On the Spreading of Liquids on Solid Surfaces: Static and Dynamic Contact Lines

TLDR: In this article, it is shown that the mutual interaction between the three materials in the immediate vicinity of a contact line can significantly affect the statics as well as the dynamics of an entire flow field.

Abstract: A contact line is formed at the intersection of two immiscible fluids and a solid. That the mutual interaction between the three materials in the immediate vicinity of a contact line can significantly affect the statics as well as the dynamics of an entire flow field is demonstrated by the behavior of two immiscible fluids in a capillary. It is well known that the height to which a column of liquid will rise in a vertical circular capillary with small radius, a, whose lower end is placed into a bath, is given by (2(j/apg) cos (), where (j is the surface tension of the air/liquid interface, f) is the static contact angle as measured from the liquid side of the contact line, p is the density, and g is the magnitude of the accelera­ tion due to gravity.! Thus, depending on the value of the contact angle, e, which is a direct consequence of the molecular interactions among the three materials at the contact line, the height can take on any value within the interval [ 2(J/apg, 2(J/apg]. In a sense, the influence of the contact angle is indirect: the contact angle, in capillaries with small radii, controls the radius of curvature of the meniscus which, in turn, regulates the pressure in the liquid under the meniscus. It is this pressure that determines the height of the column. In a similar manner, the dynamic contact angle can influence the rate of displacement of tbe meniscus through the capillary. The pressure drop