Correlation dimension scaling region

Computer simulation is invariably conducted on a model system whose size is small on the thermodynamic scale one typically has in mind when one refers to phase diagrams. Any simulation-based study of phase behavior thus necessarily requires careful consideration of finite-size effects. The nature of these effects is significantly different according to whether one is concerned with behavior close to or remote from a critical point. The distinction reflects the relative sizes of the linear dimension L of the system—the edge of the simulation cube, and the correlation length —the distance over which the local configurational variables are correlated. By noncritical we mean a system for which L E, by critical we mean one for which L [Pg.46]

By varying the impeller blade dimensions variations in power per unit volume were made at a constant impeller speed. At low power per unit volumes there was a linear increase in k a which correlated with P/V with an exponent of 0.9 to 1.2. yond the breakpoint the exponent relating the P/V dependence was 0.53. In both regions the k,a dependend on the superficial gas velocity to the 0.3 power. Tnese results are similar to those reported earlier by Blakebrough and Sambamurthy (1966) and Hamer and Blakebrough (1963) obtained in smaller scale vessels also using paper pulp suspensions. Other references on the aeration of viscous non-Newtonian fermentation broth are Banks (1977) and Blanch and Bhavaraju (1976). 

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