Models of Flow-Induced Crystallization

Coleman CJ, Tullock D, Phan-Thien N (1991) An effective boundary element method for inhomogeneous partial differential equations. Z Angew Math Phys 42 730-745 Coppola S, Grizzuiti N, Maffettone PL (2001) Microrheological modeling of flow-induced crystallization. Macromol 34 5030-5036... 

Zheng R, Tanner RI, Lee Wo D, Fan XJ, Hadinata C, Costa FS, Kennedy PK, Zhu P, Edward G (2010) Modeling of flow-induced crystallization of colored polypropylene in injection molding. Korea-Australia Rheol J 22 151-162... 

Zuidema, H., Peters, G.W.M. and Meijer, H.E.H. (2002) Development and validation of a recoverable strain based model for flow-induced crystallization of polymers, Macromol. Theory Simul. 10(5), 447-460... 

Fig. 24 Schematic pictures of flow-induced crystallization from the polymer melt (a) for the random coil model (b) using the folded-chain fringed-micellar grain model...

Doufas AK, Dairanieh IS, McHugh AJ (1999) A continuum model for flow-induced crystallization of polymer melts. J Rheol 43 85-109 Doufas AK, McHugh AJ, Miller C (2000) Simulation of melt spinning including flow-induced crystallization. Part I. Model development an predictions. J Non-Newtonian Fluid Mech 92 27-66... 

Validity of Equation (13.8) was verified by computer simulation of spherulitic crystallization [85]. Figure 13.4a shows plots of conversion degree versus time for the case of isothermal crystallization (G = const) whereas Figure 13.4b illustrates the exemplary computer simulated spherulitc pattern. It has to be mentioned that the above described model can be also useful to some extent in the case of flow-induced crystallization with row nuclei. 

A. K. Doufas, A. J. McHugh, and C. Miller, Simulation of Melt Spinning Including Flow-induced Crystallization. Part I. Model Development and Predictions, J. Non-Newt. Fluid Meek, 92, 27-66 (2000). 

Curran DAS, Cross MM, Lewis BA (1980) Solution of parabolic differential equations by the boundary element method using discretization in time. Appl Math Model 4 398-400 Dai SC, Qi F, Tanner RI (2006) Strain and strain-rate formulation for flow-induced crystallization. Polym Eng Sci 46 659-669... 

Oriented Crystallization.—Hoffman " has developed a theory for the growth of fibrous crystals with extended-chain morphology i.e., the core fibril or shish which develops on flow-induced crystallization. An embryonic fibril connected by bundle nuclei is produced. End surfaces resulting from the repulsion of amorphous chains in the regions between the nuclei build up commutatively as the nuclei mature. Volume strain in each nuclei limit the diameter of the core fibril to 15—50 nm. The model leads to a set of extended chains crystallites of stable diameters interrupted by short and highly strained amorphous regions. 

Important topics in this area are the use of chaotic nfixing to improve compounding [221], and modeling that includes flow-induced crystallization during molding processes. 

With the advent of sophisticated simulation techniques, the physics of the flow-enhanced nucleation process at the molecular level are gradually being unraveled (see Chapter 6). The results of such investigations can serve to validate and/or improve continuum-level FIC models. Some of the most advanced of these are compared here in terms of the formulation of flow-enhanced nucleation kinetics. A description of flow-induced oriented structure formation and application to IM are discussed in Section 14.4.2 and Section 14.4.3, respectively. We focus on models that calculate the number density and dimensions of nuclei since this is necessary to predict morphological features beyond merely the degree of crystallization or the volume fraction of semicrystalline material. Therefore, approaches based on a (modified) Nakamura equation are left out of consideration. 

Theoretical representation of the behaviour of a hydrocyclone requires adequate analysis of three distinct physical phenomenon taking place in these devices, viz. the understanding of fluid flow, its interactions with the dispersed solid phase and the quantification of shear induced attrition of crystals. Simplified analytical solutions to conservation of mass and momentum equations derived from the Navier-Stokes equation can be used to quantify fluid flow in the hydrocyclone. For dilute slurries, once bulk flow has been quantified in terms of spatial components of velocity, crystal motion can then be traced by balancing forces on the crystals themselves to map out their trajectories. The trajectories for different sizes can then be used to develop a separation efficiency curve, which quantifies performance of the vessel (Bloor and Ingham, 1987). In principle, population balances can be included for crystal attrition in the above description for developing a thorough mathematical model. 

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