Contact angle calculations from the contact/maximum diameter of sessile drops

This paper presents two algorithms for computing the contact angle of sessi le liquid drops given data about the drops. The first yields the contact an gle given the volume, surface tension and maximum diameter (or contact diam eter) of a single drop. This algorithm is an extension of existing algorith ms based on knowledge of the maximum diameter or of the contact diameter of a drop. A sensitivity analysis is included for this algorithm, allowing es timates to be made of the error in computed contact angle caused by errors in the measurement of the volume and/or diameter. The second algorithm requ ires only the volume and maximum or contact diameter of two different drops as input, and it produces both the contact angle and surface tension as ou tput. Both algorithms are based on Newton's method applied to a function wh ose value is computed by solving a system of ordinary differential equation s obtained from the Laplace equation of capillarity. The techniques are app licable to both hydrophobic and hydrophilic surfaces. Copyright (C) 2000 Jo hn Wiley & Sons, Ltd.