Hydrodynamic correlation length, equation

If we omit the complication introduced by the gel modes, the collective diffusion constant might be calculated using a Kawasaki-Ferrell approximation (see equations 42 and 84), which always produces a hydrodynamic correlation length proportional to the static correlation length Marginal solvents and the crossover between good and 9 solvents have been reported in detail in ref. 112 and in the review of Schaefer and Han. ... 

Equation (31) has also been used to correlate results obtained in annular channels with insufficient hydrodynamic entrance length (B2, B3). Some of the data fit Eq. (31) with a slightly smaller coefficient. A similar expression, including terms for the hydrodynamic entrance length, was used by Pickett and Ong (P3a). 

Thus, besides the Eqs. (4), (5) and (8), the known steady-state thermo-hydrodynamic correlations of the LHP should be also implemented to the model. The necessity of such mutual consideration appears obvious in case of determining transition conditions from the thermal mode 2 to the thermal mode 3, and in the analysis of heat transfer regularities of the thermal mode 3. Assuming that vapor channel length Lych is independent on the heat supply, the following equation yields a dependency between the curvature radius and surface area of the vapor-liquid interface ... 

The apparent hydrodynamic diameters of the droplets (or the correlation length), as calculated using the Stokes-Einstein equation for a number of different systems, are given in Table 2. These early findings showed that the micelle sizes measured in near-critical and supercritical solutions were similar to those found for conventional water-in-oil microemulsions in liquid alkane. At lower fluid densities, DLS probes the combined effect of the collective diffusion coefficient of the micelle cluster and that of the individual micelles. 

For those systems near a phase transition, the apparent hydrodynamic diameter of the droplets (or the correlation length), as calculated using the Stokes-Einstein equation, appears to decrease as pressure increases [2,4,39]. For example, the apparent hydrodynamic diameter of a microemulsion droplet (for [surfactant] = 150 mM and 5) in supercritical xenon [2] decreases from 6.5 to 4.5 nm as pressure is increased from 350 to 550 bar (10 bar = 1 MPa). This effect is due to the change in the extent of micelle clustering rather than an actual change in the micelle size. 

A local correlation length f(x) was defined (the length over which excluded volume effects are screened), the polymer layer at the interface then resembling a network of variable mesh size (x). When the hydrodynamic equation is integrated up to a distance correspjonding to the longest mesh size Rp (the Flory radius of polymers in solution), it is found that the hydrodynamic thickness scales... 

As a first step it is noted that a finite cutoff qo should be retained in the evaluation of both mode-coupling integrals given by equations (6.28) and (6.29), since away from the critical point will no longer be negligible compared to the finite correlation length t. Here only a solution for the transport properties in the macroscopic hydrodynamic limit A 0 is needed. From the information presented in the previous section it... 

L is the specimen length, D is the diffusion coefficient of oxygen. Re = XV/u, and Sc= v/D. The equation correlating the corrosion rates for the three hydrodynamic geometries is given as... 

Some of the widely used correlations that are applicable to the flow channels in a fuel cell are outlined here. However, before selecting an appropriate heat transfer correlation, the hydrodynamic and thermal entry lengths of flow geometry are estimated based on criteria outlined by Equations 6.33 and 6.35. 

---