Using Rivlin and Erickson constitutive equation, the rotational instability of a second order fluid contained between two concentric rotating cylinders has been examined. It is found that the marginal instability is governed by a sixth order eigen value problem. The critical Taylor's number which determines the onset of instability has been determined as a function of m (= f)2/Q1), a (ware length) and S (= 2S~ + $2), with the help of a modified Galerkin technique. Figures 1 to 4 show the effect of second order terms on Taylor's number, radial velocity and streamlines. ยง 1. Introduction. The stability of a viscous liquid contained between rotating cylinders has been treated b y T a y 1 o r i), j e f f r e y s 2), M e k s y n 3) and C h a n d r a s e k h a r 4 ) .
It was shown t h a t the instability first sets in when the Taylor number exceeds 1708.6. J a i n 5) and G r a e b e l 6) discussed this problem for a non-Newtonian fluid. G re a b el showed t h a t for fluids with a positive coefficient of crossviscosity, the critical Taylor number is appreciably smaller t h a n for the corresponding flow of a Newtonian fluid. Recently I y y e ng a r i0) showed t h a t the presence of a magnetic field inhibits the onset of instabJlity of a non-Newtonian fluid contained between rotating concentric cylinders.
In recent years a growing amount of attention is being paid towards problems in the flow of second order fluids. The constitutive equation of the Rivlin-Erickson fluid 7) expressing the stress tensor โข in terms of the rate of strain tensor A, and B, the gradient *) On study leave at the