An experimental investigation of interfacial instabilities in multilayer flow of viscoelastic fluids. III. Compatible polymer systems

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Abstract
Superposed plane Poiseuille flow of a compatible polymer system consisting of linear low‐density polyethylene (LLDPE) and high‐density polyethylene (HDPE) has been investigated. Using the apparatus and procedures developed in our previous study [G. M. Wilson and B. Khomami, J. Rheol. 37, 315 (1993)], we have investigated the role of viscosity ratio, layer depth ratio, and disturbance wave number on the stability of the interface. We have presented experimentally determined stability diagrams and growth rate curves and compared these with theoretical predictions based on the linear stability analysis using a modified Oldroyd‐B constitutive equation. Additionally, we have compared our experimentally determined growth rate curves to those presented earlier for the incompatible system of polypropylene (PP) and HDPE [G. M. Wilson and B. Khomami, J. Non‐Newt. Fluid Mech. 45, 355 (1992)]. These comparisons reveal an unexpectedly low disturbance growth rate for the LLDPE/HDPE system which is attributed to diffusive and convective mixing in the vicinity of the interface. We have shown that mixing can occur on both small and large scales. Small scale mixing occurs because of oscillatory currents that form near the interface when an interfacial wave of any amplitude is present. On the other hand, when the interfacial waves reach a critical amplitude and wave number, they bifurcate supercritically which causes a portion of the wave to be pulled into the adjacent layer (i.e., large‐scale mixing).

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