The Stress Tensor for a Solution of Rouse Chains

It IS necessary to introduce the notation that we will use here and in the next two sections regarding the successive terms that are produced when the distribution function and the momentum averages, which appear m the contributions to the stress tensor, are expanded in Taylor series. The first, second, third, terms resulting from the Taylor expansions of the fluxes (and not of the source terms ) are indicated thus it (l), it (2), it (3),the number in parentheses designating the Taylor order.  

We begin with ( ), the kinetic contnbution to the stress tensor at first order, given by the first term in the Taylor senes in the second line of Eq. 7.8. In this equation we replace f — v by f — u and then add a compensating term. This gives  

When Eq. (12.12) is used for the momentum-space average we obtain EMT  

Note that the term mvolving the vector a = VlnT vamshes. 

Next we estimate the magnitude of 5 we do this only for an isothermal system at constant composition. For this restricted situation, Eq. (13.14) becomes  

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