Tests on a Maxwell fluid—M. A viscoelastic Maxwell fluid is subjected to an oscillating strain γ0 cos ωt in a rheometer, and loss angles of δ = 0.375 and 0.158 radians are found for angular...

Tests on a Maxwell fluid—M. A viscoelastic Maxwell fluid is subjected to an oscillating strain γ0 cos ωt in a rheometer, and loss angles of δ = 0.375 and 0.158 radians are found for angular frequencies ω = 2 and 5 s−1, respectively.

(a) Show that these two data points are consistent with each other, and evaluate the relaxation time λ (s).(a) Show that these two data points are consistent with each other, and evaluate the relaxation time λ (s).

(b) At ω =2s−1, the tests show that the amplitude of the oscillations of τ /γ0 is 2.32 kg/m s2. Evaluate the viscosity η (kg/m s) of the sample.

(c) If, in another experiment, starting from zero strain and zero shear, the sample is strained by a steady amount ˙γ = c, verify that the corresponding shear stress is: τ = ηc 1 − e−t/λ. After what time will the stress have risen to half of its final asymptotic value?