The Drying Model

The Kossovich (Ko) and Posnov (Pn and PUp) numbers [(6.23), (6.28)] defined by Eqs. (6.188)-(6.190) are obtained from the drying model (Eqs. (6.178)-(6.183) completed with specific initial and boundary conditions). Moreover, they are converted into a dimensionless form by applying the pi theo-... 

Undoubtedly, in the preparation of model networks from rather long polymeric precurson by the end-hnking reactions, the strands between the junction points wid maintain the conformation of coils. In accordance with classical ideas, the cods in the dry model network should acquire unperturbed dimensions, simdar to cods in a -solvent. However, on contacting a model polystyrene network with cyclohexane at room temperature, which is far below the -point for linear polystyrene (34.5°C), its volume increases by a factor of 3. Thus, the solvent breaks some polymer-polymer interactions, stimulates swelling of the network, and may result in an increase of chain dimensions. Hence, even at room temperature, the polystyrene chains prefer replacing the alien chain segments by cyclohexane molecides. 

The function /is often established theoretically, for example, when using the drying model formulated by Lewis (1921)... 

The drying model for a single wet particle/slurry droplet is based upon a two-stage drying process [50,51]. In the first drying period, the gas phase resistance controls the evaporation rate. Similarly to heat transfer, this resistance is between the gas and the wet envelope of the particle. This may be expressed by... 

The second fundamental difference between the drying models lies in the number of space variables used to describe the process. One-dimensional models (thickness) are fast running and allow the most important phenomena to be caught (transfers and drying stress), as the transfers occur mainly over the long faces of lumber boards in a kiln. For a more refined approach, a second direction can be useful ... 

Perre, R, 1987. Measurements of softwoods permeability to air Importance upon the drying model, Int. Commun. Heat Mass Transfer, 14 519-529. 

The main goal of this section is to present an outline of the theory that can be applied to stress analysis in both convective and microwave drying. The drying model was developed on the basis of mechanics of continua, incorporating the following assumptions ... 

In the DRIS model, the ya element A(Qy Oa) of represents the rate of transition from a set of rotational angles defining configuration to another set corresponding to Q. The accurate estimation of these rates is critically important for establishing a quantitative relation between theory and experiments. As mentioned above, A(mO ) for y a may be estimated from the... 

The elements of the transition rate matrix A in the DRIS model are estimated from the multidimensional energy surface associated with the interdependent rotation of neighboring bonds u g Kramers rate theory, as described above. Accordingly, the probability of occurrence of a given isomeric state for a bond depends on the state of its first neighbors aloi the chain. Likewise, in the kinetic Ising model the transition rate Wi(Oi) of the i-th spin is assumed to be coupled to the state of its first iKighbors by the relation... 

Comparison of the results of the JS expression with those of the DRIS model shows that the latter allows for a more detailed analysis of the real chain in terms of torsional energy barriers and the three dimensional chemical structure. Furthermore, while the JS model originates from the VJGM model and accounts only for three-bond motions, the DRIS model shows the contribution of all transitions of the N bonds surrounding the bond of interest. 

Calculations of C,( 0 for polyethylene have been performed according to the DRIS model [7] and the results have been compared with BD simulations performed by Weber and Helfand [98]. Conformational autocorrelation functions for the trans and gauche states based on the kinetic Scheme 2 of the DRIS... 

Fig. 8. Dependence of relaxation rates v (q) associated with the fostest mode on the si n of the kinetk unit Empty circles are obtained with the DRIS model. Filled circles are from BD simulations [100]...

Fig. 10. Isotropic correlation times Xcon as a function of reciprocal solvent viscosity for polyoxyethylene in dilute solution. Circles represent expoimental data, the line is n-edicted by the DRIS model...

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