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Motivated by the need for a theoretical study in a planar geometry that caneasily be implemented experimentally, we study the pressure driven Poiseuilleflow of a shear banding fluid. After discussing the "basic states" predicted bya one dimensional calculation that assumes a flat interface between the bands,we proceed to demonstrate such an interface to be unstable with respect to thegrowth of undulations along it. We give results for the growth rate andwavevector of the most unstable mode that grows initially, as well as for theultimate flow patterns to which the instability leads. We discuss the relevanceof our predictions to the present state of the experimental literatureconcerning interfacial instabilities of shear banded flows, in bothconventional rheometers and microfluidic channels.

Shear banding and interfacial instability in planar Poiseuille flow