Meandering Rivulets on a Plane: A Simple Balance between Inertia and Capillarity

Abstract

Experiments on streams of water flowing down a rigid substrate have been performed for various plate inclinations and flow rates, and we focused on the regime of stationary meanders. The outcome is that (i) the flow is highly hysteretic--the shape of the meanders varies with flow rate only for increasing flow rates, and the straight rivulet regime does not appear for decreasing flow rate, and (ii) a simple force balance, including inertia, capillary forces, and also hysteresis of wetting, accounts well for the experimental instability threshold flow rate and for the final radius of curvature of the meanders.