Line Tension on Curved Surfaces: Liquid Drops on Solid Micro- and Nanospheres

Line tension for drops on spherical surfaces is approximately calculated and shown to depend on the contact angle and on the curvature of the spherical surface normalized with respect to the curvature of the drop. It is predicted that (a) the contact angle, at which the transition from positive to negative line tensions occurs, decreases with an increase in the solid surface curvature; (b) line tension is very sensitive to the curvature of the solid surface for low contact angles, but this sensitivity decreases as the contact angle increases; and (c) increased curvature of the solid surface decreases the value of line tension. The significance of line tension to wetting is discussed in terms of a critical contact-line radius, Rc, above which the effect of line tension on the contact angle is experimentally indistinguishable. For acute contact angles, except for relatively low ones, Rc is smaller than a few micrometers and sharply decreases when the contact angle approaches 90°. For obtuse contact angles, Rc is smaller than a few tens of nanometers and also sharply decreases when the contact angle approaches 90°.