| Extension to Smoluchowski's Population Balance Equation to Include Liquid Binder | ||
| Patrick R. Rynhart1, Robert MacLachlan1, Jim R. Jones2 and Robert McKibbin3, (1)Institute of Fundamental Sciences, Massey University, Tennant Drive, Palmerston North, New Zealand, (2)Institute of Technology and Engineering, Massey University, Tennant Drive, Palmerston North, New Zealand, (3)Institute of Information and Mathematical Sciences, Massey University, State Highway 17, Albany, Auckland, New Zealand
Extension to Smoluchowski's Population Balance Equation to Include Liquid Binder P. R. Rynhart, R. McLachlan, J. R. Jones, R. McKibbin College of Sciences, Massey University, New Zealand Tel +64 6 3569099 ext 3586 Email: P.R.Rynhart@massey.ac.nz In 1917 Smoluchowski developed a mathematical model for the coalescence of particles in a liquid suspension, which has since become established as the fundamental equation for population balance modelling of particle agglomeration. In this paper the Smoluchowski model is extended to include the effects of binder fluid by adding a system of differential equations. The extension uses the premise that the coalescence kernel is the product of the collision rate function and the sticking efficiency function, where the sticking efficiency function is dependent on the binder carried by both particles in each collision. The amount of binder is size dependent. Model results are compared for sticking efficiency functions which are; (i), size independent; (ii), the product of size µ rirj; (iii), cross section area µ (ri1/3 + rj1/3)2; and (iv), equi-partition of kinetic energy µ (ri-1/2 + rj-1/2). Extended Abstract Status: File Uploaded | ||