On the Critical Condition for Developing Particulate Solid in Solid-Liquid Contacting Mixers

Studies were made on the development of particulate solids in the agitator.The appearance of the development of particulate solids in the agitator changes with the variation of operating conditions. To detect these phenomena quantitatively, the relative concentration of particulate solids were measured with the photo-electric apparatus (Fig. 1).When the rotational speed was small enough, all the particles were at the bottom of the vessel.With the increase of the rotational speed, particles came to develop in the agitator and the concentration of the particles began to increase. The critical rotational speed, as we defined it, occurred when the value of concentration of particles showed a tendency of having certain definite value above the speed, This is illustrated in Fig. 2.Some considerations were given to this speed. Analogous to the method used in defining the rate of solution of fully developed particles in the agitator, the principal relative velocity υ, relative to the particle, was assumed as follows:(1)From the above relation, the measure of random external forces to the particle was expressed as follows:(2)The external force due to the gravity was as follows:(3)The ratio of the above two forces were reduced to:(4)We assumed that α is the value indicating the measure of appearance when the particles were developed in the agitator and at a certain definite value of α, denoted as αc, the particles made full development in the agitator.Experimental evidence of the above consideration was procured with the vessels sized 14, 17, and 27.4cm. respectively. The solid particles were standard sand, magnetite sand and sand made of resin. Paddles, vaned disks and flat-blade turbines were used as solid-liquid contacting impellers. The experimental results are illustrated in Fig. 4. Each value of ec was calculated from the data on critical rotational speed. As was seen in the illustration, the data satisfied the following equation in practical estimation.(5)