The measurement of surface tension by means of a vertical-plate balance

Abstract

A thermodynamic analysis of the measurement of surface tension using plates with either horizontal or vertical grooves of arbitrary cross section is presented. An exact description of the behaviour of horizontal grooves in a plate of infinite width and of vertical grooves in a plate of infinite height is given. The behaviour of a plate of finite height with vertical grooves can be the same as for an infinite plate, but in most instances this is not true. An approximate analysis of a finite plate with vertical grooves is developed and the errors in the curvatures of the resulting liquid-fluid surface are evaluated. In general, it is found that a grooved plate partly immersed in liquid requires a greater force to balance it than a smooth plate of the same overall dimensions and mass and with zero contact angle against the liquid and fluid phases. The additional force required to balance the grooved plate is approximately independent of the groove orientation but increases with width (pitch) of the groove. It is shown that if the measurements are made with the bottom of the plate at the level of the liquid-fluid surface at an infinite distance from the plate, the additional force almost equals the gravitational force on the mass of liquid adhering to the plate after complete immersion and withdrawal from the liquid, the agreement improving as the groove pitch is decreased. This conclusion helps explain the good results obtained for surface tension measurements using roughened plates with scratched surfaces. The important results are checked experimentally and in most cases the agreement is within the experimental error. The only exceptions to this are the results for finite plates with vertical grooves but even then the agreement is nearly quantitative.