A General Approach to the Linear Stability of Thin Spreading Films

Marangoni and thermocapillary driven systems represent two classes of flows in which the variation in surface tension at the gas-liquid interface can generate spontaneously spreading films. This article considers the linear stability of such flows within the lubrication approximation. Since the base state or unperturbed solutions in both cases involve spatially inhomogeneous profiles, the linearized disturbance operators are non-normal and the stability analysis must therefore be generalized beyond a simple modal decomposition. The utility of this type of analysis is first demonstrated for autonomous operators by an example involving thermocapillary spreading subject to a constant thermal gradient. Extension of this non-modal analysis to systems involving non-autonomous operators is demonstrated by an example of Marangoni spreading induced by film contact with an insoluble surfactant monolayer.