Stream meanders on a smooth hydrophobic surface

Abstract

This paper reports an experimental study of a meandering water stream upon an inclined smooth hydrophobic surface. It was found that the sinuosity (ratio of the total stream length to the length of the projection of the stream on the line of maximum slope of the surface) increases with both increasing discharge rate and surface slope. It was observed that the meandering pattern is not always stable: once the discharge rate exceeds the upper critical value, the meandering pattern becomes unstable, whereas, when the discharge rate is smaller than the lower critical value, the water stream becomes discontinuous, and normally forms droplets, sliding successively down the sloping surface. It was found that, with increasing surface slope, the upper critical value decreases exponentially, while the lower critical value decreases only gradually. It was found that, when a system of stable meanders is formed on the surface, the meander loops are smoothly curved, swinging gradually from left-handed to right-handed deflections from the line of fastest descent, and vice versa, with an almost constant amplitude and wavelength. The stable meandering pattern migrates gradually down the sloping surface.

The observations showed that the central axis of the meandering stream does not coincide with the locus of the highest points of the stream, the highest points being displaced towards the outside of each bend: the cross-sectional profile of the stream is thus usually asymmetrical. It was found that the cross-sectional area of the stream varies cyclically, with one increase and one decrease associated with each bend of the stream. This cyclic variation is repeated many times along the length of the stream, with each point of maximum cross-sectional area located close to a bend. A secondary reversing spiral flow was observed in the stream, and it was found that the sense of rotation of the flow is reversed at each bend.

A plausible mechanism of these stream meanders is proposed on the basis of the present results, involving the existence of hysteresis of the contact angle between water and Plexiglas, the presence of asymmetrical surface-tension forces on the stream, and the acceleration and deceleration of the stream as it swings from loop to loop.