Solid-liquid mixing uniform solids concentrations

Solid-liquid mixing involves the suspension, distribution, and the drawing down of solids by agitation. In addition to vessel geometiy, impeller variables include type, diameter, number, speed, and location. Process results include the desired level (quality) of suspension, such as just off-the-bottom, complete uniformity, or any intermediate condition. The slurry properties, density difference (solid/liquid), viscosity, and solids concentration all determine how difficult the task may be. As alternatives to stirred vessels, jets (see Section 9.10) can be used for light-duty suspension. Literature references deal mainly with settling solids as opposed to floating solids. We will try to address both conditions. 

Examples of solid-liquid mixing are found in kraft chemical recovery and in papermaking. In the recovery furnace, particulate material is removed from the boiler flue gases as dry solids and mixed with concentrated black liquor prior to reintroduction to the furnace. In coated papermaking production, coating preparation is critical for paper performance and uniformity. In chemical recovery, the recausticizing operation is an essential process for white liquor preparation and relies on effective solid-liquid mixing. 

Cell recycle fermentors consist of two main units a vessel where the biomass is allowed to grow, and a membrane separation unit (as in Figure 7.40). Vessels are usually designed to insure a uniform concentration of nutrients and pH throughout the whole volume. Due to complete mixing, process control and stability of the microbial slurry are not difficult to achieve.88 After anaerobic stabilization, when the biomass is well developed, the reactor biomass is pumped to the UF unit where solid-liquid separation occurs. The sludge is flushed back to the reactor. In most cases, the flow rate of nutrient feed is kept equal to the permeate flow rate thus keeping a constant liquid level in the anaerobic reactor. 

In step 3, choosing the holes to be uniformly distributed in the solvent ensures that the molecules spread out to achieve a uniform average concentration. This is part of the entropy of mixing AS ix, which accounts for the spreading out of the drug molecules when they go from the condensed phase (liquid or solid) into solution, and is given by (Atkins 1998)... 

We now leave pure materials and the limited but important changes they can undergo and examine mixtures. We shall consider only homogeneous mixtures, or solutions, in which the composition is uniform however small the sample. The component in smaller abundance is called the solute and that in larger abimdance is the solvent. These terms, however, are normally but not invariably reserved for solids dissolved in Kquids one liquid mixed with another is normally called simply a mixture of the two liquids. In this chapter we consider mainly nonelectrolyte solutions, where the solute is not present as ions. Examples are sucrose dissolved in water, sulfur dissolved in carbon disulfide, and a mixture of ethanol and water. Although we also consider some of the special problems of electrolyte solutions, in which the solute consists of ions that interact strongly with one another, we defer a full study until Chapter 5. The measures of concentration commonly encoimtered in physical chemistry are reviewed in Further information 3.2. 

Wiedmann et al. (1980) have compared the mixing of nonaerated liquids, aerated liquids, and slurries in a turbulent flow. They found that the torque required for stirred, aerated liquids is lower than that for nonaerated stirred liquids because of the decrease in the density of the gas-liquid mixture. The concentration distribution of the particles in aerated suspension becomes more uniform with increasing impeller speed, whereby the torque is higher than that for aerated liquids but lower than that for nonaerated slurries. For gas-liquid-solid systems, very limited data on dispersion of solids and gas phase are available, and further studies are necessary with different designs and for systems with different physical properties. The available literature has been reviewed by Stiegel et al. (1978), Shah et al. (1982), and Shah and Sharma (1986). 

Another technique of solid foam preparation is based on gas formation in a melted polymerising bulk or in concentrated water suspension of binding materials (cement, gypsum, lime), occurring after physical or chemical processes. It is also possible to incorporate air in a polymerising or solidifying substance bulk. For example, cellular-concrete represents a material in which gas bubbles are uniformly distributed in the bulk. The material produced when suspensions of binding substances are mixed with a foam is called cellular (foam) concrete. If the gas is formed in the concrete bulk as a result of a chemical reaction, for instance, in the reaction of aluminium powder with the liquid phase of the concrete solution, a gas-concrete is produced. 

The above-described mixers are essentially low-viscosity devices. In many operations where the viscosity is high, when dealing with concentrated multiphase gas-liquid-solid binary or tertiary systems, or when liquid-to-solid phase transformation occurs during mixing, novel equipment designs are needed to intensify the heat/mass transfer processes. The multiphase fluids also represent an important class of materials that have microstructure developed during processing and subsequently frozen-in, ready for use as a product. To deliver certain desired functions, the control of microstructure in the product is important. This microstructure is developed in most cases by the interaction between the fluid flow and the fluid microstructure hence, uniformity of the flow field is important. 

Zhou et al. (1994) divided the calibration methods for concentration probes used in liquid—solid systems into two parts. For voidages less than 0.8, calibration was carried out in a fluidized bed because particles are quite uniformly distributed in such a system. Calibrations at high voidages was carried out in a beaker a certain volume of solid particles is put into a beaker and mixed with a known volume of water, and the liquid—solid mixture is then stirred until the particles are uniformly distributed in the water. Different voidages were attained by mixing different volumes of particles... 

Once a set of data has been obtained which correlates, the flocculant consumption, if used, needs to be optimised. Alternative polymers might be examined if centrate quality had been difficult to maintain or if the quantity needed was considered excessive. The relative flow rates of polymer solution, and feed, would be assessed to see whether the polymer concentration needs to be adjusted to make it minimum strength, without causing it to be a large fraction of the total flow. This should not be more than, say, 10 or 15%. Polymer tends to be most efficient when it is most dilute. Moreover it is easier to get a uniform mix of two liquids when they are both of comparable size. However the larger the volume the flocculant is, then the greater is the clarification capacity lost unnecessarily to the clean flocculant. The location for admitting the polymer may be questioned, and considered for introduction further upstream, if flocculation in the centrate has been observed, or if extra dryness is required at the expense of extra polymer in dry solids work. 

Let us proceed to model the system using one of our formulations, the compartmental model. To do this we assume the liquid to be well mixed witii a uniform concentrahon of This is not an unreasonable assmnption as the size of the pool is quite small, typically 50 to 200 pm in width. The solid phase, on the other hand, caimot be considered uniform because solid-phase diffusivities are several orders of magnitude smaller than those prevailing in the liquid (see Section 3.1 in the next chapter). Concentrations... 

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