Immersion depth independent computer analysis of Wilhelmy balance hysteresis curves

Abstract

Computerized methods and algorithms have been developed for operator-independent, batch processing of data from regular Wilhelmy balance hysteresis curves. Regular hysteresis curves were generated by measuring wetting forces along the perimeter of an object as it was immersed into or withdrawn from a liquid phase of interest by initially contacting liquid, repeating an arbitrary number of advancing and receding cycles, and terminating in a final removal step. Data were analyzed in sequential point-number space rather than in conventional immersion-depth coordinates to eliminate need for and reliance on a separately calibrated displacement transducer. Two methods of locating turning points were compared and statistics of wetting measurements discussed. Good agreement between computerized and manual methods was obtained for advancing and receding wetting tensions of water on siliconized glass slides and rods.

Redefining the Wilhelmy and Young equations to imaginary number space and implications for wettability measurements

“…In the paper by Martin and Vogler (1991) on the Wilhelmy balance [5] the authors clearly demonstrated the dilemma outlined in this paper by identifying and labelling all data points of cos >1 as undefined. In the ensuing literature search an interesting paper entitled "Imaginary Contact Angles and the Jones-Ray Effect" by A.S. Coolidge from 1949 [27] was found.…”

“…An operator will therefore continuously report false zero degree contact angles in good faith [15]. A literature search revealed that indeed such "undefined contact angles" (cos > 1) have had been reported [5] and discussed [26]. Reexamination of the raw data of Fig.…”

“…Based on this work Ludwig Wilhelmy invented the Wilhelmy balance nearly 150 years later combining tensiometry with the contact angle measurements in the Wilhelmy equation [3]. Force measurements on the Wilhelmy balance constitute one of the most powerful and sensitive procedures for measuring contact angles [3][4][5] and the method is also viewed as the "gold standard" [6,7]. In this procedure the sample is lowered into and retracted from pure water during force measurements.…”

“…By abolishing the boundary condition of the "perfectly smooth surface" the barrier of 6 > 119 8 was thus overcome by nature [9] in implementing extreme surface roughness and heterogenous wetting [13] to reach contact angles of = 160 8 and more. In the second case ( 6 < 0 8) on the hydrophilic side the contact angle cannot fall below zero for the mathematical reason that cos > 1 is undefined [5]. On considerations of symmetry we had previously suggested an "inverse lotus effect" for the hydrophilic branch of contact angles [14,15].…”

Wetting forces and meniscus pinning at geometrical edges

“…Our "modified Wilhelmy method" is an extension of a method that was introduced later 15 and is still widely used, according to which method the plate is first immersed to some extent and then pulled back until the lower edge of the plate comes flush with the liquid surface; at that moment the force is measured and the surface tension is derived from the value obtained. Variations of that method are measuring the force continuously 14 or moving the partly-immersed plate up and down over some distance 16 ; both methods yield additional information about advancing and receding angles.…”