A method for estimating interfacial tensions and contact angles from sessile and pendant drop shapes

Abstract

When interfacial tensions are ultralow, even the very small sessile drops used during measurement of tension and contact angle tend to be flat; and that portion of the meridional curve between the equator and substrate, that is integral to inference of contact angle, is often somewhat obscure and of very limited extent. Under these circumstances, estimates of contact angle may be encumbered with large errors, even when the corresponding tension is well known. In this paper, optimal estimation techniques for tension and contact angle are developed that derive from the best match of a fourth order Runge-Kutta integration of the meridional curve to discrete data representing the magnified drop profile. The objective function, R, for optimization is based on a good approximation to the normal from the calculated meridional curve to a datum. The method is applied to sessile drops, bubbles, and pendant configurations. Even though in some cases large errors in contact angle persist, this approach assures results are the best that can be inferred from the data, in the sense of R.