The role of discretization in video image processing of sessile and pendant drop profiles

Abstract

In the present work we have analyzed the errors in determining the parameters of pendant and sessile drops arising due to discreteness of interface profile representation, using the methods of digital image processing. We have shown that in the case of pendant drops, the errors in interfacial tension are most significant at low values of the Bond numbers, Bo=Δ ρgR 0 2/ γ (where Δ ρ is the difference in the densities between the two phases, g is the gravitational acceleration, R 0 is the radius of the drop at its apex, and γ is the interfacial tension), and can reach up to fractions of a percent. For the case of sessile drops, the accuracy is strongly affected by the completeness of the shape representation of the drop. The latter might be characterized through the value of contact angle. It is shown that the accuracy of interfacial tension measurement using the sessile drop method is reduced by decreasing the contact angle for drops with the same shape parameters. For drops with small contact angles or small shape parameters the digitalization of drop profile coordinates may lead to crucial errors in the calculated values of surface tension, up to tens of percent. Nevertheless, the accuracy of the contact angle determination still remains rather high.