1. Effect of a surface tension imbalance on a partly submerged cylinder
- Author
-
Stoffel D. Janssens, Vikash Chaurasia, and Eliot Fried
- Subjects
Convection ,Surface (mathematics) ,Materials science ,FOS: Physical sciences ,02 engineering and technology ,Surface pressure ,01 natural sciences ,010305 fluids & plasmas ,Cylinder (engine) ,law.invention ,Surface tension ,law ,Physics - Chemical Physics ,0103 physical sciences ,Torque ,Physics - Biological Physics ,Janus ,Chemical Physics (physics.chem-ph) ,Marangoni effect ,Mechanical Engineering ,Applied Mathematics ,Fluid Dynamics (physics.flu-dyn) ,Physics - Fluid Dynamics ,Mechanics ,021001 nanoscience & nanotechnology ,Condensed Matter Physics ,Biological Physics (physics.bio-ph) ,Mechanics of Materials ,0210 nano-technology - 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.
- Published
- 2017