Centrifugal stability of a viscoplastic fluid interface and the amplitude threshold for yielding

The linear stability of the interface between a Newtonian inner fluid and a Bingham outer fluid under centrifugal body force is analysed. A Papanastasiou regularisation of the yield-stress term yields a single damped-oscillator dispersion relation σ 2 + 2 β n σ + ω n 2 = 0 , parametrised by the regularisation parameter M . The inviscid, Newtonian, and strict Bingham regimes emerge as limits of this expression, with the strict limit consistent with the Frigaard–Nouar ordering criterion. A one-dimensional axisymmetric nonlinear calculation confirms that the slow-fast decay structure identified at linear order extends to finite amplitude and approaches the finite-time-decay envelope of the strict yield-stress problem as the regularisation parameter is increased. For liquid egg white the physical point lies deep in the overdamped regime, identifying the yield stress as the dominant stabilisation mechanism.