Shrinkage kinetics

Many theories describe the shrinkage kinetics during hot pressing. ... 

Gabas, A.L., Telis-Romero, J., and Menegalli, EC. Determination of concentration dependent effective moisture diffusivity of plums based on shrinkage kinetics. Transport Phenomena in Food Processing, J. Welti-Chanes, J.F. Velez-Ruiz and G.V. Barbosa-Canovas, eds., CRC Press, Boca Raton, FL, pp. 153, 2002. 

Two sets of keys open the way to understanding solidification. One is the basics of phase equilibria - liquid-vapor, liquid-liquid, and liquid-solid - of reaction equilibria, polymer gelation and vitrification, and colloidal transitions. The other is heat and mass transport processes reaction, transformation, and shrinkage kinetics and stress phenomena in polymeric systems and polymer-particulate composites. Engineering approximations... 

D.C. Watts, A. al Hindi, Intrinsic soft-start polymerization shrinkage-kinetics in an acrylate-based resin-composite. Dent. Mater. 15 (1999) 39-45. 

Key words rheology, shrinkage, kinetics, swelling, evaporation, radio-opaque, solvent exchange, chemical gel. 

With this equation, the temporal profile of porosity during the SPS of A1 powder can be derived numerically, with the available experimentally measured temporal profile of temperature, together with the applied voltage gradient and constant pressure. It is found that the model satisfactorily predicts the shrinkage kinetics of the powder compacts. 

The viscous flow mechanism, which was first proposed by Frenkel," can be operative in the sintering of viscous materials like glass. If the material follows the behaviour of a Newtonian fluid, the neck growth and shrinkage kinetics are expressed as follows. 

Figure 11.37 Shrinkage kinetics for unconstrained thick film of gold particles and LTCC tape consisting of cordierite and glass particles. The data points are fitted with smooth curves. (From Ref 52.)...

Figure 12.2 Schematic diagram of a dual push-rod dilatometer for continuous monitoring of shrinkage kinetics.

We propose some models (both phenomenological and computer ones), which allow one to analyze the influence of a nanoshell s size and structure on the process of its shrinkage into a solid nanoparticle and to estimate the stability of nanoshells. Shrinkage kinetics and collapse time are generally determined by a slowly diffusing component, which makes nanoshells more stable than expected. 

Thus, the smaller the ratio D JD%, the sharper is the segregation at the boundaries. The shrinkage kinetics is governed by the equations... 

Figure 7.8 Nanoshell shrinkage kinetics (only equatorial cross sections are given) in vacuum for the pure element (a, b, c) and for the alloy (d, e, f) a, d - initial configuration, b, e - after 1800 MCS, c, f - after 3600 MCS.

The steady state approximation for both vacancies and atoms provides a reasonable and simple scheme for predicting the shrinkage kinetics. In order to properly describe the details of segregation, one must take into account the non-steady state redistribution of atoms however, the steady state for vacancies can also be used. kMC simulations confirm the main predictions of the phenomenological models. 

SpineU, T., Schedle, A., Watts, D.C., 2009. Polymerization shrinkage kinetics of dimethacrylate resin-cements. Dental Materials 25, 1058—1066. 

Polymerization reactions of multifunctional monomers such as those used in dental restorations occur in the high crosslinking regime where anomalous behavior is often observed, especially with respect to reaction kinetics. This behavior includes auto acceleration and autodeceleration [108-112], incomplete functional group conversion [108,109,113-116], a delay in volume shrinkage with respect to equilibrium [108, 117,118], and unequal functional group reactivity [119-121]. Figures 3 and 4 show a typical rate of polymerization for a multifunctional monomer as a function of time and conversion, respectively. Several distinctive features of the polymerization are apparent in the rate profiles. 

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