. While the tumble bin rotates with rotational speeds of 5–20rpm, I-bars rotate at 1000–4000rpm, with tip speeds of ~14–19m/s. I-bars thus impart significant mechanical dispersive energy into the blend, both in terms of shear stress and in terms of shear strain.Because I-bars impart so much energy into the blend, it is critically important to devise a good scale-up strategy, thus ensuring that blending conditions that have been established at a small scale can be reliably reproduced at a large scale. In this work, the blending process is described using a first order rate constant, k, to describe the fraction of powder that has been processed by the I-bar. A mathematical model is derived to predict how k changes when scaling to a larger tumble bin with a larger I-bar running at a different tip-speed. The model indicates that the quantity vLD2/V4/3 largely determines the blending rate during scale-up where v, L, D, and V, denote the I-bar tip speed, I-bar length, I-bar diameter, and tumble bin volume, respectively. To keep the extent of blending constant between two scales, we find that the dimensionless number vLD2t/V4/3 should be held constant where t is the blending time.Experimental data are summarized and used to assess the validity of the scale-up model. A novel characterization method involving tracer particles and X-ray image analysis was developed and used to quantify the extent of mixing. Experimental data are provided from 59 blends, covering a range of tumble bin scales from 8L to 700L, and producing 296 samples that were analyzed by X-ray imaging. The data show that the process can be reasonably approximated by a first order rate equation, with the rate constant being linearly proportional to vLD2/V4/3.