Long-wave perturbation analysis to the stability of a thin viscoplastic material flowing on a rotating circular disk

Abstract

This paper investigates the stability of a thin axisymmetric viscoplastic material designated as Bingham model flowing on a rotating circular disk. Long-wave perturbation analysis is proposed to derive a generalized kinematic model of the film flow with a small Reynolds number. The method of normal mode is applied to study the linear stability. Weakly nonlinear dynamics of film flow is studied by the multiple scales method. The finite amplitude of the instability is governed by a Ginzburg–Landau equation. The study reveals that the Rotation number generates a destabilizing effect. The yield stress of a viscoplastic material serves as the stabilizing factor in the thin film flow. Further, the results also indicate that the sub-critical instability and supercritical stability are possible.