A THEORETICAL INVESTIGATION OF INTERFACIAL INSTABILITIES IN THE 3-LAYER SUPERPOSED CHANNEL FLOW OF VISCOELASTIC FLUIDS

The effects of viscosity and elasticity stratification on interfacial instabilities of symmetric and asymmetric three-layer superposed press ure driven channel flows have been investigated theoretically using li near stability analysis. The results indicate that the presence of an additional interface has a significant effect on the stability of the flow. Specifically, it has been shown that resonant instabilities as w ell as finite wavenumber interfacial instabilities could occur in this class of flows. Moreover, it has been demonstrated that a thin layer of less viscous fluid adjacent to the solid wall can stabilize longwav e disturbances in both symmetric and asymmetric superposed Newtonian f lows. In addition, in asymmetric superposed Newtonian flows it has bee n shown that when the jump in the shear rate across both the interface is positive then both the interfacial modes are unstable. In case of purely elastic instabilities, longwave disturbances can be stabilized if the more elastic fluid occupies the majority of the channel, irresp ective of its position. Moreover in both purely elastic and viscous in stabilities the dominant mode of the instability has been shown to hav e wavenumbers of O(1). It has also been demonstrated that stability of viscoelastic flows can not be deduced based on the guidelines develop ed for purely elastic and viscous instabilities (i.e., the effects are non-additive). Furthermore, nonlinear constitutive equations which ac curately depict the steady as well as transient viscoelastic propertie s of typical polymeric melts and solutions with various degrees of fle xibility and accuracy have been used to assess the constitutive comple xity required to accurately describe the stability characteristics of this class of flows by comparing the results of the stability analysis with the experimental results of Khomami and Ranjabaran [9]. It is sh own that the multimode Giesekus model, which can accurately describe t he steady as well transient behavior of the polymeric test fluids used in the experiments, can quantitatively describe the interfacial insta bility phenomenon in terms of the neutral stability contour as well as the growth/decay rate behavior when the effect of interfacial tension is taken into account. A rigorous energy analysis based on a disturba nce-energy equation for viscoelastic flows has also been performed to investigate the mechanism of the purely viscous and purely elastic int erfacial instabilities in pressure driven channel flows. The mechanism s of purely viscous and purely elastic instabilities of the three-laye r flows are found to be identical to those of the two-layer flows. Nam ely, the mechanism of shortwave purely viscous instability is found to be due to the viscosity mismatch and the subsequent perturbation vort icity mismatch at the interface (i.e., interfacial friction), whereas the mechanism of the longwave purely viscous instability is found to b e due to the bulk Reynolds stresses. The mechanism of purely elastic i nstability is found to be due to the coupling between the perturbation velocity and the jump in normal stresses across the interface at long waves as well as shortwaves. Finally, the possibility of non-normal in teractions between the two interfacial modes or interfacial and bulk m odes has been demonstrated and it has been shown that these interactio ns should be carefully considered when the disturbance growth/decay ra tes are experimentally determined. (C) 1998 Elsevier Science B.V. All rights reserved.