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Effect of a surface tension imbalance on a partly submerged cylinder

  • Stoffel D. Janssens (a1), Vikash Chaurasia (a1) (a2) and Eliot Fried (a1)
Abstract

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.

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Copyright
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Corresponding author
Email address for correspondence: eliot.fried@oist.jp
References
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A cylinder at a water–air interface for several parameters

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