Oscillatory flow birefringence

The above description refers to a Lagrangian frame of reference in which the movement of the particle is followed along its trajectory. Instead of having a steady flow, it is possible to modulate the flow, for example sinusoidally as a function of time. At sufficiently high frequency, the molecular coil deformation will be dephased from the strain rate and the flow becomes transient even with a stagnant flow geometry. Oscillatory flow birefringence has been measured in simple shear and corresponds to some kind of frequency analysis of the flow... 

Cross-sectional view of the Miller-Schrag thin fluid layer (TFL) transducer, used to generate a precise sinusoidally time-varying shear flow for the oscillatory flow birefringence experiment (see Section 9.4.6). 

M. G. Minnick and J. L. Schrag. Polymer-solvent interaction effects in oscillatory flow birefringence studies of polybutadienes and polyisoprenes in Aroclor solvents. Macromolecules, 13 (1980), 1690-1695. 

T. P. Lodge and J. L. Schrag. Initial concentration dependence of the oscillatory flow birefringence properties of polystryene and poly(a-methylstyrene solutions. Macromolecules, 15 (1982), 1376-1384. 

The frequency-dependent response of star polymer solutions has also been studied by oscillatory flow birefringence [116]. The magnitude and the phase angle of the complex mechano-optic factor are obtained. Theoretical cal-... 

Fig. 2.5. Steady-state and dynamic oscillatory flow measurements on a 2 wt. per cent solution of polystyrene S 111 in Aroclor 1248 according to Philippoff (57). ( ) steady shear viscosity (a) dynamic viscosity tj, ( ) cot 1% from flow birefringence, (A) cot <5 from dynamic measurements, all at 25° C. (o) cot 8 from dynamic measurements at 5° C. Steady-state flow properties as functions of shear rate q, dynamic properties as functions of angular frequency m. Shift factor aT which is equal to unity for 25° C, is explained in the text, cot 2 % and cot 8 are expressed in terms of shear (see eqs. 2.11 and 2.22)...

In section 4.7, the Onuki-Doi theory for form birefringence and dichroism was developed and presented in equations (4.91) and (4.92). It is left to calculate the structure factor, S (q), as a function of flow. This was done in the limit of weak oscillatory flow for the... 

Failure to use Eq. (7.9) has resulted in several errors in the literature Zimm s (79) calculation of flow birefringence, as pointed out by Williams (76) Kirkwood and Plock s (40) calculation of large amplitude oscillatory response, as pointed out by Paul (62) Williams and Bird s (78) calculation of oscillatory normal stresses, as pointed out by themselves in a later publication (77). 

The geometry used for flow birefringence measurements in an oscillatory shear (Miller and Schrag, 1975) consists of two flat, parallel surfaces, one of which is fixed the other is made to oscillate in the plane parallel to the fixed surface. The liquid is confined to the thin layer between the surfaces. The light beam propagates through the layer in a direction perpendicular to the flow direction and parallel to the surfaces. This experimental arrangement and its application are discussed in detail below. 

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