11. Interfacial Mechanism and Kinetics of Phase-Transfer Catalysis

The extractive effectiveness factor , defined as the effect of the diffusion boundary layeron the extraction rate of quaternary salt can be characterized in terms of the ratio of Eq.(62) to Eq (65): ¼ K o m½QXŠ m½QXŠ k m m½QXŠ m½QXŠ ð66Þ¼ðBi o þ Bi a þ 1Þ 1in which Bi o ð¼ mk m =k o Þ and Bi a ð¼ mk m =k a Þ are Biot numbers for the organic phase andaqueous phase, respectively. Equation (66) represents the mass transfer ratio of conductionrate to convection rate of the quaternary salt at the interface. According to theexperimental data of Lin [127], the values of , Bi o ,andBi a are calculated to be around0.96, 0.04, and 0.002, respectively, when the agitation rate is lower than 100 rpm. Hence, itclarified again that the membrane resistance at high agitation rates controls the masstransfer resistance of the membrane extraction.Usually, mass transfer coefficients can be correlated from the classical equation:Sh ¼ aRe b Sc cð67Þwhere Shð¼ k m d=DÞ is the Sherwood number; Re (¼ du=Þ is the Reynolds number, Sc(¼ =D) is the Schmidt number, D is the diffusivity in the bulk fluid, u is a characteristicvelocity of the fluid such as the mean fluid flow velocity, is the density, is the viscosity,and d is a characteristic dimension of the system.In Eq. (67), a is an experimental constant and c usually has a value of 1/3 [128–130].The value of b depends on the type of equipment and system, and most of the theoriespredict a one-half power on the Reynolds number [131]. The mass transfer from bulksolution to the surface of the membrane is mainly controlled by the turbulence of the fluidmotion created by stirring. The characteristic velocity is defined in terms of the stirringspeed ðu ¼ ndÞ. The values of a and b were determined from the intercept and slope of theline of Sh=Sc 1=3 against Re for the specified mass transfer coefficients of k a , k o , and K o .These parameters are different and are dependent on the system geometry and flow pattern.However, it can be concluded that the exponent value on Re varied from 0.2 to 1.0,depending on the design of the membrane permeation system.The correlating equation [67] established here can be used to evaluate the masstransfer coefficient and the thickness of the diffusion boundary layer, ð¼ d=shÞ. Thethickness of this layer calculated for an organic solvent and aqueous solution were10 3 –10 2 and 10 9 –10 7 cm, respectively, for the four types of quaternary salts studied.For a solute crossing a mass transfer resistance film, the transfer time can be approximatelyestimated by the following equation [131]:ðfilm thickness)2Transfer time ¼ð68Þdiffusion coefficientBased on the data presented here, the estimated transfer times for a solute crossing theorganic and aqueous mass transfer resistance film are about 1–10 and 10 11 –10 8 s, respectively.E. Interfacial Phenomena in LLPTCStarks [132] proposed that the transfer rate of an anion across the interface is largelygoverned by four factors: (1) interfacial area, (2) anion activity and hydration at theCopyright © 2003 by Taylor & Francis Group, LLC