Continuous-smooth-layer model

There is a great deal of theoretical and experimental information from micrometeorological research on the transfer of momentum, heat, and mass at solid and liquid surfaces and across their associated air boundary layers (hence the term boundary layer models for relationships arising from this approach). Based on the analogy between transfer of momentum and mass, it has been shown that k is proportional to the friction velocity in air (u ) and that k is also proportional to Sc. Apart from an assumption that the surface was smooth and rigid, it was also necessary to assume continuity of stress across the interface in order to convert the velocity profile in air to the equivalent profile in the water (Deacon, 1977). The relationship developed by Deacon is as follows ... 

Deacon [28] developed a boundary layer model based on turbulent fluid flow in the vicinity of a smooth rigid wall. By assuming that the wind stress is continuous across the air-water interface, producing a constant flux of momentum, the friction velocity on the water side can be determined as u = w a(9a/9w)° in which a and w refer to air and water, respectively. This approach has been found to provide a reasonable description of gas transfer in wind tunnels at low wind speeds [10]. Another boundary layer model [35] allows some surface divergence and predicts the -2/3 power of the Sc for low wind speeds and -1/2 power at higher wind speeds. 

A decisive factor for the physical behaviour of a composite is the adhesion efficiency at the boundaries between phases. In all theoretical models this adhesion is considered as perfect, assuming that the interfaces ensure continuity of stresses and displacements between phases, which should be different because of the proper nature of the constituents of composites. However, such conditions are hardly fulfilled in reality, leading to imperfect bonding between phases and variable adhesion between them. The introduction of the mesophase layer has as function to reconcile in a smooth way the differences on both sides of interfaces. 

Theocaris [85] proposed a model that incorporates an interphase which he named a mesophase, which constitutes a boundary layer between the main phases of the composite. From a physical basis, a continuous and smooth transition of the properties from one phase to the other is assumed. Because the mechanical properties of this region also contribute to the composite properties, the determination of the local mechanical modulus is important. Dynamic mechanical analysis is used to identify the mesophase properties, primarily the glass transition temperature (Tg), through changes in the loss modulus peak. 

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