Ciystallization

This is because on one hand, heav wave is weaker and on the other hand, photoelastic testing method is unfavorable for observing the sound field of axial symmetry. The sound field (see Fig.4) excited by strip ciystal in solid is observed with photoelastic testing method. The wavefront of head wave can be see in Fig.4, which is a circumstantial evidence of wavefront of head wave excited just by point-shape crystal. We can calculate... 

Fig. VIII-8. Surface structures (a) (1 x 1) structure on the (100) surface of a FCC crystal (from Ref. 76) (b) C(2 x 1) surface structure on the (100) surface of a FCC ciystal (from Ref. 76). In both cases the unit cell is indicated with heavy lines, and the atoms in the second layer with pluses. In (b) the shaded circles mark shifted atoms. (See also Ref. 77.)...

Although there are examples of enzymes which maintain their catalytic activity even when ciystallized, they normally work in their natural (i.e., aqueous) environment. This is the reason why the majority of the simulations are carried out applying a technique that accounts for solvent effects. But what is the effect of a solvent ... 

Fig. 4. Model of the ciystal structure of zeolites X, Y, and the mineral faujasite. At the tight is shown the tetrahedral arrangement of tmncated octahedra surrounding one large cavity. On the left the packing model of zeohte X is shown, containing three types of Na cations.

Potassium Heptafluorotantalate. Potassium heptafluoiotantalate [16924-00-8], K TaF, ciystallizes in colodess, rhombic needles. It hydroly2es in Foiling water containing no excess of hydrofluoric acid. The solubility of potassium heptafluorotantalate in hydrofluoric acid decreases from 60 g/100 mL at 100°C to 0.5 g/100 mL at room temperature. The different solubility characteristics of K TaF and K NbOF are the fundamental basis of the Matignac process (16). A phase diagram exists for the system K TaF —NaCl—NaF—KCl (68). Potassium heptafluorotantalate has an LD q value of 2500 mg/kg. The recommended TWA maximum work lace exposure for K TaF in air is 2.5 mg /m (fluoride base) (69). 

Cooling Ciystalli rs use a heat sink to remove both sensible heat from the feed stream and the heat of crystallization released as crystals are formed. The heat sink may be no more than the ambient surroundings of a batch crystallizer, or it may be cooling water or another process stream. 

Piezoelectric Transducers Certain ciystals produce a potential difference between their surfaces when stressed in appropriate directions. Piezoelectric pressure transducers generate a potential difference proportional to a pressure-generated stress. Because of the extremely high electrical impedance of piezoelectric crystals at low frequency, these transducers are usually not suitable for measurement of static process pressures. 

Head meters with density compensation. Head meters such as orifices, venturis, or nozzles can be used with one of a variety of densitometers [e.g., based on (a) buoyant force on a float, (b) hydrauhc couphug, (c) voltage output from a piezoelectric ciystal, or (d) radiation absolution]. The signal from the head meter, which is proportional to pV" (where p = fluid density aud V = fluid velocity), is multiphed by p given by the densitometer. The square root of the produc t is proportional to the mass flow rate. 

Co.). In direct contact with the scraped surface is the process fluid which may deposit ciystals upon chilling or be extremely fouhng or of very high viscosity. Motors, chain drives, appropriate guards, and so on are required for the rotating element. For chilling service with a refrigerant in the outer shell, an accumulator drum is mounted on top of the unit. 

Scraped-surface exchangers are particularly suitable for heat transfer with crystalhzation, heat transfer with severe folding of surfaces, heat transfer with solvent extraction, and heat transfer of high-viscosity fluids. They are extensively used in paraffin-wax plants and in petrochemical plants for ciystallization. 

Salt Brines The typical curve of freezing point is shown in Fig. II-IIO. Brine of concentration x (water concentration is I-x) will not solidify at 0°C (freezing temperature for water, point A). When the temperature drops to B, the first ciystal of ice is formed. As the temperature decreases to C, ice ciystals continue to form and their mixture with the brine solution forms the slush. At the point C there will be part ice in the mixture /(/i+L), and liquid (brine) /i/(/i-t-L). At point D there is mixture of mi parts eutectic brine solution Di [concentration mi/(mi-t-mg)], and mo parts of ice [concentration mol m -t- mo)]. Coohng the mixture below D solidifies the entire solution at the eutectic temperature. Eutectic temperature is the lowest temperature that can be reached with no solidification. 

