Discontinuous Transition in a Laminar Fluid Flow: A Change of Flow Topology inside a Droplet Moving in a Micron-Size Channel

Even at moderate values of Reynolds number [e. g., Re = O(1)] a curved interface between liquids can induce an abrupt transition between topologically different configurations of laminar flow. Here we show for the first time direct evidence of a sharp transition in the speed of flow of a droplet upon a small increase of the value of the capillary number above a threshold and the associated change of topology of flow. The quantitative results on the dependence of the threshold capillary number on the contrast of viscosities and on the direction of transition cannot be explained by any of the existing theories and call for a new description.