Obtaining surface tension from pendant drop volume and radius of curvature at the apex

Axisymmetry of the height versus radius data z(r) of pendant drops is used to simplify the integral equation of the first kind for the third derivative d3z/dr3. This equation is solved by Tikhonov regularization and the derivative is used to calculate the radius of curvature at the apex. This key property of pendant drops together with the droplet volume is then used to obtain the surface tension. This is done by referring to the relationship between dimensionless droplet volume and dimensionless apex curvature for different bond numbers. The performance of this route to surface tension is demonstrated by applying it to several sets of data taken from the literature. A key limitation of this method is identified and a number of simple extensions are described.