Recoil after Cessation of Steady Shearing Flow

By substituting tp+ from Eq. (12.3) into Eq. (12.2) and equating like powers of k one can obtain integro-differential equations for the 

In doing this one must be careful to expand the -quantides thus  

Here we have omitted terms like 8ip//8t, Atp/, and — S2sc)0 since they are obviously zero. 

For very dilute suspensions 0,1,1 is quite small so that the quadratic terms in Eqs. (12.16) and (12.17) are very nearly the same. In the limit of small shear rates comparison of Eqs. (12.16) and (12.17) gives  

This relation between y from recoil and the zero-shear-rate properties j0 and 60 from steady shear flow has also been obtained by Lodge [(46), p. 141] for his elastic liquid model which is derivable from a network entanglement theory his model does not, however, give the higher 

Also once K (t) and v (6,0 are known, the behavior of the normal stresses during recoil can be obtained from Eqs. (5.3) and (5.4). 

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Constrained Recoil after Cessation of Steady Shearing Flow [Bird, Evans, and Warner (3)]... 

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