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In this paper, the stability of unidirectional Couette flows of a spatially inhomogeneous complex fluid is investigated via the means of a linear stability analysis. The employment of a classical normal-mode analysis results in a fourth-order polynomial eigenvalue problem that is solved numerically via a Chebyshev polynomial method. The results of this study suggest that the flow of interest is unconditionally unstable but nevertheless the growth rates remain small so that the observability of the instability requires a very large time window. The observed instability manifests itself through the formation of downstream-propagating concentration waves that, due to their location at the bottom of the channel, closely resemble a series of superposed, high-concentration piles

Stability analysis of Couette flows of spatially inhomogeneous complex fluids