Viscosity wave vector-dependent

The viscosities depend on the wave-vector q and are closely related to the twist viscosity The effect on relaxation due to the wave-vector dependent rja has been examined [6.30] in smectic A phases and was found to be small. The wave-vector dependence in rjoc is ignored below. To obtain the mean square amplitude of each transverse mode, Eq. (6.18) and the equipartition theorem of energy are used to give... 

Ngai and Phillies(61) extend the Ngai-Rendell coupling model(62) to treat probe diffusion and polymer dynamics in polymer solutions. This is not an experimental paper it forces extant experimental data to confront a particular theoretical model, which in the paper was extensively reconstructed to treat the particular experimental methods under consideration. Ngai and Phillies consider zero-shear viscosities and optical probe diffusion spectra for HPC solutions, extracting from them the Ngai-Rendell model relaxation time tq and coupling exponent n. Optical probe spectra and other measurements were used to obtain n in four independent ways, namely from r](c) and from the concentration, time, and wave-vector dependences of g q,t). The four paths from t] and lead to consis-... 

The associated maximal growth scales with the forth power of the dominant growing wave vector, proportional to the surface tension and depending inversely on the viscosity for a given 2 ... 

An extrapolation of the form r] k) = /(0)/(l + a k ) where a is a state-dependent constant enabled the zero-wave vector Newtonian viscosity to be calculated. The fit gave 9.71 mP which compares well with the experimental value (8.9 mP). Guo and Zhang used equilibrium molecular dynamics to calculate the shear and bulk viscosities of liquid water. Using the SPC/E model they fotmd that these were 6.5 and 15.3 mP, respectively, as opposed to the experimental values 8.9 and 21.3 mP. 

Here 71 and K22 are the twist viscosity and elastic constant, g is a wave vector of the distortion mode under investigation (it depends on the geometry of the experiment, in particular, on the light scattering angle), the signs (+) and (—) in (6.34) are related to the cases q > Qq, and < 0 where qo = 2ttIPq is the equilibrium pitch. 

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