Effect of a surface tension imbalance on a partly submerged cylinder

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 $\Delta \gamma ={\gamma }_a-{\gamma }_b$ between the uniform surface tension ${\gamma }_a$ of the surfactant-free portion of the interface and the uniform surface tension ${\gamma }_b$ 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 $\Delta \gamma$ in magnitude, when measured per unit length of the cylinder. With an energetic argument, we show that this relation also applies to rod-like barriers 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.

References in corpus (3)

• Viscous Marangoni propulsion
• Thermally driven Marangoni surfers
• Behavior of self-propelled acetone droplets in a Leidenfrost state on liquid substrates