The Diffusivity Tensor for Steady-State Shear and Elongational Flows

4 The Diffusivity Tensor for Steady-state Shear and Elongational Flows 

As an illustration of Eq. (15.15) we can consider a steady simple shear flow of the form u, = yy, Vy = 0, and = 0, where y is the constant shear rate. For this flow field the diffusion tensor may be obtained by using the a tensors for the Rouse model (see end of Sect. 13.3) and the sum of the time constants given in DPL, Eq. 15.3-15.25  

If the concentration gradient is in the y-direction, then the Rouse model predicts no change in the mass flux in the y-direction, but does give a cross-diffusion term in the x-direction. If, on the other hand, the concentration gradient is in the x-direction, then - according to the Rouse chain model - the mass flux in the x-direction is altered by the flow, and there is a cross-diffusion effect in the jMlirection. 

Similarly for steady elongational flow with r, = — ex, Vy= — Jey, and Pj = ez, we get for very small elongation rates e  

That IS, in steady elongational flow the velocity gradients can have an effect on the mass flux. 

---