Fourier transform viscosity calculations

This surprising result prompted Mazenko, Ramaswamy and Toner to examine the anharmonic fluctuation effects in the hydrodynamics of smectics. We have already shown that the undulation modes are purely dissipative with a relaxation rate given by (5.3.39). To calculate the effect of these slow, thermally excited modes on the viscosities, we recall that a distortion u results in a force normal to the layers given by (5.3.32). This is the divergence of a stress, which, from (5.3.53), contains the non-linear term 0,(Vj uf. Thus, there is a non-linear contribution (Vj uf to the stress. Now the viscosity at frequency co is the Fourier transform of a stress autocorrelation function, so that At (co), the contribution of the undulations to the viscosity, can be evaluated. It was shown by Mazenko et that Atj(co) 1 /co. In other words, the damping of first and second sounds in smectics, which should go as >/(oo)oo , will now vary linearly as co at low frequencies. 

We used the Batchelor theory in combination with the MM-Model to calculate the interfacial stress waves for a number of varying emulsion parameters and frequencies as a function of strain amplitude yo resembUng a strain sweep experiment. Initially monodisperse emulsions were considered, characterized by a single droplet radius R, the interfacial tension F and the viscosities of the eonstituents tjd and r]m. The two functions f and fz depend on the viscosity ratio A and the capillary number Ca (Eq. 11). The modelled stress oscillatory signals were Fourier transformed and the relative intensities of the third and fifth harmonic were extracted from the spectra to obtain their ratio, I5/3 = h/i/h/i as a function of strain amplitude yo. 

Alumina with neutral, basic and acidic (both Lewis type) surfaces was introduced into PE0ME-LiC104 electrolytes of various concentrations and examined with a variety of techniques. At higher salt concentrations when aggregation of ions occurs, fillers led not only to a decrease of the viscosity, but also to an increase in the fraction of free ions. The best results were obtained in the case of acidic fillers (Fig. 2.7). This results from interaction of acidic surface states with anions (Lewis bases) present in electrolyte as free ions, ion pairs, triplets, etc. The latter especially affect the viscosity and cation transference number. With the use of acidic filler, the fraction of free ions was increased as confirmed by Fuoss-Kraus calculations, as well as by Fourier transform infrared (FT-IR) investigations (Marcinek et al. 2005). The increase in the fraction of free ions means an increase of the number... 

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