A numerical study on nonlinear dynamics of oscillatory time-depended viscoelastic flow between infinite parallel plates: utilization of symmetric and antisymmetric Chandrasekhar functions

The one-dimensional viscoelastic fluid flow between two infinite parallel plates with oscillatory inlet condition is examined using the Johnson–Segalman model. The symmetric and antisymmetric Chandrasekhar functions in space are utilized to represent the velocity and stress fields. The non-dimensional form of the conservation laws in addition to the constitutive equations are solved numerically based on the Galerkin projection method. Two critical Weissenberg numbers (We) for various Reynolds numbers (Re) and viscosity ratios (ε) are obtained to determine the stable range of nonlinear system behavior. Moreover, for the unsteady case, the effects of Re, viscosity ratio of solvent to solution as well as We are investigated. According to the obtained results, increasing of oscillations frequency in subcritical zone, the same as low frequency case, has almost no effect on the velocity and its gradient. Nevertheless, the normal stress amplitude of oscillations is reduced. The Re number determines the number of oscillations and the needed time prior to the steady condition. For lower Re, due to higher effect of viscosity, the initial fluctuations are intensely occurred in a short time period in contrary to the high Re case.