Triphasic equilibrium

Intraparticle diffusion limits rates in triphase catalysis whenever the reaction is fast enough to prevent attaiment of an equilibrium distribution of reactant throughout the gel catalyst. Numerous experimental parameters affect intraparticle diffusion. If mass transfer is not rate-limiting, particle size effects on observed rates can be attributed entirely to intraparticle diffusion. Polymer % cross-linking (% CL), % ring substitution (% RS), swelling solvent, and the size of reactant molecule all can affect both intrinsic reactivity and intraparticle diffusion. Typical particle size effects on the... 

An example of this phase-coexistence is shown in Fig. 13. We will call this macroscopic phase boundary a bottleneck due to its shape. In fact, this coexistence includes three phases, i.e. swollen gel, shrunken gel and pure solvent phases surrounding the gel, and has been called triphasic equilibrium in the... 

The phase coexistence of gels at the first-order transition is accompanied by a number of unusual features, of which a few will be mentioned below. First, the fact that the triphasic equilibrium persists over a wide temperature range is an apparent contradiction to the Gibbs phase rule. This rule predicts that the... 

The opposing reactant contactor mode applies to both equilibrium and irreversible reactions, if the reaction is sufficiently fast compared to transport resistance (diffusion rate of reactants in the membrane). This concept has been demonstrated experimentally for reactions requiring strict stoichiometric feeds, such as the Claus reaction, or for kinetically fast, strongly exothermic heterogeneous reactions, such as partial oxidations. Triphasic (gas/liquid/solid) reactions, which are limited by the diffusion of the volatile reactant (e.g., olefin hydrogenation), can also be improved by using this concept. 

Relevant kinetic parameters (half-life, body pool, and mean transit time in organs) can be calculated. According to Equation 1 the specific activity in plasma shows a triphasic decay with half-lives of ti = 1.1 h, t2 == 22 h, and 3 == 61 h. The half-lives ti and 2 essentially describe the distribution of the compound into the system. The third half-life of 61 h (2.5 d) is valid for all tissues after attainment of the distribution equilibrium and represents the overall half-life of elimination from the body under the special conditions of the study (ascorbate status of the animals). 

Under the action of DC electric field the redistribution in the double electric layer occurs and shrinking of the specimen from both side takes place. It is interesting to note that the coexistence of three phases (triphasic equilibrium), i.e. 

Each phase behavior type is associated with an emulsion type, but near optimum formulation either a monophasic (micioemulsion) or triphasic (microemulsion at equilibrium with excess oil and water) is exhibited, dqiending on the amphiphile surfactant/alcohol mixture (S -f- A) concentration. When lempenituie... 

Fig. 6.20 Triphasic F + I2 + N equilibrium in dispersions of boehmite rods plus polystyrene chains in ortho-dichlorobenzene [43]. Picture was kindly offered by J. Buitenhuis, IFF, Forschungszentrum Jiilich, Germany...

Later, Burning and Lekkerkerker [37] observed isotropic—nematic phase separation in a dispersion of sterically stabilized boehmite rods, which approximate hard rods, in cyclohexane. Buitenhuis et al. [43] studied the effect of added 35 kDa polystyrene (/ g = 5.9nm) on the hquid crystal phase behaviour of sterically stabilized boehmite rods with average length L = 1.1 nm and average diameter D = ll.lnm in ortho-dichlorobenzene. Different phase equihbria were observed. Two biphasic equilibria dilute isotropic phase Ij + nematic N, concentrated isotropic phase I2 + nematic N and a triphasic equilibrium 1 -F I2 + N (see photo. Fig. 6.20). In this system the boehmite rods are quite polydisperse. Therefore comparison with theory should be done with an approach including polydisperse rods. We further note no li +12 coexistence was observed experimentally but... 

We now compare this with experiment. Dogic [49] extended the earlier work of Dogic and Fraden [29] on mixed suspensions of fd and dextran to higher dextran concentrations. The phase diagram he observed is plotted in Fig. 6.22. Above dextran concentrations of 55 mg/ml the I-N transition is indeed superseded by the I-Sm transition (as predicted, see Fig. 6.23). No observations were reported on the (narrow) triphasic I-N-Sm equilibrium that is expected between the biphasic I-N and I-Sm phase equilibria. 

Critical constants saturates vapour pressure for the triphase equilibrium. 

With triphasic spiral CT, results are even better for characterization of liver hemangioma. In a series of 375 liver lesions, 86% (51/59) of the hemangiomas had peripheral nodular enhancement of vascular attenuation on arterial and portal phase imaging and were hyperattenuating with possible central hypoattenuation or isoattenuation to vascular space in the equilibrium phase (van Leeuwen et al. 1996). In this series, there were no false-positive cases. Conversely 13.6% of the hemangiomas were atypical hypoattenuating on all... 

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