Superposition of Steady Shearing Flow with Transverse Small-Amplitude Oscillations

The final non-shearing flow to be considered is the superposition of steady shearing flow with transverse small-amplitude oscillations. Here vx — kz, vy — Ske K°e z, and vz = 0. The diffusion equation for this flow is obtained from Eq. (3.9) with the first line of the right side omitted, and Eqs. (3.11) and (3.12) with kxz = k, Kyz = 9tf. kV , and all other 

The quantity in Eq. (22.8) is rj (to) of the small-amplitude oscillatory experiment and is obtained, as expected, in the limit of vanishingly small k. It should be noted that when Act) = kQ and (AOT)=Ak, the expressions for tj of Eq. (22.8) and xxJ(—QY) of Eq. (21.6) are equivalent except for the final term in the series. Bird and Harris (4) found these two series to be equivalent to any order of terms from a calculation made using an integral continuum model. From the above result for the rigid dumbbell model we conclude that Bird and Harris result is a fortuitous one and that, in general, these two series are not equal. The only data to date on the transverse superposition experiment are those of Simmons (69 a), which show that tf —tjs as a function of cw decreases with increasing k, and that the curves of rf as a function of to go through a maximum. 

The final non-shearing flow to be considered is the superposition of steady shearing flow with transverse small-amplitude oscillations. Here v =Kz, = and v = 0. The diffusion equation for this 

One of the aims of a molecular theory is to find interrelations among the theoretical results, in the hope that such interrelations may be useful in interpreting experimental data or in catalyzing interest in new experiments. From several of the previous sections we can conclude the following  

In addition to the above relations, one finds a relation between the non-Newtonian viscosity curve and tte complex viscosity. By comparing the results in Eq. (6.7) and Eq. (7.17) to the order of terms in the square of the shear rate or frequency, it is found that tj — q ) vs. ic is the same as i — sl vs. kto where k = [/60/49= 1.1. This agrees reasonably well 

This idea of comparing results from several experiments and cancelling out the model is a rather important idea. It may well be that further structural studies will prove useful for obtaining id about interrelatioifi among several experiments. Often it is found that the interrelations obtained in this way are better than the expressions for individual experiments which rest on a model which k manifestly inadequate. 

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Superposition of Steady Shearing Flow with Transverse Small-Amplitude Oscillations [Warner and Bird (75)1... 

Superposition of steady shearing flow with transverse small-amplitude oscillations... 

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