Critical length scale, definition

Thus, the available data related to transition in circular micro-tubes testify to the fact that the critical Reynolds number, which corresponds to the onset of such transition, is about 2,000. The evaluation of critical Reynolds number in irregular micro-channels will entail great difficulty since this problem contains a number of characteristic length scales. This fact leads to some vagueness in definition of critical Reynolds number that is not a single criterion, which determines flow characteristics. 

According to this definition dilute solutions of long macromolecules are critical. The role of the correlation length is played by the radius of gyration Rg rsj Nu — oo N — oo, and by virtue of the chain structure a polymer coil shows density fluctuations on all scales r < Rg. Indeed, a blob of size r is just a correlated fluctuation of the density. 

Since in Fig. 19 critical temperatures have been estimated by a rough extrapolation only, this study [39] could not make too definitive statements about the shift of the critical temperature due to confinement. A more extensive study has been possible for the bond fluctuation model [55], extracting both critical temperatures and the coexistence curves by use of the finite size scaling technique [236-239,280]. Figs.21, 22 present the results for chain length N=32. While mean field theory Eqs. (36) and (37) in Sect. 2.1 has predicted a crossover from... 

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