Effect of a surface tension imbalance on a partly submerged cylinder

TL;DR

This paper analyzes how surface tension imbalance across a partly submerged cylinder affects its force and torque, revealing a direct relation between surface tension difference and horizontal force, with implications for Marangoni propulsion.

Contribution

It provides a static force analysis of a cylinder at a liquid interface considering surface tension imbalance, including a general relation for horizontal force and applications to Janus cylinders.

Findings

Surface tension imbalance induces a horizontal force equal to the tension difference.

The force relation applies to barriers with arbitrary cross-section shapes.

Implications for Marangoni propulsion and surface pressure measurements.

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.