Critical regime

When the voltage is critical, regime b), there is no concentration polarization because the electrophoretic transport is equal to the convective transport. Any build up of species on the membrane will be dissipated due to diffusion driven by the concentration difference. In this regime, increasing the tangential velocity is expected to have no influence on the flux because fluid shear can only improve the transport of particles down a concentration gradient. In this case, there is no concentration gradient. 

As an example, the dependence of hydrodynamic parameters of critical regime for the sand-water mixture and sand-glycol (80 % glycol solution in water) mixture is illustrated in Figure 1. The volumetric concentration C of the mixtures varied from 5 to 30 %, a mean diameter of sand was d = 0.25 mm and a pipe diameter was D = 50.4 mm. The values of the critical velocity VCr and critical pressure gradient ICr differ substantially according to the used carrier liquid. 

As discussed in [79], there is no critical enhancement of the thermal diffusion coefficient Dj, which retains its background value Db throughout the asymptotic critical regime. It appears reasonable to assume the same activation temperature Ta both for ab andZ) f ... 

Although the asymptotic critical regime with the Ising-like scaling exponents has been neglected in this description, the fit curves in Fig. 8 are a reasonable parameterization for all three coefficients in the one-phase regime. This parameterization then serves as input for the numerical model. A more detailed discussion of the whole procedure can be found in [100],... 

The polymer blend PDMS/PEMS with molar masses of Mw = 16.4 and 22.3kgmol 1, respectively, is similar to the one which has previously been used for the investigation of transport properties in the critical regime [81]. A 515nm and 20 mW laser was used for local heating. The blend with a PDMS weight fraction of c = 0.536 is almost critical with a critical temperature of Tc = 37.7°C. A minute amount of an inert dye (quinizarin) was added for optical absorption at... 

Fig. 3.9. W vs. T for a PPy-PF6 sample in the critical regime. The pressure-induced transition to the metallic regime and the field-induced transition to the...

The parameter r can be optimized for thermodynamic consistency between the virial and compressibility routes to the free energy of the system. As discussed in Section 5.3.2, the KHM closure (7) brings about an additional long-range term in the direct correlation functions in the critical regime. 

In the insulating (semiconducting) regime W has a negative temperature coefficient, in the intermediate (critical) regime it is temperature independent and in the metallic regime it has a positive temperature coefficient (Menon et al., 1998). W is plotted in the upper panel of Fig. 9.36 and shows that sample A, which had a conductivity of 8 x 103 at 20 mK, is in the metallic... 

The temperature at which the phase transition occurs is called the critical temperature or Tg. Most, but not all, magnetic phase transitions are continuous , sometimes called second order . From a microscopic point of view, such phase transitions follow a scenario in which, upon cooling from high temperature, finite size, spin-correlated, fractal like, clusters develop from the random, paramagnetic state at temperatures above Tg, the so-called critical regime . As T Tg from above, the clusters grow in size until at least one cluster becomes infinite (i.e. it extends, uninterrapted, throughout the sample) in size at Tg. As the temperature decreases more clusters become associated with the infinite cluster until at T = 0 K all spins are completely correlated. 

Now, let us go back to the methods of forecasting conditions for obtaining critical regimes for keroplast flow. As demonstrated in [20], critical tension of melted filled polymer can be calculated as a regular point on the flow curve, i.e. 

Fig. VI-4 shows R(to) for samples (A-F) as measured at room temperature. For the most metallic sample (A), R(w) exhibits distinct metal-like signatures a free carrier plasma resonance as indicated by the minimum in R(w) around 1.5 x 10 cm and high R(a)) in the far-IR (R 90% for (o<20 cm ). As PPy-PF goes from the metallic to the insulating regime via the critical regime (Samples A"F), R(w) is gradually suppressed in the IR. In the insulating regime (F), R(o)) remains well below that of the metallic sample (A) throughout the IR (R = 65% at w = 50 cm ). Note that the R(t>)) spectra are in excellent correspondence with the transport results (this is especially clear at low frequencies in Fig.VI-4b) the...

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