Couette flow anisotropic fluid

Figure 5.8 The geometrical set-up for one t)rpe of Couette flow. The anisotropic fluid or liquid crystal is placed in the annular region between two concentric cylinders of radii Ri and R2 which have corresponding angular velocities fli and Q2, respectively. The usual cylindrical polar coordinates (r, z) are used as discussed in the text, with the z-axis perpendicular to the page and coincident with the common axis of the cylinders. The velocity v is assumed to have a component only in the direction. The director n makes an angle with respect to the local coordinate axes and as shown.

The complete solution to this particular Couette flow problem for an anisotropic fluid is given by the results for and uj in equations (5.252) and (5.268), respectively, with the Lagrange multiplier A being given by (5.251) and the pressure p by (5.270). 

It is worth commenting on these results. It is known that for an incompressible isotropic viscous fluid in the above form of Couette flow, ve r) = ruj r) is identical to that obtained above [159, p.60]. In particular, for Qi = Q2 = we have = rf2, which shows that the entire fluid rotates rigidly with the cylinders. Also, when the outer cylinder is absent, so that Q2 = 0 and = 00, it is seen from equations (5.268) and (5.269) that vs = The main difference for an anisotropic fluid... 

We now investigate the Couette flow of a nematic liquid crystal in precisely the same type of experiment discussed above for an anisotropic fluid described in Fig. 5.8 and in essence follow the work of Atkin and Leslie [6]. The one-constant approximation for the nematic elastic energy will be assumed in order to simplify the presentation ... 

P.D.S. Verma, Couette Flow of Certain Anisotropic Fluids, Arch. Rat. Mech. Anal, 10, 101-107 (1962). 

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