Similitude particles

Analysis of a method of maximizing the usefiilness of smaH pilot units in achieving similitude is described in Reference 67. The pilot unit should be designed to produce fully developed large bubbles or slugs as rapidly as possible above the inlet. UsuaHy, the basic reaction conditions of feed composition, temperature, pressure, and catalyst activity are kept constant. Constant catalyst activity usuaHy requires use of the same particle size distribution and therefore constant minimum fluidization velocity which is usuaHy much less than the superficial gas velocity. Mass transport from the bubble by diffusion may be less than by convective exchange between the bubble and the surrounding emulsion phase. 

Equation (14.91) contains only the mass flow ratio /u as a characteristic number of the mechanics of similitude of the mixture. All the other irnpor rant factors, such as particle size, solid density, etc., are contained in the additional pressure-loss coefficient of the solid particles, A, which is determined separately for each material. 

A technique which can assist in the scale-up of commercial plants designs is the use of scale models. A scale model is an experimental model which is smaller than the hot commercial bed but which has identical hydrodynamic behavior. Usually the scale model is fluidized with air at ambient conditions and requires particles of a different size and density than those used in the commercial bed. The scale model relies on the theory of similitude, sometimes through use of Buckingham s pi theorem, to design a model which gives identical hydrodynamic behavior to the commercial bed. Such a method is used in the wind tunnel testing of small model aircraft or in the towing tank studies of naval vessels. 

For point particles governed by Stokes law, the Stokes number is the only criterion other than geometry that determines similitude for the shape of the particle trajectories. To ensure hydrodynamic similarity, in general, the collector Reynolds number also must be preserved, as well as the ratio I = R/a, called the interception parameter. Then, the collection efficiency of particles hitting an obstacle such as a cylinder has the form ... 

The blood then, being drove out of the heart in an oblique direction against the sides of the aorta, strikes and presses on them in a very acute angle (...) Hence therefore the particles of the blood will every moment receive a different motion, collision, and rotation as also a constant attrition, attenuation, and compactness, with an abrasion or levigation of their angles, and an uniformity or similitude in each particle. From all which will arise that fluidity, heat and colour observable in the whole mass, with that division of its parts fitting them to pass through all the small vessels. 

For R —> 0 ( point particles), theories of particle and molecular diffusion are equivalent. Schmidt numbers for particle diffusion are much larger than unity, often of the same order of magnitude as for molecular diffusion in liquids. The principle of dimensional similitude tells us that the results of diflusion experiments with liquids can be used to predict rates of diffusion of point particles in gases, at the same Reynolds number. 

DIFFUSION AT LOW REYNOLDS NUMBERS SIMILITUDE LAW FOR PARTICLES OF FINITE DIAMETER... 

For particles of finite diameter, the interception effect becomes important. A useful similitude law that takes both diffusion and interception into account can be derived as follows (Friedlander, 1967) It is assumed that the concentration boundary layer is thin and falls... 

Diffitsinn at Low Reynolds Numbers Similitude Law for Particles of Fin ite Diameter 67... 

This is the similitude law for the diffusion of particles of finite diameter but with R < 1 in low-speed Rows. For fixed Rc, the group should be a single-valued function... 

On the basis of experimental data, with the use of similitude theory, a relationship has been established between the drag coefficient Cx and the Reynolds number Re [273]. The particle drag coefficient Cx is the ratio of the dragF r to the product of the particle midsection S by the dynamic pressure... 

The particle formation is the result of fast competing processes, nucleation and growth, thus it is influenced by mixing actually many different mechanisms may be involved, especially when drugs and excipients have to be incorporated, and when oily phases are presents, as previously discussed in detail. A similitude analysis or a dimensional analysis of the problems evidences the role of several different dimensionless... 

In scaling-down of EBR, it has to be assured that hydrodynamic characteristics be identical, maintaining phase holdups unchanged. The key parameters in scaling-down are catalyst particle diameter, reactor diameter, as well as liquid and gas superficial velocities. For scaling-up, methods based on geometric and dynamic similitude are very useful. 

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