Modeling a vibratory mixer for soybean meal suspension

Abstract

Traditional paddle and propeller mixers do not provide sufficient shear action to break up agglomerates at high solids concentrations making vibratory mixers a promising solution. The rheological properties of the suspension are described by the Ostwald-de Waele model which characterizes the suspension as a pseudoplastic fluid: with an increase in shear rate, its effective viscosity decreases. The developed model involves the kinematics of the working element, the shear and stress fields, the drive dynamics, heat generation, and the kinetics of agglomerate breakdown. The working element, a rod with perforated disks, performs harmonic oscillations with an amplitude of A = 0.009 m at various frequencies. The critical radius of the effective impact zone when the shear stress exceeds the threshold value required to break up agglomerates increases with increasing frequency; the zone area increases from 21 to 264% of the working element cross-sectional area. The average viscous power loss for meal suspension exceeds that for water 142–191 times; with each change in vibration direction, the effective viscosity increases sharply creating peak loads on the drive. Using the Newtonian model systematically underestimates power consumption and does not allow for accurate determination of the effective zone of action. During short-term operation, thermal heating is insignificant; however, for long-term operation, cooling of the working chamber is necessary. The electric motor should be selected based on the Ostwald model with a torque safety factor of at least 1.25–1.35 times the maximum design value. The results are applicable to the design of vibratory mixers for feed production and processing industries.