Sphere and Cylinder Drying

In this section, we will discuss in detail the linked differential equations for mass and heat transfer which describe the drying of a spherical green body. This same analysis can also be used for plate and cylinder green bodies with corrections for the geometry. The equations for cylinder and plate drying are presented in Tables 14.3 and 14.4. 

Giving the Drying Rate for the Constant Rate Period 

Consider a spherical green body of radius Rq, where all the pores are filled and the surface is initially wet with solution. For this condition, the rate of mass transfer, J, from the surface of the green body 

The mass transfer coefficient, jK, , for a sphere can be determined from the Sherwood number, Ns (= Q2Rq/Aib where is the molecular diffusion coefficient of the solvent, species A, in the drying gas, species B), and the following engineering correlation [15]  

The mass transfer, J, is related to the heat transfer, Q, required to evaporate those molecules 

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Catalysts are manufactured by various methods (such as precipitation, extrusion and spray drying) in the form of cylinders, rings, multi-lobed extru-dates and other shapes. They range in size from a few millimetres to several centimetres small spheres are used in fluidized bed reactors. Active phases can be dispersed on the pre-shaped support by several methods such as by impregnation of a solution of the active components. Alternatively the catalysts can be made by the extrusion of mixtures of solid components the support, active phase, and binder. For some reactions that are diffusion limited, the catalyt-ically active species are not uniformly distributed instead they are deposited on the outer shell of the catalyst particle (egg-shell catalysts), since those inside the particle cannot be involved in the reaction. 

Gamson, Thodos, and Hougen (1943) Drying Air Porous celite Spheres, cylinders 2-19 ... 

Stresses in the CRP at the surface of drying plates, cylinders or spheres decrease in the ratio l/3 l/4 l/5 respectively and so the highest stress level is found at the surface of plates. 

FIGURE 24.5 Moisture content distribution during dehydration, at the center of (a) an infinite slab (b) a cylinder and (c) a sphere. (From Ramaswamy, H.S. and Lo, K.V., Simplified Relationships for Moisture Distribution during Drying of Regular Solids, ASAE Paper No. 81-103, American Society of Agricultural Engineers, St. Joseph, MI, 1981. With permission.)... 

Having described the structural elements of foams approaching the dry-foam limit (O —> 1), it is still a daunting task to describe the structure and properties of the system as a whole. The task is even more difficult for systems in which O Q is exceeded, but the polyhedral regime has not yet been reached. In this case, the drops have exceedingly complex shapes, and linear and tetrahedral Plateau borders, as defined above, are not present. Much can be learned about the qualitative behavior by considering 2-D model systems, in which the drops do not start out as spheres but as parallel circular cylinders, and tetrahedral Plateau borders do not arise. We shall first consider the particularly simple monodisperse case, with a subsequent gradual increase in complexity. 

The maximum pressure authorized for carbon monoxide cylinders is 1000 psig at 70°F (6900 kPa at 21.1 °C) except, if the gas is dry and sulfur-free, the cylinders can be charged to 5/6 of the service pressure, but never more than 2000 psig at TOT (13 790 kPa at 21.UC). See 49 CFR 173.302 (f). In Canada, carbon monoxide may be filled to service pressure in aluminum cylinders. See CAN/CSA B340, Selection and Use of Cylinders, Spheres, Tubes, and Other Containers for the Transportation of Dangerous Goods, Class 2 [4, 7]. 

As opposed to Scherer, recent models are non-isothermal and not restricted to essentially one-dimensional problems (such as an infinite plate, cylinder or sphere). Some of them consider the drying gel as a biphasic medium, that is, a solid matrix that remains saturated, so that the second drying period cannot be described. Others can also simulate shrinkage and stress after the liquid/gas phase boundary has receded into the gel, as already explored by Scherer (1987b) for a flat plate by assuming a constant evaporation rate until the gel is completely dry. 

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