The end-correction in the Wilhelmy technique for surface tension measurements

Abstract

Deduction, observation, and experiment all agree that the meniscus on a Wilhelmy plate is perturbed downward at the ends of the plate by the sharp meniscus curvature associated with the turn made by the adhering film as it rounds the end. It is hypothesized that less liquid is accordingly suspended near the plate ends than in the central region of the plate and that this deficit generates the known need for an end-correction in the calculation procedure. The experimental results support this point of view. A corner-correction is defined for one corner of a Wilhelmy plate, and an experimental technique is devised to measure it. The total end-correction is the sum of four corner-corrections. In the procedure devised, the surface tension pull is measured on each of a set of similar plates of constant thickness but with differing lengths on a given air-liquid system. For practical reasons, it is essential to vary the plate length over a wide range; a 20-fold ratio was used here. The program devised to test the model comprised the use of 16 smooth glass plates in combinations of four lengths (about 0.23, 0.40, 2.1, and 5.0 cm) and four thicknesses (0.007, 0.015, 0.024, and 0.10 cm). Four liquids were tested with air at 30.0°C, namely, water, benzene, isooctane, and isopropyl ether. The net correction to the surface tension was found to be inherently small, raising the indicated value characteristically from 0.1% to 1.0%. Two dimensionless groups were devised that correlated in excellent fashion the corner-correction c with the plate thickness and the physical properties of the system. One group, C = c t , is a dimensionless corner-correction. The other, T = g Δ ρ t 2 σ , is the dimensionless plate thickness squared. It was found that C varied from 0.085 to 0.86 as T varied from 0.00072 to 0.417 and that C = 1.1946 ( T × 10 4) −0.2775.