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Contact Line Pinning Effects Influence Determination of the Line Tension of Droplets Adsorbed on Substrates

The precise determination of the line tension of sessile droplets still represents a major challenge. At present, the estimates of the line tension from contact angle measurements can differ by 4–5 orders of magnitude. Here we show that the pinning effect of the droplet contact line caused by the substrate inhomogeneities influences the apparent contact angle of the droplet, affecting the determination of the line tension via the corrected Young’s equation. We introduce the contribution of pinning effects into the Gibbs free energy differential and derive a modified version of the Young’s equation. Using classical density functional theory, we isolate the line tension and the pinning force contributions for substrates with different heterogeneity. The pinning effect leads to metastability of wetting states and influences the contact angle, hence introducing errors in the estimation of line tensions using the traditional analysis of contact angles, based on the modified Young’s equation.