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Does the contact angle of a drop depend theoretically on the size of the drop?

Physics Asked on June 14, 2021

According to Wikipedia, contact angle depends on the hydrophobicity of the surface and on thermodynamic equilibrium. But how does it in theory depend on the drop size? In other words, how would a theoretical curve of contact-angle ($theta$) vs. drop-volume ($V$) look like, for a given surface?

  1. According to Drelich et. al. and to Good & Koo, in some liquids there’s dependence, while in other the dependence is very weak.
  2. According to attension TN6, droplet volume “has significant influence on contact angle only with substrates that have large contact angle hysteresis (e.g. due to chemical heterogeneity and surface roughness)”.
  3. According to C. Elif Cansoy, on superhydrophobic surfaces there’s very small dependance between contact angle and drop volume.

One Answer

Vafaei & Podowski derived such theory, which seems to agree well with experimental data. Another interesting relation between contact angle and drop height appears in a paper by Srinivasan et. al. (pp. 16-17):

Assessing the Accuracy of Contact Angle Measurements for Sessile Drops on Liquid-Repellent Surfaces, Siddarth Srinivasan

Answered by Sparkler on June 14, 2021

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