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The role of wetting heterogeneities in the meandering instability of a partial wetting rivulet

Rivers are subject to a meandering instability caused by sediment transport. A liquid rivulet on an inclined plate in partial wetting conditions exhibits a similar instability at sufficiently high flow rates. It takes a sinuous shape: curves become bigger and bigger, growing by inertia from contact line defects. Meanders are eventually stationary because of the pinning force. The way the initial rivulet is created has consequences on the contact line's shape. We run experiments to study how the critical flow rate depends on initial conditions. We measure a strong dependence, in particular by modifying the initial state from which meanders are growing: it shows that the pinning force plays the main role in the meandering instability. This is in contrast with the previous approach in which only a balance is considered between inertia and a line tension of capillary origin. Because of wetting hysteresis, rivulets have the capacity to deform without any movement of the contact line. We show that the rivulet deforms in response to the centrifugal force. This deformation also helps us to understand how the critical flow rate depends on the initial rivulet shape.