Localized states in a film-dragging experiment

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Abstract
When a viscous fluid is dragged up the retreating wall of a partially filled cylinder, rotating horizontally, a localized structure can occur corresponding to the spatial coexistence of two different states of the viscous layer. By changing two control parameters, the angular velocity and the amount of fluid, we were able to characterize the domains of stability of coexisting states. Localized structures are stable and stationary in a small region of parameter space where the transition between these two states is large. In analogy with a phase transition with a conserved order parameter, it is suggested that the size of the localized structure is selected from both a law of conservation of total volume of liquid in the cylinder and a stability criterion. By studying the profile and the dynamics of disturbances of the viscous layer, we have shown that both states are well described by the lubrication approximation, but this approximation fails to explain the coexistence of the states.