Normal Stresses in Couette Flow

52 mm diameter aluminum rod rotating at 20 r rad/s in a large vat oi (a) Newtonian oil and (b) polyisobutylene solution. From Beavers and Joseph (1975). 

The latter uncertainty can be reduced by operating at large gap. The relations for this situation can be obtained by integrating eq. 5.3.28a from Rg to 

If the gap is not too large, vg varies approximately linearly across the gap and the second integral becomes 

Either inertial correction given above can be added to the measured pressure difference Apr to give an effective pressure difference, which will be a function only of A i = - r  

To evaluate the other integral, we can use eq. 5.3.7 to change variables from r to t as we did in deriving the shear rate relations 

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Because the coefficients of the invariants are not specified, the use of the Reiner-Rivlin equation is rather arbitrary. On the other hand, the time-dependent characteristics of viscoelastic fluids are not described by this equation. Neither are normal stresses in Couette flow correctly described by Eq. (13.3). 

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