MOVING CONTACT LINES AND RIVULET INSTABILITIES - 1. THE STATIC RIVULET.

A rivulet is a narrow steam of liquid located on a solid surface and sharing a curved interface with the surrounding gas. Capillary instabilities are investigated by a linearized stability theory. The formulation is for small, static rivulets whose contact (common or three-phase) lines are fixed, move but have fixed contact angles or move but have contact angles smooth functions of contact-line speeds. The linearized stability equations are converted to a disturbance kinetic-energy balance showing that the disturbance response exactly satisfies a damper linear harmonic-oscillator equation. The 'damping coefficient' contains the bulk viscous dissipation, the effect of slip along the solid and all dynamic effects that arise in the third contact-line condition. For small disturbances changes in contact angle with contact-line speed constitute a purely dissipative process. Results are independent of slip model at the liquid-solid interface as long as a certain integral inequality holds. Sufficient conditions for stability are obtained in all cases. Refs.