The measurement of surface and interfacial tension by the axisymmetric drop technique

Abstract

We have used a variety of systems to present a recently developed analytical scheme which calculates surface and interfacial tensions from the shapes of pendant and sessile drops. The computational algorithm constructs an objective error function for a Laplacian curve, which is minimized using the incremental loading method coupled with a Newton—Raphson iterative scheme. The drops were transilluminated using a fibre-optic light source and photographs were taken through a horizontal microscope equipped with polarizing filters. From enlarged photographs or tracings, approximately 35 coordinate points were generated along the drop profile with a Talos 600 Series digitizer. These, along with the local gravity constant and density difference, are the only data required to obtain a solution to the Laplace equation of capillarity. The surface tensions calculated for 1-Methylnaphthalene and dodecane, and the interfacial tension of ethyl acetate/water agreed with literature values, within our standard error estimates. Correct values of surface or interfacial tension were obtained from sessile drops independent of contact angle; i.e. the method accomodates drops with contact angles above and below 90° equally well. To explore the method's usefulness for calculating low and ultralow interfacial tensions, we produced a series of poly(ethylene glycol)/dextran phase separated aqueous polymers of various concentrations (3.0–13.6%, w/w). We determined interfacial tensions as low as 3.4 × 10 −4 mJ m −2 without difficulty and a smooth curve of polymer concentration vs. interfacial tension was constructed. An aqueous sodium dodecyl sulphate/cholesterol system was used to estimate the error in the digitizing procedure and the gross error associated with the experimental technique. In addition to the surface or interfacial tension, the program calculates the drop volume, surface area, and contact angle.