Dynamics and stability of flows with moving contact lines

The intersection of the interfacial region between two immiscible fluid phases with a solid surface forms a three phase region. Under the continuum hypothesis this three phase region is replaced by a contact line. This property of a contact line along with its other properties is formulated into boundary conditions necessary for the development of well-posed mathematical models governing systems possessing contact lines. Two fluid/fluid/solid systems possessing contact lines are considered. A three-dimensional rivulet flowing down a vertical plane is examined. There exists a basic state with fully developed flow and straight contact lines. In the absence of contact-angle hysteresis the slope of the contact angle versus contact-line speed relationship measures the mobility of these contact lines. The stability characteristics of flat rivulets subject to long wave disturbances are examined using lubrication theory. This research also considers the effects of contact-angle hysteresis on the motion if the contact line formed as a plate is immersed/emerged into and out of a bath of liquid. Wilhelmy plate experiments leading to the measurement of dynamic contact-angle characteristics are based upon such an apparatus.