HW4 - Rheology and Polymer Processing Problem Set 4 due...

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Rheology and Polymer Processing Problem Set 4 due Monday May 3 1. Stress Relaxation after Cessation of Steady Shear Flow Consider a situation where a viscoelastic fluid is being sheared between two flat plates at a constant shear rate of ˙ γ 0 for a long time. At time t=0, the shearing motion is suddenly stopped. For a Newtonian fluid, if the shear rate suddenly goes to zero, then the shear stress does also. However, since this fluid is viscoelastic, the stress will decay to zero over a time determined by the spectrum of relaxation times. Use the general linear viscoelastic model τ = G(t t')˙ γ dt' −∞ t together with the Generalized Maxwell Model form for the relaxation modulus G(t-t') to derive an expression for the exponential relaxation of the stress to zero in terms of λ k and η k . 2. The Kelvin Model The Kelvin (sometimes called "Voigt") linear viscoelastic model is given by τ yx (t) = G γ yx + η ˙ γ yx . If a sample of material at rest is suddenly subjected to a stress
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This note was uploaded on 06/16/2010 for the course ECH 111 taught by Professor Gohan during the Spring '10 term at UC Davis.

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HW4 - Rheology and Polymer Processing Problem Set 4 due...

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