Resonance in Laminar Pipe Flow of Non-Linear Viscoelastic Fluids

The relaxation response of viscoelastic fluids associated with the natural frequencies of oscillation that arise as a consequence of the structure of the constitutive equation is explored for the case of pulsating flow. The matching of the forcing frequency to the fluid’s natural frequencies induces a multiple resonance phenomenon. In this paper, the resonance phenomenon is investigated in pulsating flow in straight circular tubes when the fluid is characterized by the Johnson-Segalman constitutive model. An analytical solution is developed based on an asymptotic expansion in terms of a material parameter. The analysis reveals that the forcing frequency associated with the pressure gradient can generate a sequence of resonances of decaying intensity dependent on the material parameter and other fluid constitutive constants. The effects of resonance on the rate of flow and oscillating velocity field are explored for several values of the relevant parameters.