Study on the constitutive equation with fractional derivative for the viscoelastic fluids - Modified Jeffreys model and its application

Based on the classic linear viscoelastic Jeffreys model, a modified Jeffreys model is suggested. The corresponding five-parameter equation with fractional derivatives of different orders of the stress and rate of strain is stated and the characteristic material functions of the linear viscoelasticity theory, such as the dynamic moduli, are derived. The comparison between the measured dynamic moduli of Sesbania gel and xanthan gum and the theoretical predictions of the proposed phenomenological model shows an excellent agreement.