Thickening theory

The design, construction and application of thickeners, centrifuges and filters is a specialised subject, and firms who have expertise in these fields should be consulted when selecting and specifying equipment for new applications. Several specialist texts on the subject are available Svarovsky (2001), Ward (2000) and Wakeman and Tarleton (1998). The theory of sedimentation processes is covered in Volume 2, Chapter 5 and filtration in Chapter 7. 

IC Sanchez. Theory of polymer crystal thickening during annealing. J Appl Phys 45 4216-4219, 1974. 

There are three kinds of diffusion (i) within the isotropic phase (ii) the interface (between the isotropic and the crystalline phases) and (iii) the crystalline phase. In the case of a polymer system, the topological nature of polymer chains assumes an important role in all three kinds of diffusion, which has been shown in the chain sliding diffusion theory proposed by Hikosaka [14,15]. It is obvious that any nucleus (a primary nucleus and a two-dimensional nucleus) and a crystal can not grow or thicken without chain sliding diffusion. 

Uassett, N. J. Industrial Chemist 37 (1961) 25. Theories of the operation of continuous thickeners. 

One of the successes of the EH theory is its ability to provide an exphcit result for the lamellar thickness, based on kinetic considerations of secondary nucleation. In the EH theory, 8L is a natural result of the steady state and not due to any subsequent thickening. The form of Eq. (1.94) is exactly the same as Eq. (1.1), observed experimentally. However, one of the serious difficulties posed by Eq. (1.94) is that it predicts a divergence in 5L at... 

The ultramicroscopic examination of a gelatinising sol reveals the presence of very small particles termed ultramicrons, it is assumed on the fibrillar theory that the ultramicrons aggregate to invisible threads or fibrils. As the gelatinisation proceeds the fibrils thicken and lengthen and in many cases may actually be rendered visible by powerful magnification under the microscope. The fibrils are diffused at random in the form of a felt through the material and may, as we have noted, be markedly crystalline in the filamentous, somewhat flexible in the fibrillary and distinctly mobile and flexible in the streptrococcic forms visible under the microscope. 

The addition of a new chain at the growth front is not hindered by a barrier, in contradiction with the underlying assumptions of the LH theory. Simultaneous to the addition of new chains at the growth front, chains inside the lamella move cooperatively. The center of mass of the lamella diffuses in space while the lamella thickens by a process of internal rearrangements for details, see [30]. The mean squared displacement of a labeled monomer varies with the elapsed time, t, with an effective power law of t0Ji by shuffling back and forth between the lamellar and amorphous regions. 

There are three chapters in this volume, two of which address the microscale. Ploehn and Russel address the Interactions Between Colloidal Particles and Soluble Polymers, which is motivated by advances in statistical mechanics and scaling theories, as well as by the importance of numerous polymeric flocculants, dispersants, surfactants, and thickeners. How do polymers thicken ketchup Adler, Nadim, and Brenner address Rheological Models of Suspensions, a closely related subject through fluid mechanics, statistical physics, and continuum theory. Their work is also inspired by industrial processes such as paint, pulp and paper, and concrete and by natural systems such as blood flow and the transportation of sediment in oceans and rivers. Why did doctors in the Middle Ages induce bleeding in their patients in order to thin their blood ... 

Polymer crystal growth is predominantly in the lateral direction, because folds and surface entanglements inhibit crystalliza- 4 don in the thickness direction. Neverthe-1 less, there is a considerable increase in the fold period behind the lamellar front during crystallization from the melt and, as we have j seen, polymers annealed above their crys-tallization temperature but below Tm also irreversibly thicken. Nevertheless, in most theories of secondary nucleation, the most i widely used being the theory of Lauritzen and Hoffman,28 it is assumed that once a part of a chain is added to the growing crystal, its. fold period remains unchanged. 

An anaerobic digester is a no-recycle complete mix reactor. Thus, its performance is independent of organic loading but is controlled by hydraulic retention time (HRT). Based on kinetic theory and values of the pseudo constants for methane bacteria, a minimum HRT of 3 to 4 days is required. To provide a safety factor and compensate for load variation as indicated earlier, HRT is kept in the range 10 to 30 days. Thickening of feed sludge is used to reduce the tank volume required... 

---