Steady-State Maxwell Orthogonal Rheometer Flow

As an example of a flow which is neither a shearing flow or an elon-gational flow we consider the Maxwell orthogonal rheometer flow (see Fig. 10). In this flow the velocity profile is vx = — Q y — Yz), vy = Ox, and v. = 0 where Y = a/l. Here the diffusion equation is obtained from Eq. (3.9) with the first line of the right side omitted, and Eqs. (3.11) and (3.12) with Kxy= —Q, kxz = YQ, and Kyx = Q  

When y (6, f ) has been obtained from Eq. (21.1), the stresses in the system are then calculated from the appropriate simplification of Eq. (4.19)  

After this series is substituted into Eq. (21.1) and the coefficients of (6/ r Q)J are equated, the resulting set of differential equations are solved to give the ipj. In this way one obtains finally  

The quantities in Eqs. (21.6) and (21.7) are tj (Q) and tj (Q) where tj and rf are the quantities defined in 7 for the small amplitude oscillatory experiment. Hence when the limit is taken as T- 0, xXJ(—QY) - rj and xyJ(— QY)- t) . The same limiting result was obtained for this flow by Bird and Harris (4) using an integral continuum model. Thus, this gives additional support to the argument that the Maxwell orthogonal rheometer flow provides the possibility of measuring the dynamic properties of fluids. 

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Steady-State Maxwell Orthogonal Rheometer Flow [Warner and Bird (75)J... 

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