Stress relaxation after cessation of shear flow. A viscoelastic fluid is in steady-state flow between a pair of parallel plates, with v_x = ?y If the flow is suddenly stopped (i.e., ?/becomes zero), the stresses do not go to zero as would be the case for a NewtonJan fluid. Explore this stress relaxation phenomenon using a 3-constant Oldroyd model (Eq. 8.5-3 with ?₂ = ?₁ = ?₀ = 0).?

(a) Show that in steady-state flow to what extent does this expression agree with the experimental data in Fig. 8.2-4??

(b) By using Example 8.5-1 (part a) show that, if the flow is stopped at t = 0, the shear stress for t > 0 will be this shows why ?_xx is called the "relaxation time." This relaxation of stresses after the fluid motion has stopped is characteristic of viscoelastic materials.?

(c) What is the normal stress ?_xx during steady shear flow and after cessation of the flow?

Transcribed Image Text:

Tyx Part (a) -noy 1 1 + (₁)² Part (b) 1 Tyx = -Toy 1 + ₁)²