A solution to the distributed parameter model of a continuous grinding mill at steady state

✍ Scribed by T.S. Mika

• Publisher: Elsevier Science
• Year: 1976
• Tongue: English
• Weight: 623 KB
• Volume: 31
• Category: Article
• ISSN: 0009-2509
• DOI: 10.1016/0009-2509(76)85069-5

✦ Synopsis

A distributed parameter model of an open-circuit size reduction device at steady state is considered. The model is applicable to tumbling or vibratory mills. Material transport is described in terms of a size-dependent axial convective velocity and a size-dependent axial dispersion coefficient. For n size fractions, the model consists of a set of n coupled ordinary differential equations of second order with two-point boundary conditions. An explicit solution to the model equations is derived for the case in which these equations are linear with constant coefficients. This corresponds to the circumstance in which the axial convective velocities, axial dispersion coefficients and the quantities used to describe the size reduction process are independent of the axial position or of the dependence of the material holdup or size distribution on axial position in the device. These assumptions are not too restrictive and the solution appears to be a useful approximation for a broad range of material-mill combinations. Applications to other process-unit operations are suggested.