Mixtures critical slowing-down

Near the critical point a fluid is known to behave differently, and many anomalies appear in the static and dynamical properties. The important anomalies in the dynamical properties are the critical slowing down of the thermal diffusivity (Dt) in a one-component fluid and the interdiffusion of two species in a binary mixture and also the divergence of the viscosity in a binary mixture. 

Second-order phase transitions also show up via the critical slowing down of the critical fluctuations (Hohenberg and Halperin, 1977). In structural phase transitions, one speaks about soft phonon modes (Blinc and Zeks, 1974 Bruce and Cowley, 1981) in isotropic magnets, magnon modes soften as T approaches Tc from below near the critical point of mixtures the interdiffusion is slowed down etc. This critical behavior of the dynamics of fluctuations is characterized by a dynamic critical exponent z one expects that some characteristic time r exists which diverges as T - TCl... 

The coefficient of sell-diffusion does not appear to have an anomaly near the critical point. For the engineer, however, the mutual dift usion coefficient is the more important property. The binary dilfusion coefficient approaches zero at the mixture critical point ("critical slowing-down"). In dilute mixtures, however, the decrease of the binary dilfusion coefficient is not seen until the critical line is approached very closely. For many practical purposes, such as supercritical extraction and chromatography, the mixture is dilute, and it can be assumed that the coefficient of binary diffusion is intermediate between that in the vapor and that in the liquid. Since the diffusion coefficient decreases roughly inversely proportional to the density, dilfusion in supercritical solvents is much more rapid than in liquid solvents, thus increasing the speed of diffusion-controlled chemical processes. 

This critical slowing-down also shows up on the other side of the phase boundary, when for a critical mixture the critical temperature is approached... 

Hence, the behavior of the mass-diffusion coefficient of a mixture in the critical region is controlled by the behavior of (dn/dx)T,p = x As pointed out in Section 6.1, in binary mixtures the osmotic susceptibility x diverges near a consolute point and leads to the critical slowing down of the mass diffusion. Near a vapor-liquid critical point, on the other hand, where the thermodynamic properties undeigo a crossover from pure-fluid-like behavior before they display their asymptotic mixture behavior (Jin et al. 1993), the osmotic susceptibility does not exhibit a critical behavior except at temperatures very close to the plait-point temperature (for the system mentioned above, the reduced temperature has to be smaller than 5 x 10 ). Therefore, not too close to the critical point, the mutual diffiisivity is dominated by its background value d/(px)> and the critical slowing down that follows the Stokes-Einstein diffusion law is not seen in the mass diffusion coefficient. 

This critical slowing down also shows up on the other side of the phase boundary, when for a critical mixture the critical temperature is approached from the one phase region. The kinetic parameter of interest, to be used on both sides, is the collective diffusion coefficient, Dcoi, defined as... 

Raising a mixture of fuel and oxidizer to a given temperature might result in a combustion reaction according to the Arrhenius rate equation, Equation (4.1). This will depend on the ability to sustain a critical temperature and on the concentration of fuel and oxidizer. As the reaction proceeds, we use up both fuel and oxidizer, so the rate will slow down according to Arrhenius. Consequently, at some point, combustion will cease. Let us ignore the effect of concentration, i.e. we will take a zeroth-order reaction, and examine the concept of a critical temperature for combustion. We follow an approach due to Semenov [3],... 

Some reactions can be stopped by adding a suitable component. This is sometimes possible for catalytic reactions where a catalyst killer can be added in small amounts. For pH-sensihve reactions, a pH modification may also slow down or even stop the reaction. In these cases, the addition of only a small amount of a compound will suffice. Agitation is a critical factor, especially to ensure that a small amount of an inhibitor must be dispersed homogeneously in a large volume of reaction mixture. In order to achieve a fast and homogenous dispersion, often the vessel containing the inhibitor is pressurized, for example, nitrogen and nozzles are used to spray it into the reaction mass. 

The first two-hour lecture session starts with a discussion of the fission process, toe production of neutrons during fission, the role of neutrons in inducing fission. Cross sections are introduced as measures of reaction probabilities, including capture-to-fission ratios. This leads into a discussion of fast fissioning systems, followed by neutron slowing down, moderator effects, and the criticality of solutions. Mixtures of finely divided fissile material, such as foil, wire, or powders, in moderating media are dtocussed as pseudo-solutions. 

IKI Ikier, C. and Klein, H., Slowing down of the diffusion process in polystyrene/ cyclohexane mixtures approaching the coexistence curve and the critical point. Macromolecules, 28, 1003, 1995. 

Some reactions can be stopped by the addition of a suitable component. Dilution by an inert and cold material may lower the temperature to slow down the reaction. For this type of measure, the critical factors are the amount and rate of addition and the temperature of the quenching material. The required empty volume must be also be available in the reactor. Calorimetric methods are of great help in the design of such measures, because they allow measurement of the heat of mixing, which is often important, and the thermal stability of the resulting mixture. 

We present here a forward recoil spectrometry (FRES) study of thermodynamic slowing down" of mutual diffusion in isotopic polymer mixtures and of the diffusion of homopolymers into symmetric diblock copolymer structures. The measurements of "thermodynamic slowing down" were performed on binary mixtures of normal and deuterated polystyrene (PS). Both the Flory interaction parameter, the upper critical... 

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