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 γ = γ a − γ b between the uniform surface tension γ a of the surfactant-free portion of the interface and the uniform surface tension γ 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 γ 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.

Water Harvesting Strategies through Solar Steam Generator Systems

“…In addition to this, previous studies showed that liquid surface tension contributes to the object's buoyancy force. As a result, elongated hydrophobic objects are able to float in spite of its high overall density [127] . Since wetting can lead to water permeation, hydrophobic materials are ideal solution to be used as a floating platform due to its low surface energy and wettability [128] .…”

“…As a result, elongated hydrophobic objects are able to float in spite of its high overall density. [127] Since wetting can lead to water permeation, hydrophobic materials are ideal solution to be used as a floating platform due to its low surface energy and wettability. [128] When a hydrophobic material is in contact with water, meniscus is formed around the edges of the object and is proportional to the object's cross section perimeter bounded by the triple line.…”

Surface tension force on a partially submerged horizontal concave cylinder

“…However, the horizontal resultant force will be non-zero if considering a surface tension imbalance on the cylinder (Janssens et al. 2017).…”

“…The surface tension imbalance can induce the twisting of a Janus cylinder (Oratis, Farmer & Bird 2017). The surface tension imbalance also can induce self-powered locomotion of a hydrogel water strider (Zhu et al 2021) or an isotropic particle with different surface tension coefficients on its surface (for example, a partially submerged cylinder having surface tension imbalance; see Janssens, Chaurasia & Fried (2017)). Even if convex to the fluids, a Janus particle, half of which has a different contact angle from the other half, possibly has a jump of contact line at its surface when it moves through a fluid-fluid interface.…”

“…It is noted that the horizontal component of F S is always zero whether the configuration is symmetric or not, because the sum of the horizontal components of F T and F P at one side is constant regardless of the meniscus shape (Mansfield, Sepangi & Eastwood 1997;Keller 1998;Finn 2010). However, the horizontal resultant force will be non-zero if considering a surface tension imbalance on the cylinder (Janssens et al 2017).…”