Transfer Principles Dilute Systems

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-liquid 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 equilibrium. Thus, it is assumed that the thermodynamic equilibrium is reached at the gas-liquid interface almost immediately when a gas and a liquid are brought into contact. 

For systems in which the solute concentrations in the gas and liquid phases are dilute, the rate of transfer may be expressed by equations which predict that the rate of mass transfer is proportional to the difference between the bulk concentration and the concentration at the gas-liquid interface. Thus 

The mass-transfer coefficients k G and k L by definition are equal to the ratios of the molal mass flux NA to the concentration driving forces (p Pt) and (ct — c) respectively. An alternative expression for the rate of transfer in dilute systems is given by 

The mass-transfer coefficients defined by Eqs. (5-261) and (5-262) are related to each other as follows  

The above equations may be used for finding the interfacial concentrations corresponding to any set of values of x and y provided the ratio of the individual coefficients is known. Thus 

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Mass-Transfer Principles Concentrated Systems When solute concentrations in the gas and/or liquid phases are large, the equations derived above for dilute systems no longer are applicable. The correct equations to use for concentrated systems are as follows ... 

Pneumatic Conveying Pneumatic conveying systems can generally be scaled up on the principles of dilute-phase transport. Mass and heat transfer can be predicted on both the slip velocity during acceleration and the slip velocity at full acceleration. The slip velocity increases as the solids concentration is increased. 

Drop size distribution in dilute suspensions of electrical conducting liquids may be determined using the Coulter principle but the need to add what may be undesirable conductive materials limits its applicability [213-215]. The use of chemical means to measure interfacial area has been used extensively for gas-liquid dispersions. Chemical reaction methods for determining the interfacial area of liquid-liquid systems involve a reaction of a relatively unchanging dispersed-phase concentration diffusing to the continuous phase. The disadvantage of this approach is that the mass transfer can affect the interfacial tension, and hence the interfacial area [216-218]. 

The principle of extraction method used to separate PTC and product is based on solubility of quaternary ammonium salt in alkaline aqueous solution. " For example, tetrabutylammonium bromide is soluble to the extent of 27% in dilute (1% NaOH) aqueous solutions, but when the solution is made more concentrated (15% NaOH), the solubility of Bu4N Br decreases to 0.07%. When the products are obtained in PTC system, they can be usually separated from PTC by distillation method. PTC catalyst in the distillation residue may sometimes be reusable. With quaternary ammonium salts as catalysts, temperatures above 100-120 C usually result in partial or total decomposition of the quaternary salts to trialkylamines and other products. Mieczynska et al. and Monflier et al. investigated the hydrogenation and hydroformylation under phase transfer catalytic conditions. They found that the yield of aldehydes obtained in hydroformylation of 1-hexene strongly depends on solvent 24% in toluene, 53-86% in toluene-water-ethanol mixture and 77-94% in water-ethanol solution. The mixture of water-ethanol as a solvent was also found to be the best for hydrogenation of 1-hexene (96% of hexane). Conversion of Ph2PCH(CH3)(COOH) phosphine into sodium salt Ph2PCH(CH3)(COONa) yields aldehyde in toluene, 92% in toluene-water and 94% in toluene-water-ethanol mixture. 

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