Solid-liquid mixing power

In solid-liquid mixing design problems, the main features to be determined are the flow patterns in the vessel, the impeller power draw, and the solid concentration profile versus the solid concentration. In principle, they could be readily obtained by resorting to the CFD (computational fluid dynamics) resolution of the appropriate multiphase fluid mechanics equations. Historically, simplified methods have first been proposed in the literature, which do not use numerical intensive computation. The most common approach is the dispersion-sedimentation phenomenological model. It postulates equilibrium between the particle flux due to sedimentation and the particle flux resuspended by the turbulent diffusion created by the rotating impeller. 

In a biphasic solid-liquid medium irradiated by power ultrasound, major mechanical effects are the reduction of particles size leading to an increased surface area and the formation of liquid jets at solid surfaces by the asymmetrical inrush of the fluid into the collapsing voids. These liquid jets not only provide surface cleaning but also induce pitting and surface activation effects and increase the rate of phase mixing, mass transfer and catalyst activation. 

Some of the most difficult of all mixing problems involve cohesive solids such as pastes, plastic materials, and rubber. In some ways these substances resemble liquids, but their enormously high viscosity means that the mixing equipment must be different from and much more powerful than the mixers described in Chap. 9. With cohesive solids the mixing elements cannot generate flow currents instead they shear, fold, stretch, and compress the material to be mixed. 

Hence, the local mass transfer coefficient scales as the two-thirds power of a, mix for boundary layer theory adjacent to a solid-liquid interface, and the one-half power of A, mix for boundary layer theory adjacent to a gas-liquid interface, as well as unsteady state penetration theory without convective transport. By analogy, the local heat transfer coefficient follows the same scaling laws if one replaces a, mix in the previous equation by the thermal conductivity. 

B.9.1.6 Mixing Time in Three-Phase (Gas-Liquid-Solid) System There are no reported experimental data on gas-liquid-solid systems that are relevant to animal cell culture using microcarrier beads as support for the cells. As mentioned earlier in the case of gas-liquid and solid-liquid systems, because of (i) the low density difference (Ap 30-50 kg/m ) and (ii) low aeration rates, there is insignificant impact of introduction of the solid and gas phases. Further, if an upflow impeller is used, the power drop due to aeration is less than 10% at low aeration rates (Fig. 7A.6). Therefore, Equation 7B.11 can be used in this case also. 

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