Solid hold

The precise nucleation mechanism occurring in any particular case is often a subject of debate, however, and in practice the data are normally correlated empirically by an expression including a dependence on solids hold up of the form ... 

It was shown in Chapter 3 that the ideal eontinuous MSMPR erystallizer eould be analysed using the population balanee approaeh eoupled with mass balanees and erystallization kineties to yield equations deseribing erystallizer perform-anee in terms of the erystal size distribution, solids hold up ete. These eoneepts will now developed further to yield methods for eontinuous erystallizer design. Firstly, however, it is useful to eonsider how erystallization kineties and erystallizer performanee interaet. 

Combining the equations for mass balanee, mean size and kineties for the solids hold up gives (for j = 1)... 

The solids hold-up. Mi, is related to the CSD by the third moment equation... 

In general bed voidage is dependent on the paeking eharaeteristies of the material (a funetion of the orientation of the partieles in the bed), whieh is both partiele size and shape dependent. Unfortunately, at present it is only possible to prediet bed porosity for eertain distributions of regular partieles. Porosity ean be related to erystallizer solids hold-up empirieally, however, by an expression of the form... 

The observed dependenee of nueleation rate on solids hold-up and the low supersaturation order both imply the seeondary mode oeeurring. 

Mathews and Rawlings (1998) successfully applied model-based control using solids hold-up and liquid density measurements to control the filtrability of a photochemical product. Togkalidou etal. (2001) report results of a factorial design approach to investigate relative effects of operating conditions on the filtration resistance of slurry produced in a semi-continuous batch crystallizer using various empirical chemometric methods. This method is proposed as an alternative approach to the development of first principle mathematical models of crystallization for application to non-ideal crystals shapes such as needles found in many pharmaceutical crystals. 

For a constant filtration rate dV/df, the fractional solids hold-up (1 — ev) increases linearly with time, until it reaches a limiting value when the resistance to flow of liquid within the slurry becomes significant. The filtration rate then drops rapidly to a near zero value. 

The interfacial area in the contactor, which is directly related to the solids hold-up, strongly influences the mass transfer rate. To maximise the overall mass-transfer rate per unit volume of equipment, a high solids hold-up is necessary. On the other hand, the solids hold-up also influences the pressure drop over the contactor. The pressure drop has a hydrostatic and a dynamic component, both of which rise with increased solids hold-up. Since the adsorbent consists of extremely small particles, fluid friction between liquid and solids may lead to a relatively high dynamic pressure drop. The hydrostatic pressure drop is attributable to the density difference between the suspension in the contact zone and in the liquid. 

To understand what makes something a solid, you have to look at the smallest parts—the atoms.The particles in solids are bound tightly into a particular shape.The atoms can still vibrate, a bit like a string on a violin vibrates, but they can t change places with each other. Because the atoms in solids stay in the same place, solids hold their shape and don t flow to fit a container. If you take a basketball and place it in a bucket, the basketball doesn t change its shape. 

The effective viscosity depends on the solid hold-up, on particle size and distribution, on the surface properties, on the particle shape and density, on the properties of the liquid (p, p, d), on temperature, and the shear stress in the column. Depending on the solid concentration encountered in BSCR, we can classify the suspensions into "dilute" and "concentrated" groups. 

The works of Fukuma et al. [23], Morooka et al. [24] and Clark [25] has indicated that the presence of solid particles in the reactor favours the transition to the heterogeneous flow regime. A critical solid hold-up exists, beyond which the coalescence of bubbles is more frequent. This critical value is higher with smaller particles. Clark [25], studied operation at pressure above 100 bar, and inferred that... 

Particles of a sulphide ore are to be roasted in a fluidised bed using excess air the particles may be assumed spherical and uniform in size. Laboratory experiments indicate that the oxidation proceeds by the unreacted core mechanism with the reaction rate proportional to the core area, the time for complete reaction of a single particle being 16 min at the temperature at which the bed will operate. The particles will be fed and withdrawn continuously from the bed at a steady rate of 6 tonnes of product per hour (1.67 kg/s). The solids hold-up in the bed at any time is 10 tonnes. 

Decanters are frequently used in conjunction with disc-stack-type centrifuges in the pre-preparation of clear juices and juice concentrates, where the initial decanter treatment results in a partially clarified juice with a low level of suspended solids. This is followed by a clarification stage using a disc-stack whereby the solids are thrown outwards from the through-flow juice stream into a solids-holding space and automatically discharged therefrom as and when an optimum level of solids is reached (see Figure 3.6). 

They are best suited to liquid-liquid separations and clarification duties, but not high solids concentrations due to the limited solids hold-up capacity. They can handle small-density difference separations and best suited to batch processes. They are difficult to clean, and as large-scale laboratory units, best avoided unless another type of centrifuge design will not work. 

Solid bowl centrifuges are similar to tubular centrifuges, but with a larger diameter bowl and running at slower speeds. Feed rates can be as high as 10 m3/hr, provided that the solids concentration in the feed is not too high, as the solids hold-up is again limited. 

Selection of Type of Thickener or Clarifier Selection of the type of unit thickener or clarifier depends primarily on the optimization of performance requirements, installation cost and operating cost. For example, the inclined-plate type of clarifier provides for less solids-holding capacity than a circular or rectangular clarifier, but at a lower installation cost. The high-density thickener maximizes underflow solids concentration, requiring a higher torque rating than conventional thickeners. 

However, the measured values of elasticity modulus are several orders of magnitude lower than the values predicted by these equations. Perhaps the bed elasticity may have a role to play for fine cohesive particles at high solid hold-ups. In that case, this can be included in future in the equation of motion for the particle phase as an extra force arising out of particle-particle interaction, without affecting the fundamental approach of linear stability analysis. 

Ratio of solid hold-up in bubble wakes to that in liquid fluidization, in equation (208)... 

Experimental and theoretical studies [32, 33, 35, 37] showed that, for different plastic waste feeds (PE, PP, PET, their mixtures) and under a fixed reactor temperature, the time of occurrence of defluidization for a bed of a given material is linearly related to the value of the ratio between the bed solids hold-up and the polymer feed rate. The latter is a key parameter of the process. Diagrams in Figure 16.6 summarize all the data obtained in these experiments under different operating conditions and report the linear relationships that fit the data very well for the specific temperature and plastic waste feeding. 

Moreover, according to Eq. (10.31), the following expression for a viscoelastic standard solid holds ... 

Heterogeneous tar cracking. If the tar cracking rate is proportional to the solids hold-up (char) more cracking occurs near the wall. 

The unknown parameters are the characteristic particle diameter, dp, the gas-to-particle mass transfer coefficient, k and the solid hold-up e,. 

For the very small particles and the very dilute two-phase system considered, the mass transfer number can be estimated by Sh=kgdp/D=2 (Ranz and Marshall, 1952). The diffiision coefficient, D, can be estimated by Fuller et al, (9) The solids hold-up equals G,/psU, (10), with G. as the solids flux in kg/(m, s), p, the particle density with u, approximating the gas velocity Ug. Values for these parameters are listed in Table 3. 

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