The shortcomings of the current formulation for calculating the adhesion force for drops and bubbles with noncircular contact lines are discussed. A general formulation to evaluate the adhesion force due to surface forces is presented. Also, a novel methodology, that is, IBAFA, image based adhesion force analysis, was developed to allow implementation of the general formulation. IBAFA is based on the use of multiple profile images of a drop. The images are analyzed (1) to accurately reconstruct the contact line shape, which is analytically represented by a Fourier cosine series, and (2) to measure contact angles at multiple locations along the contact line and determine the contact angle distribution based on a linear piecewise interpolation routine. The contact line shape reconstruction procedure was validated with both actual experiments and simulated experiments. The procedure for the evaluation of the adhesion force was tested using simulated experiments with synthetic drops of known shapes. A comparison with current methods showed that simplifying assumptions (e.g., elliptical contact line or linear contact angle distribution) used in these methods result in errors up to 76% in the estimated adhesion force. However, the drop adhesion force evaluated using IBAFA results in small errors on the order of 1%.
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