Onset of flow in a vibrated thin viscoplastic layer

•Faraday instability of Herschel–Bulkley fluid.•Lubrication flow analysis.•Stabilizing spreading modes.•Unstable anti-diffusive motions.•Yield limit for static layer. The onset of flow in vibrated layer of viscoplastic fluid is investigated theoretically, using a lubrication approximation. The rheological behavior of the fluid is described by the Herschel–Bulkley model. The equation describing the evolution of the free surface is derived. Four different regimes are found depending on the ratio χ of the gravitational acceleration to the acceleration of vibration and the ratio of the yield stress to the shear-stress at the vibrated wall. Furthermore, a necessary condition for instability is derived. The different regimes are illustrated in the case of a 1D problem.