Mechanics of Interfaces Lecture notes Shreyas Mandre Department of Engineering, University of Cambridge sdm63@cam.ac.uk ©2022 Shreyas Mandre CC-BY-NC-ND ( Last updated: 18 February 2022 ) Contents 1 Introduction to surface tension 1.1 Molecular origin of surface tension 1.2 Surface energy and surface tension 1.3 Surfactants 1.4 Conclusion 2 Static equilibrium of liquid interfaces 2.1 Planar liquid interfaces 2.2 Curved liquid interfaces 2.2.1 Derivation for a rectangular interface patch 2.2.2 General derivation for a curved interface patch 2.2.3 Consequences of Laplace pressure – equilibrium shape of a liquid blob 3 Three-phase contact lines 3.1 Liquid-liquid-fluid contact line 3.1.1 Application: Two drops in contact 3.2 Solid-liquid-fluid contact line 3.2.1 Equilibrium based on energetic considerations 3.2.2 Equilibrium based on force balance considerations 3.2.3 Contact line motion 3.3 Conclusion 4 Surface tension and gravity 4.1 Dimensional analysis 4.2 Planar capillary meniscus