Dilute systems

Applications of optical methods to study dilute colloidal dispersions subject to flow were pioneered by Mason and coworkers. These authors used simple turbidity measurements to follow the orientation dynamics of ellipsoidal particles during transient shear flow experiments [175,176], In addition, the superposition of shear and electric fields were studied. The goal of this work was to verify the predictions of theories predicting the orientation distributions of prolate and oblate particles, such as that discussed in section 7.2.I.2. This simple technique clearly demonstrated the phenomena of particle rotations within Jeffery orbits, as well as the effects of Brownian motion and particle size distributions. The method employed a parallel plate flow cell with the light sent down the velocity gradient axis. 

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I umber of Transfer Units. Eor relatively dilute systems the ratios involvingjgj, jy gj, and 1 — y approach unity so that the computation of from equation 50 and -Nq from equation 49 may be simplified to... 

The tme driving force for any diffusive transport process is the gradient of chemical potential rather than the gradient of concentration. This distinction is not important in dilute systems where thermodynamically ideal behavior is approached. However, it becomes important at higher concentration levels and in micropore and surface diffusion. To a first approximation the expression for the diffusive flux may be written... 

The ammonia—air dilution system dilutes the vaporized ammonia by a factor of 20 to 25 with air for better admixing through the AIG and to prevent explosive ammonia—air mixtures. Once the catalyst volume is selected, the NO removal is set by the NH /NO mole ratio at the inlet of the SCR system (39). 

Gas-phase mass-transfer coefficient for dilute systems kmoP[(s-m )(kPa solute partial pressure)] lbmol/[(h-fF)lbf/in solute partial pressure)]... 

Mass-Transfer Principles Dilute Systems When material is transferred from one phase to another across an interface that separates the two, the resistance to mass transfer in each phase causes a concentration gradient in each, as shown in Fig. 5-26 for a gas-hquid interface. The concentrations of the diffusing material in the two phases immediately adjacent to the interface generally are unequal, even if expressed in the same units, but usually are assumed to be related to each other by the laws of thermodynamic equihbrium. Thus, it is assumed that the thermodynamic equilibrium is reached at the gas-liquid interface almost immediately when a gas and a hquid are brought into contact. 

Tbe mass-transfer coefficients k c and /cf by definition are equal to tbe ratios of tbe molal mass flux Na to tbe concentration driving forces p — Pi) and (Ci — c) respectively. An alternative expression for tbe rate of transfer in dilute systems is given by... 

In dilute systems the logarithmic-mean insoluble-gas and nonvolatile-hquid concentrations approach unity, and Eq. (5-261) reduces to the dilute-system formula. For equimolar counter diffusion (e.g., binary distillation), these log-mean factors should be omitted. See Eq. (5-189). 

This equation is identical to the one for dilute systems since Icq = cyBM 3nd /cl = Note, however, that when /c and /cl are given,... 

All these equations reduce to their dilute-system equivalents as the iuei t concentrations approach unity in terms of mole fractious of inert concentrations in the fluids. 

T] Low MT rates. Dilute systems, Ap/p 1. Nq,.Nsc < 10 - Use with arithmetic concentration difference, x = length from plate bottom. 

When two or more gases are absorbed in systems involving chemical reac tions, the situation is much more complex. This topic is discussed later in the subsection Absorption with Chemical Reac tion. Graphical Design Method for Dilute Systems The following notation for multicomponent absorption calculations has been adapted from Sherwood, Pigford, and Wilke (Mass Transfer, McGraw-Hill, New York 1975, p. 415) ... 

Algebraic Design Method for Dilute Systems The design method described above can be performed algebraically by employing the following modified version of the Kremser formula ... 

For dilute systems in countercurrent absorption towers in which the equilibrium curve is a straight line (i.e., yj = mXi) the differential relation of Eq. (14-60) is formulated as... 

For example, the packed-tower design equation for a dilute system in which gas-phase reaciant A is being absorbed and reacted with liquid-phase reagent B is... 

For dilute systems it can be assumed that Gm, Em, and Pl are constant, and it normaUv is assumed that the interfacial area a of the packing is constant and is equal to the value that would exist without reaction. This last assumption needs careful consideration, since different methods for measuring a may give different results. Sharma and Danckwerts [Br Chem. Eng., 15(4), 522 (1970)] have reviewed various techniques for measuring interfacial areas. 

Under the above assumptions for dilute systems Eq. (14-70) can be integrated as follows ... 

This is the gas-phase mass-transfer limited condition, which can be substituted into Eq. (14-71) to obtain the following equation for calculating the height of packing for a dilute system ... 

For an isothermal absorber involving a dilute system in which a liquid-phase mass-transfer limited first-order irreversible chemic reaction is occurring, the packed-tower design equation is derived as... 

For a dilute system in which the liquid-phase mass-transfer limited condition is valid, in which a veiy fast second-order reaction is involved, and for which Nna E veiy large, the equation... 

The treatment here is restricted to the Langmuir or constant separation factor isotherm, single-component adsorption, dilute systems, isothermal behavior, and mass-transfer resistances acting alone. References to extensions are given below. Different isotherms have been considered, and the theory is well understood for general isotherms. 

The above apphes for very dilute systems, usually on the order of 1 grain/fF, or 2.3 g/m where a grain equals 1/7000 of a pound. When an appreciable amount of sohds are present, the efficiency increases... 

Install dilution system to keep flammable concentration below lower flammable limit (LEL)... 

Odor control by the addition of dilution air involves a problem associated with the breakdown of the dilution system. If a dilution fan, motor, or control system fails, the odorous material will be released to the atmosphere. If the odor is objectionable, complaints will be noted immediately. Good operation and maintenance of the dilution system becomes an absolute requirement, and redundant systems should be considered. 

Provision and use of appropriate health surveillance, e.g. for signs of dermatitis, asthma, effects of specific solvent exposures. Full use of any spray booth, enclosure, exhaust ventilation or dilution systems, and automatic handling equipment. (The efficiency of all local exhaust ventilation and other control systems should be maintained, and checked by testing.) Where appropriate, atmospheric monitoring of airborne pollution levels. 

For dilute systems, Stoke s law is applicable to particle settling. References cited at the end of this chapter provide design and sizing information. 

For dilute systems, the following approximations can be made dX dC /Cy, and dY dpA Pu- Note the following nomenclature used in the above correlations. 

Starting point for evaluating the settling characteristics of suspended solids for dilute systems. Note that from the definition of the Reynolds number, we can readily determine the settling velocity of the particles from the application of the above expressions (u, = /xRe/dpp). The following is an interpolation formula that can be applied over all three settling regimes ... 

Hence, the application of these formulas only applies to very dilute systems. At high particle concentrations, mutual interference in the motion of particles exists, and the rate of settling is considerably less than that computed by the given expressions. In the latter case, the particle is settling through a suspension of particles in a fluid, rather than through a simple fluid medium. 

Chemical reactions are sometimes conducted in a dilute solution to moderate reaction rates, to provide a heat sink for an exothermic reaction, or to limit maximum reaction temperature by tempering the reaction. In this example there are conflicting inherent safety goals—the solvent moderates the chemical reaction, but the dilute system will be significantly larger for a given production volume. Careful evaluation of all of the process risks is required to select the best overall system. 

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