Isothermal impingement

Trapaga and Szekely 515 conducted a mathematical modeling study of the isothermal impingement of liquid droplets in spray processes using a commercial CFD code called FLOW-3D. Their model is similar to that of Harlow and Shannon 397 except that viscosity and surface tension were included and wetting was simulated with a contact angle of 10°. In a subsequent study, 371 heat transfer and solidification phenomena were also addressed. These studies provided detailed... 

The kinetic theory presented by Johnson and Mehl [2] and Avrami [3] predicts the volume fraction transformed, as a function of time, t, during an isothermal phase transformation. The derivation of the Johnson-Mehl-Avrami kinetics is based on the grouping of the three individual partial processes, that is, nucleation, growth, and impingement of growing particles [5],... 

In obtaining the Langmuir isotherm equations, several aspects of the adsorption system were presupposed in the derivations. The most important of these,and the one that has been subject to the greatest doubt, is that a uniform surface is assumed. In other words, any active site has the same attraction for an impinging molecule as does any other site. Isotherms different from the Langmuir types may be derived based on various assumptions concerning the adsorption system, including different types of nommiform smfaces. 

Dependent upon temperature and additive concentrations, any of the above can be the rate-limiting step controlling film formation. The issue is further complicated by the temperature-variable influence of interactions of molecules in solution. These can influence the equilibrium between surface and solution by influencing the flux of molecules/unit time impinging upon the surface and the probability of reaction at the surface. To a reasonable approximation, the kinetics of these processes can be described by the Langmuir isotherm. Equation (3.4) ... 

R. Viskanta, Heat Transfer to Impinging Isothermal Gas and Flame Jets, Exp. Thermal Fluid Sci., 6, pp. 111-134,1993. 

The consideration outlined above agrees with the assumption that substrates influence the structure formation of barnacle adhesive indirectly via properties that hold the barnacle base at a distance from the surface (e.g., fiber coatings, thick biofilm layers) or cause large interfacial gaps (e.g., PDMS coatings). These factors affect the concentration in the dispersion, and hence the position on the adsorption isotherm as compared to the micellar or hemi-micellar concentration, by impinging on the interfacial volume that needs to be filled with adhesive. 

The central part of the spherulites and spherulitic impinging lines is degraded first, followed by the other parts of the spherulites (Fig. 16). It was also found that a sample isothermally crystallized at 60°C, which had a spherulite composed of less densely packed fibrils, had a higher degradation rate compared with a melt-quenched sample, in spite of similar crystallinity. This result indicates that the internal stmcture of the spherulite also played an important role in hydrolytic degradation. 

K " and n can be extracted from the intercept and the slope of Avrami plot, lg[-ln(l-.A0] versus lg(f-f ), respectively. The prime requirement of Avrami model is the ability of spherulites of a polymer to grow in a free space. Besides, Avrami equation is usually only valid at low degree of conversion, where impingement of polymer spherulites is yet to take place. The rate of crystallization of polymer can also be characterized by reciprocal half-time (/ 5). The use of Avrami model permits the understanding on the kinetics of isothermal crystallization as well as non-isothermal crystallizatioa However, in this chapter the discussion of the kinetics of crystallization is limited to isothermal conditions. 

Expressions are developed for the rate of transfer of polymer molecules towards and from an adsorbing surface under the condition of a fully relaxed adsorbed layer. The special form of the adsorption isotherm for polymers leads to rather simple expressions for the rate of adsorption (up to 85% saturation) and for the rate of desorption (in the neighbourhood of saturation). We compare these results with experimental data that we obtained using novel techniques (reflectometry combined with impinging jet flow for adsorption and streaming potential in a capillary for desorption,respectively). Good ovendl agreement is found, which implies that PEO layers on silica equilibrate rapidly. 

Crystallisation processes in PEEK have been the subject of many academic papers [10-13]. However, the crystallisation of PEEK generally matches the classic behaviour of other polymers. The effect of time is described by Avrami kinetics ( 3) and secondary crystallisation occurs after the spherulites have impinged. This secondary crystallisation results from an increase in the crystallinity within the spherulites and is probably related to the existence of the low-temperature melting peaks (LTMP) described later. A number of non-isothermal crystallisation models have been developed. 

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