Area per unit volume

Efficient use of a catalyst requires high rates of reaction per unit volume and, since reaction takes place on the surface of a solid, catalysts have high surface areas per unit volume. Therefore, tlie typical catalyst is porous, witli... 

In industrial equipment, however, it is usually necessary to create a dispersion of drops in order to achieve a large specific interfacial area, a, defined as the interfacial contact area per unit volume of two-phase dispersion. Thus the mass-transfer rate obtainable per unit volume is given as... 

Direct photography of drops in done with the use of fiber optic probes using either direct or reflected light. StiU or video pictures can be obtained for detailed analysis. The light transmittance method uses three components a light source to provide a uniform collimated beam, a sensitive light detector, and an electronic circuit to measure the amplified output of the detector. The ratio of incident light intensity to transmitted intensity is related to interfacial area per unit volume. 

R is rate of reaction per unit area, a is interfacial area per unit volume, S is solubiHty of solute in continuous phase, D is diffusivity of solute, k is rate constant, kj is mass-transfer coefficient, is concentration of reactive species, and Z is stoichiometric coefficient. When Dk is considerably greater (10 times) than Ra = aS Dk. 

High Surface Sodium. Liquid sodium readily wets many soHd surfaces. This property may be used to provide a highly reactive form of sodium without contamination by hydrocarbons. Powdered soHds having a high surface area per unit volume, eg, completely dehydrated activated alumina powder, provide a suitable base for high surface sodium. Other powders, eg, sodium chloride, hydride, monoxide, or carbonate, can also be used. 

At high Reynolds numbers the friction factor becomes nearly constant, approaching a value of the order of unity for most packed beds. In terms of S, particle surface area per unit volume of bed,... 

According to this method, it is not necessaiy to investigate the kinetics of the chemical reactions in detail, nor is it necessary to determine the solubihties or the diffusivities of the various reactants in their unreacted forms. To use the method for scaling up, it is necessaiy independently to obtain data on the values of the interfacial area per unit volume a and the physical mass-transfer coefficient /c for the commercial packed tower. Once these data have been measured and tabulated, they can be used directly for scahng up the experimental laboratory data for any new chemic ly reac ting system. 

Principles of Rigorous Absorber Design Danckwerts and Alper [Trans. Tn.st. Chem. Eng., 53, 34 (1975)] have shown that when adequate data are available for the Idnetic-reaciion-rate coefficients, the mass-transfer coefficients fcc and /c , the effective interfacial area per unit volume a, the physical solubility or Henry s-law constants, and the effective diffusivities of the various reactants, then the design of a packed tower can be calculated from first principles with considerable precision. 

The area that is theoretically available for separation is equal to the sum of the projected areas or all channels on the horizontal plane. Figure 18-88 shows the horizontally projected area A, of a single channel in a clarifier of unit width. If X is the uniform distance between plates (measured perpendicularly to the plate surface), the clarifier will contain sin Ci/X channels per unit length and an effective collection area per unit clarifier length of A, sin O/X, where Ot is the angle of inclination of the plates to the horizontal. It follows that the total horizontally projected plate area per unit volume of sludge in the clarifier Aj is... 

Kp, = Overall mass transfer coefficient, g/m s a = Surface area per unit volume of adsorbent particle, mVm ... 

Imposing a limit on reactor size, to ensure adequate heat transfer area per unit volume. 

This form is partieularly appropriate when the gas is of low solubility in the liquid and "liquid film resistanee" eontrols the rate of transfer. More eomplex forms whieh use an overall mass transfer eoeffieient whieh ineludes the effeets of gas film resistanee must be used otherwise. Also, if ehemieal reaetions are involved, they are not rate limiting. The approaeh given here, however, illustrates the required ealeulation steps. The nature of the mixing or agitation primarily affeets the interfaeial area per unit volume, a. The liquid phase mass transfer eoeffieient, kL, is primarily a funetion of the physieal properties of the fluid. The interfaeial area is determined by the size of the gas bubbles formed and how long they remain in the mixing vessel. The size of the bubbles is normally expressed in terms of their Sauter mean diameter, dj, whieh is defined below. How long the bubbles remain is expressed in terms of gas hold-up, H, the fraetion of the total fluid volume (gas plus liquid) whieh is oeeupied by gas bubbles. 

Oxygen transfer rate (OTR) The product of volumetric oxygen transfer rate kj a and the oxygen concentration driving force (C - Cl), (ML T ), where Tl is the mass transfer coefficient based on liquid phase resistance to mass transfer (LT ), a is the air bubble surface area per unit volume (L ), and C and Cl are oxygen solubility and dissolved oxygen concentration, respectively. All the terms of OTR refer to the time average values of a dynamic situation. 

The speeifie surfaee Sp defines the surfaee area per unit volume (or mass) of partiele... 

The significance of this novel attempt lies in the inclusion of both the additional particle co-ordinate and in a mechanism of particle disruption by primary particle attrition in the population balance. This formulation permits prediction of secondary particle characteristics, e.g. specific surface area expressed as surface area per unit volume or mass of crystal solid (i.e. m /m or m /kg). It can also account for the formation of bimodal particle size distributions, as are observed in many precipitation processes, for which special forms of size-dependent aggregation kernels have been proposed previously. 

FIG. 15 The projected surface area per unit volume S, divided by the surfactant volume fraction for different structures along the bifurcation line as a function of surfactant volume fraction Note that due to the geometrical constraints this quantity cannot exceed the length of the surfactant a. Here we set a = 1 for convenience. 

The interfacial area per unit volume and a = AN is incorporated into (3.11.7) ... 

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