Highest heat-transfer coefficients are obtained in FC evaporators when the liquid is aUowed to boil in the tubes, as in the type shown in Fig. 11-122 7. The heating element projects into the vapor head, and the hquid level is maintained near and usuaUy slightly below the top tube sheet. This type of FC evaporator is not well suited to salting solutions because boiling in the tubes increases the chances of salt deposit on the waUs and the sudden flashing at the tube exits promotes excessive nucleation and production of fine ciystals. Consequently, this type of evaporator is seldom used except when there are headroom hmitations or when the hquid forms neither salt nor scale. 

The effect of temperature on diffusivities in zeolite ciystals can be expressed in terms of the Eyring equation (see Ruthven, gen. refs.). 

Thermal decrepitation occurs frequently when crystals are rearranged because of transition from one form to another or when new compounds are formed (i.e., calcination of limestone). Sometimes the strains in cases such as this are sufficient to reduce the particle to the basic ciystal size. 

Richard C. Bennett/ B.S. Ch.E./ Registered Professional Engineer, Illinois Member, Amencan Institute of Chemical Engineers (AlChE), President of Ciystallization Technology, Inc. Former President of Swenson Proce.ss Equipment, Inc. (C lystallization)... 

CiystaUization may be carried out from a vapor, from a melt, or from a solution. Most of the industrial applications of the operation involve crystalhzation from solutions. Nevertheless, crystal sohdifica-tion of metals is basically a crystalhzation process, and much theoiy has been developed in relation to metal ciystallization. This topic is so specialized, however, that it is outside the scope of this subsection, which is hmited to ciystaUization from solution. 

Another method of fractional crystallization, in which advantage is taken of different ciystallization rates, is sometimes used. Thus, a solution saturated with borax and potassium chloride will, in the absence of borax seed ciystals, precipitate only potassium chloride on rapid coohng. The borax remains behind as a supersaturated solution, and the potassium chloride crystals can be removed before the slower borax crystalhzation starts. 

Crystal Formation There are obviously two steps involved in the preparation of ciystal matter from a solution. The ciystals must first Form and then grow. The formation of a new sohd phase either on an inert particle in the solution or in the solution itself is called nucle-ation. The increase in size of this nucleus with a layer-by-layer addition of solute is called growth. Both nucleation and ciystal growth have supersaturation as a common driving force. Unless a solution is supersaturated, ciystals can neither form nor grow. Supersaturation refers to the quantity of solute present in solution compared with the quantity which would be present if the solution were kept for a veiy long period of time with solid phase in contac t with the solution. The latter value is the equilibrium solubility at the temperature and pressure under consideration. The supersaturation coefficient can be expressed... 

Butchart and Whetstone, Ciystal Giowth, (Faraday See.) Butterworths, 1949, p. 259. 

Nyvit, J., Indushial Ciystallization, Verlag Chemie Publishers, New York, 1978, pp. 26-.31. 

In order to be consistent with normal usage, the particle-size distribution when this parameter is used should Be a straight line between approximately 10 percent cumulative weight and 90 percent cumulative weight. By giving the coefficient of variation ana the mean particle diameter, a description of the particle-size distribution is obtained which is normally satisfactory for most industrial purposes. If the product is removed from a mixed-suspension ciystallizer, this coeffi-... 

If L is a charac teristic dimension of a ciystal of selected material and shape, the rate of growth of a ciystal face that is perpendicular to L is, by definition,... 

For a steady-state ciystallizer receiving sohds-free feed and containing a well-mixed suspension of ciystals experiencing neghgible breakage, a material-balance statement degenerates to a particle balance (the Randolph-Larson general-population balance) in turn, it simplifies to... 

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