Meandering instability of a rivulet

Abstract

A rivulet is a narrow stream of liquid flowing down a solid surface. When its flow rate exceeds a certain limit, it tends to meander, exhibiting instability of the interface. Here we report a perturbation analysis of this meandering rivulet. We find that the combined effects of the tangential velocity difference across the interface and the dynamic wetting are responsible for the instability. The Weber number represents the ratio of the destabilizing force, inertia, to the stabilizing force, surface tension. As the Weber number increases, both the wavenumber of maximum instability and the cutoff wavenumber increase. The effects of the capillarity are such that the wavenumber of maximum instability asymptotically increases as the sensitivity of the dynamic contact angles to the contact line speed increases. However, the cutoff wavenumber remains constant despite wetting parameter changes when the Weber number is constant.