Wetted Surface Model

Extensive work has been done in developing theories of drying, such as the theory of simultaneous transport, theories involving flow through porous media, and simplified models, like the wetted surface model and the receding-plane model. The characteristic drying rate curve has also found use in design. Details of these theories are available in Refs. [3,13,17,26]. 

Mass transfer Generalized model of Bravo, et al. [113], with discount factors for wetted surfaces. 

FIGURE 26.26 Braking force as function of the slip on a wet surface in the presence of side forces at different set slip angles (calculated with the brush model). 

The diffusion layer model satisfactorily accounts for the dissolution rates of most pharmaceutical solids. Equation (43) has even been used to predict the dissolution rates of drugs in powder form by assuming approximate values of D (e.g., 10 5 cm2/sec), and h (e.g., 50 pm) and by deriving a mean value of A from the mean particle size of the powder [107,108]. However, as the particles dissolve, the wetted surface area, A, decreases in proportion to the 2/3 power of the volume of the powder. With this assumption, integration of Eq. (38) leads to the following relation, known as the Hixon-Crowell [109] cube root law ... 

Capillary condensation can be illustrated by the model of a conical pore with a totally wetting surface (Fig. 2.12). Liquid will immediately condense in the tip of the pore. Condensation continues until the bending radius of the liquid has reached the value given by the Kelvin equation. The situation is analogous to that of a bubble and we can write... 

Since liquid does not completely wet the packing and since film thickness varies with radial position, classical film-flow theory does not explain liquid flow behavior, nor does it predict liquid holdup (30). Electrical resistance measurements have been used for liquid holdup, assuming liquid flows as rivulets in the radial direction with little or no axial and transverse movement. These data can then be empirically fit to film-flow, pore-flow, or droplet-flow models (14,19). The real flow behavior is likely a complex combination of these different flow models, that is, a function of the packing used, the operating parameters, and fluid properties. Incorporating calculations for wetted surface area with the film-flow model allows prediction of liquid holdup within 20% of experimental values (18). 

In this model, the temporal change of the molar quantity of the element calcium is due to the temporal change of the molar quantity on the fluidized-bed material. With a constant liquid film thickness, this problem reduces to the temporal change of the wetted surface ... 

A two-parameter model is obtained if wetting is incomplete (tice < 1) > but the inactively wetted surface is assumed to have negligible mass transfer resistance (Bi - °°). This latter condition was used by Mata and Smith (13) and physically corresponds to the inactively wetted area being dry, or to the presence of stagnant liquid film which is at equilibrium with the gaseous reactant. The expression for the conversion given by Equation 10 reduces to ... 

Here, is the viscosity of fluid, g the gravitational constant, and a , the wetted surface area. According to this model, an expression for the RTD for an impulse input is given by... 

The rate of flow between fluids in fractures and in the rock matrix is a crucial factor for transport and reaction in fractures. For consistency with the formulation for flow between fractures and matrix used in the Yucca Mountain Project, the reactive surface area for minerals in unsaturated fractures has been related to the fracture-matrix interaction area based on a modified form of the Active Fracture Model (Liu et al., 1998 Sonnenthal el al., 2003). In this way, the wetted surface area for mineral-water reactions is consistent with that for flow and diffusion. 

Here the coefficients a and b characterize the surface-energy anisotropy and can be computed from the surface-energy dependence on the surface orientation. Naturally, the nonhnear operator Too i is invariant with respect to rotations by 7t/2, as well as any of the transformations x —s- —x, y — —y, x y, while Finis invariant with respect to rotations by 27t/3 as well as the transformation y —s- —y, b —b. The functions Wo 2,zih) are determined by the type of a wetting interaction model and can also differ for different orientations of the film surface. 

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