A very effective new method to solve the population balance equation with particle-size growth

Numerical solution of the spatially distributed population balance equation describing the hydrodynamics of interacting liquid–liquid dispersions

“…Consequently, a numerical solution is required if precise simulation of the dispersed phase processes is required. In the last two decades there are many published papers concerned with the numerical solution of many special cases of the PBE arising from the modeling of many chemical and physical processes (Gelbard and Seinfeld, 1978;Sastry and Gaschignard, 1981;Gelbard et al, 1980;Casamatta and Vogelpohl, 1985;Al Khani et al, 1988, 1989Hounslow et al, 1988;Marchal et al, 1988;Guimaraes et al, 1992;Hounslow, 1990;Kronberger et al, 1994;Hill and Ng, 1995Kronberger et al, 1995;Ribeiro et al, 1995Ribeiro et al, , 1997Zimmermann et al, 1995;Ramkrishna, 1996a,b, 1997;van Peborgh Gooch and Hounslow, 1996;Zamponi et al, 1996;Liou et al, 1997;Song et al, 1997;Nicmanis and Hounslow, 1998;Toutain et al, 1998;Vanni, 1999Vanni, , 2000Lee et al, 2001;Wulkow et al, 2001;Bennett and Rohani, 2001;Liu and Cameron, 2001;Motz et al, 2002;Lim et al, 2002;Verkoeijen et al, 2002;Mahoney and Ramkrishna, 2002;Diemer and Olson, 2002a,b;Attarakih et al, 2003a,b;Campos and Lage, 2003;Goodson and Kraft, 2003). Despite this inte...…”

Scale Up of Pan Coating Process Using Quality by Design Principles

“…In terms of spray location and spray angle, generally spraying onto the top part of the tablet bed is desirable to provide sufficient time for tablets to dry as they cascade out of the spray zone. If the pan load is low and baffles are protruding through the bed, the spray zone should be focused in the middle to avoid depositing coating material on the surface of the baffles . Spray characterization experiments can be conducted to evaluate spray gun type, solution/suspension properties, spray rate, atomization air pressure, pattern air pressure, air flow rate, and gun‐to‐bed distance and to identify adequate system requirements and operating ranges to achieve elliptical spray pattern with uniform droplet size and intensity (discussed in detail in subsequent sections).…”

“…can be simplified further to Eq. , where D is the pan diameter In the absence of pan brim volume data and lack of geometrically similar pans, one can aim to keep the h / D ratio constant across scales (Eq. )…”

“…A constant tip speed scale‐up rule amounts to using a slightly lower pan speed at larger scales in comparison to Froude number rule, and therefore also helps to reduce tablet surface abrasion that may sometimes be observed at larger scales (Fig. ) . If the tablet cores are known to have friability concerns, it is good practice to use a slightly slower speed during the initial part of the process to ensure that tablets receive a first layer of coat and then increase the speed for the remainder of the coating run.…”

“…Some scale-up rules have been developed as a guide on how to scale up some of the important thermodynamic-, pan-, and spray-related process parameters and have been proven to work successfully in the past. 7,10,11,30…”