Three region model

The interfacial diffusion model of Scott, Tung, and Drickamer is somewhat open to criticism in that it does not take into account the finite thickness of the interface. This objection led Auer and Murbach (A4) to consider a three-region model for the diffusion between two immiscible phases, the third region being an interface of finite thickness. These authors have solved the diffusion equations for their model for several special cases their solutions should be of interest in future analysis of interphase mass transfer experiments. 

This approach is also used to model batch treatments with high recycle rates in which the products generated electrochemically can react rapidly. Consequently, a three region model is required to separate the high reaction rates that occur close to the anodic and cathodic regions from the other slower reactions that occur on the whole volume of the solution (4.13)—(4.15). The initial conditions for these equations arc ([5 /]b)(,=0) = ([Si]b) t=0) = ([>V ]b)(/=0) = [Si],=0... 

Figure 3. Two models describing the microphases of swollen Nation membranes. Top Gierke s [48] suggestion of aqueous inverse spherical micelles connected by water-filled cylindrical channels. Bottom Yeager and Steck s [49] three-region model of a water/ionomer mixture without regular structure. Regions A, B and C are the hydrophobic polymer, the solvent bridges and the hydrophilic regions, respectively.

A first model of solvation - the three region model for aqueous electrolyte solutions... 

A FIRST MODEL OF SOLVATION - THE THREE REGION MODEL... 

Considering hydrodynamics of the spouted bed, the most logical description of the drying process appears to be provided by the three-region model (TRM) (Oliveira and Freire, 1996). This model is based on a generalized assumption that each distinct region of the bed (an annulus, a spout, and a fountain) contributes to water evaporation in a proportion determined by their respective heat and mass transfer coefficients, residence times within the zones, and the local temperature and humidity gradients. 

The three-region model is built on the assumption that the solids temperature (inert particle and drying material) is equal to the wet bulb temperature at the outlet from each region. In our opinion, better accuracy from the model could be expected when allowing for material temperature higher than the wet bulb temperature, as shown in several papers revieved in the previous paragraph. 

Oliveira WP, Freire IT. Analysis of evaporation rate in the spouted bed zones during drying of liquid materials using a three region model. In StrumiUo C, Pakowski Z, eds. Drying 96. Proc. lO Inti. Drying Symposium (IDS 96), Krakow, Poland, 1996, pp 504-512. 

Figure 7.6 One-dimensional three-region model used in the computer simulation of relaxation in a heterogeneous system. The overall repeat distance is indicated. The calculations are carried out over the unit indicated in the lower half of the figure, comprising half of the regions A and C and the whole of B for which the dimensions, spin diffusion coefficients and relaxation rates are indicated. Redrawn and adapted with permission from [79].

---