Effect of a surface tension imbalance on a partly submerged cylinder

• Published in: Journal of fluid mechanics 2017-11, Vol.830, p.369-386
• Main Authors: Janssens, Stoffel D., Chaurasia, Vikash, Fried, Eliot
• Format: Article
• Language: English
• Subjects: Bearing capacity; Circular cylinders; Cross-sections; Cylinders; Fluids; Forces (mechanics); Horizontal loads; Hydrophobicity; Pressure; Shape; Surface tension; Surfactants; Tension
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2017.537

We perform a static analysis of a circular cylinder that forms a barrier between surfactant-laden and surfactant-free portions of a liquid–gas interface. In addition to determining the general implications of the balances for forces and torques, we quantify how the imbalance $\unicode[STIX]{x0394}\unicode[STIX]{x1D6FE}=\unicode[STIX]{x1D6FE}_{a}-\unicode[STIX]{x1D6FE}_{b}$ between the uniform surface tension $\unicode[STIX]{x1D6FE}_{a}$ of the surfactant-free portion of the interface and the uniform surface tension $\unicode[STIX]{x1D6FE}_{b}$ of the surfactant-laden portion of the interface influences the load-bearing capacity of a hydrophobic cylinder. Moreover, we demonstrate that the difference between surface tensions on either side of a cylinder with a cross-section of arbitrary shape induces a horizontal force component $f^{h}$ equal to $\unicode[STIX]{x0394}\unicode[STIX]{x1D6FE}$ in magnitude, when measured per unit length of the cylinder. With an energetic argument, we show that this relation also applies to a rod-like barrier with cross-sections of variable shape. In addition, we apply our analysis to amphiphilic Janus cylinders and we discuss practical implications of our findings for Marangoni propulsion and surface pressure measurements.