Suspensions large solid particles

Liquid droplets cannot be treated the same as solid particles in their codispersed systems. This behavior has been indicated by equation 66 or 68, in which the Einstein constant increases with increasing viscosity ratio of the dispersed phase to the continuous phase. As is shown by Yan et al. (195, 197, 198), liquid droplet and solid particle effects are additive only when the solid concentration is low, say s < 0.05, and when both solid particles and liquid droplets have comparable sizes. However, when the particle-to-droplet size ratio is large, the particles and the droplets become additive (192) for a wider solid concentration range (Figures 34 and 35). The apparent viscosity of the system may be added in terms of the two distinct model systems pure emulsion characterized by solid-free dispersed phase volume fraction and pure suspension characterized by the volume fraction of the solids. The additive rule for the ternary systems is similar to the rule for bimodal solid particle suspensions due to Farris (139) ... 

There are a large number of processes in the chemical industries that handle a variety of suspensions of solid particles in liquids. The application of filtration techniques for the separation of these heterogeneous systems is sometimes very costly. If, however, the discrete phase of the suspension largely contains settleable particles, the separation can be effected by the operation of sedimentation. The process of sedimentation involves the removal of suspended solid particles from a liquid stream by gravitational settling. This unit operation is divided into thickening,... 

The USP has numerous requirements, e.g., ophthalmic solutions [need be] essentially free from foreign particles, suitably compounded and packaged for instillation into the eye, or ophthalmic suspensions [need contain] solid particles dispersed in liquid vehicle intended for application to the eye [1]. Ophthalmic suspensions are required to be made with the insoluble drug in a micronized form to prevent irritation or scratching of the cornea. A finished ophthalmic ointment must be free from large particles and must meet the requirements for leakage and for metal particles under ophthalmic ointments . These and other requirements will be discussed further in subsequent sections. 

Solid particles can be removed from a dilute suspension by passing the suspension through a vessel that is large enough that the vertical component of the fluid velocity is lower than the terminal velocity of the particles and the residence time is sufficiently long to allow the particles to settle out. A typical gravity settler is illustrated in Fig. 12-2. If the upward velocity of the liquid (Q/A) is less than the terminal velocity of the particles (Ft), the particles will settle to the bottom otherwise, they will be carried out with the overflow. If Stokes flow is applicable (i.e., NRe < 1), the diameter of the smallest particle that will settle out is... 

This result follows from the Richardson-Zaki equation. In their original work, Richardson and Zaki (1954) studied batch sedimentation, in particular the settling of coarse solid particles through a liquid in a vertical cylinder with a closed bottom. Richardson and Zaki found that the settling speed uc of the equal-sized particles in the concentrated suspension was related to the terminal settling speed u, of a single particle in a large expanse of liquid by the equation... 

Because polymer adsorption is effectively irreversible, and because adsorption and floe growth occur simultaneously, flocculation is a non-equilibrium process. As a result, performance is largely determined by the kinetics of adsorption and aggregation. Both of these can be regarded as collision processes involving solid particles and polymer molecules. In each case, collisions can arise due to either Brownian motion or agitation of the suspension. The collision frequency v between particles and polymer molecules can be estimated from °... 

Example 3.2 Consider a large number of uniformly charged solid particles initially kept in a spherical barrier of radius R with a symmetric density distribution. When the barrier is suddenly removed, the particles start to emerge from that spherical domain. The viscous drag in the gas is assumed to be negligible. Find the ratio of the force due to dipole to that due to electrostatic repulsion and show that for dilute suspensions, the dipole effect due to self-field is negligible. Also discuss the spreading of the solid particles in this simple symmetric system. 

Microcarriers are small solid particles (kept in suspension by stirring) upon which cells may grow as a monolayer. They confer the advantage of large scale suspension cultures on anchorage dependent cells. They thus offer the following advantages. 

The main difference is the particle size. In three-phase fluidized beds these are so large that a net upward liquid flow is necessary to keep the solids in suspension, whereas in slurry reactors the turbulence of the liquid is sufficient to keep the solids suspended particle sizes in slurry reactors are usually below 200 ftm. Particularly for fast reactions where intraparticlc dif-... 

Power or energy dissipated in the aerated suspension has to be large enough (a) to suspend all solid particles and (b) to disperse the gas phase into small enough bubbles. It is essential to determine the power consumption of the stirrer in agitated slurry reactors, as this quantity is required in the prediction of parameters such as gas holdup, gas-liquid interfacial area, and mass- and heat-transfer coefficients. In the absence of gas bubbling, the power number Po, is defined as... 

Most of the early experimental investigations were performance studies concerned with the homogeneity of solid-liquid suspensions or with the rate of solution of solid particles as related to various operating characteristics. This class of systems has not been studied to any extent from a fundamental standpoint the following sections will indicate the large regions of interest which remain to be investigated. 

We first consider brielly why a polymer solution would be expected to have a higher viscosity than the liquid in which it is dissolved. We think initially of a suspension of solid particles in a liquid. The particles are wetted by the fluid, and the suspension is so dilute that the disturbance of the flow pattern of the suspending medium by one particle docs not overlap with that caused by another. Consider now the flow of the fluid alone through a tube which is very large compared to the dimensions of a suspended particle. If the fluid wets the tube wall its velocity profile will be that shown in Fig. 3-5a. Since the walls are wetted, liquid on the walls is stationary while the flow rate is greatest at the center of the tube. The flow velocity v increases from the wall to the center of the tube. The difference in velocities of adjacent layers of liquid (velocity gradient = civ/dr) is greatest at the wall and zero in the center of the tube. 

Rate constants for interfacial reactions have mainly been determined from experiments using particle suspensions where the concentration of reactive solute is monitored as a function of time. In these experiments, the solid surface is in large excess and the consumption of reactive solute follows first order kinetics. By plotting the pseudo-first-order rate constant against the solid surface area to solution volume ratio, the second-order rate constant can be obtained (from the slope). The main limitation here is that only relatively stable solutes can be studied experimentally. It is not possible to study the reactivity of short-lived species such as radicals using this approach. 

For monodisperse or unimodal dispersion systems (emulsions or suspensions), some literature (28-30) indicates that the relative viscosity is independent of the particle size. These results are applicable as long as the hydrodynamic forces are dominant. In other words, forces due to the presence of an electrical double layer or a steric barrier (due to the adsorption of macromolecules onto the surface of the particles) are negligible. In general the hydrodynamic forces are dominant (hard-sphere interaction) when the solid particles are relatively large (diameter >10 (xm). For particles with diameters less than 1 (xm, the colloidal surface forces and Brownian motion can be dominant, and the viscosity of a unimodal dispersion is no longer a unique function of the solids volume fraction (30). 

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