Determination of contact angle from the maximum height of enlarged drops on solid surfaces

Measurement of the liquid/solid contact angle provides useful information on the wetting properties of fluids. In 1870, the German physicist Georg Hermann Quincke (1834-1924) published the functional relation between the maximum height of an enlarged drop and its contact angle. Quincke's relation offered an alternative to the direct measurement of contact angle, which in practice suffers from several experimental uncertainties. In this paper, we review Quincke's original derivation and show that it is based on a hidden assumption. We then present a new derivation that exposes this assumption and clarifies the conditions under which Quincke's relation is valid. To explore Quincke's relation experimentally, we measure the maximum height of enlarged water drops on several substrates and calculate the contact angle in each case. Our results are in good agreement with contact angles measured directly from droplet images. (C) 2012 American Association of Physics Teachers. [DOI: 10.1119/1.3678306]