Applying Tikhonov regularization to process pendant droplet tensiometry data.
The problem of obtaining the first and second derivatives of the profile of a pendant droplet is formulated as an integral equation of the first kind. This equation is solved by Tikhonov regularization in which the method of general cross validation is used to guide the selection of the regularization parameter. These derivatives are converted into mean curvature as a function of droplet height. Surface tension is then obtained by regression computation between the mean curvature and two possible algebraic expressions suggested by the Laplace-Young equation. This way of obtaining surface tension is demonstrated by applying it to a number of published droplet profiles. Some of the problems encountered are discussed and solutions suggested.
Yeow
Y Leong
YL
Department of Chemical and Biomolecular Engineering, The University of Melbourne, Victoria 3010, Australia. yly@unimelb.edu.au
McGowan
Krista L
KL
Ong
S Ian
SI
Leong
Yee-Kwong
YK
D008962:Models, Theoretical; D013500:Surface Tension