THE EFFECT OF TRANSIENT VISCOELASTIC PROPERTIES ON INTERFACIAL INSTABILITIES IN SUPERPOSED PRESSURE-DRIVEN CHANNEL FLOWS

In a recent study, Ganpule and Khomami (submitted to J. Non-Newtonian Fluid Mech.) have shown that in order to accurately describe the exper imentally observed interfacial instability phenomenon in superposed ch annel how of viscoelastic fluids, a constitutive equation that can acc urately depict not only the steady viscometric properties of the exper imental test fluids, but also their transient viscoelastic properties must be used in the analysis. In the present study, the effect of diff erences in transient viscoelastic properties which can arise either du e to the differences in the predictive capabilities of various constit utive models or from the presence of multiple modes of relaxation on t he interfacial instabilities of the superposed pressure driven channel flows has been investigated. Specifically, a linear stability analysi s is performed using nonlinear constitutive equations which predict id entical steady viscometric properties but different transient viscoela stic properties. It is shown that different nonlinear constitutive equ ations give rise to the same mechanism of interfacial instability, but the boundaries of the neutral stability contours and the magnitudes o f the growth/decay rates, especially at intermediate and shortwaves, a re shifted due to the overshoots in the transient viscoelastic respons es predicted by the constitutive equations. In addition, the effect of the presence of multiple modes of relaxation on interfacial stability is studied using single and multiple mode upper convected Maxwell (UC M) fluids and it is shown that pronounced differences in the intermedi ate and shortwave linear stability predictions arise due to the fact t hat the increase in the number of modes gives rise to additional fast as well as slow relaxation modes and the presence of these additional relaxation modes gives rise to differences in the transient viscoelast ic response of the fluids in the absence of any overshoots. The effect of fluid inertia on the interfacial stability of viscoelastic liquids is examined and it is shown that at longwaves, inertia has a pronounc ed effect on the stability of the interface, whereas at shortwaves, el astic and viscous effects dominate. Furthermore, the mechanism of visc oelastic interfacial instabilities is studied by a careful examination of disturbance eigenfunctions as well as performing a disturbance ene rgy analysis. The results indicate that the mechanism of viscoelastic interfacial instabilities can be described in terms of interaction of mechanisms of purely viscous and purely elastic instabilities. However , since more than one mechanism for the instability is at work, the di sturbance energy analysis can not clearly distinguish between them due to the fact that the eigenfunctions used in the energy analysis conta in the information regarding both viscous and elastic effects. Hence, the mechanism of the instability must be determined by a careful exami nation of disturbance eigenfunctions. (C) 1999 Elsevier Science B.V. A ll rights reserved.