Capillary Forces on a Small Particle at a Liquid-Vapor Interface: Theory and Simulation

Abstract

We study the meniscus on the outside of a small spherical particle with radius $R$ at a liquid-vapor interface. The liquid is confined in a cylindrical container with a finite radius $L$ and has a contact angle $\pi /2$ at the container surface. The center of the particle is placed at various heights along the central axis of the container. By varying $L$, we are able to systematically study the crossover of the meniscus from nanometer to macroscopic scales. The meniscus rise or depression on the particle is found to grow as $\ln (2L/R)$ when $R\ll L\ll {\kappa }^{-1}$ with ${\kappa }^{-1}$ being the capillary length and saturate to a value predicted by the Derjaguin-James formula when $R\ll {\kappa }^{-1}\ll L$. The capillary force on the particle exhibits a linear dependence on the particle's displacement from its equilibrium position at the interface when the displacement is small. The associated spring constant is found to be $2\pi \gamma {\ln }^{-1}(2L/R)$ for $L\ll {\kappa }^{-1}$ and saturates to $2\pi \gamma {\ln }^{-1}(3.7{\kappa }^{-1}/R)$ for $L\gg {\kappa }^{-1}$. At nanometer scales, we perform molecular dynamics simulations of the described geometry and the results agree well with the predictions of the macroscopic theory of capillarity. At micrometer to macroscopic scales, comparison to experiments by Anachkov \textit{et al.} [Soft Matter {\bf 12}, 7632 (2016)] shows that the finite span of a liquid-vapor or liquid-liquid interface needs to be considered to interpret experimental data collected with $L\sim {\kappa }^{-1}$.

arXiv comment16 pages, 11 figures

References in corpus (16)

• Wet Granular Materials
• Colloidal Jamming at Interfaces: a Route to Fluid-bicontinuous Gels
• Interaction potentials for soft and hard ellipsoids
• Dynamic stratification in drying films of colloidal mixtures
• Structure Formation in Soft Matter Solutions Induced by Solvent Evaporation
• Structure and Diffusion of Nanoparticle Monolayers Floating at Liquid/Vapor Interfaces: A Molecular Dynamics Study
• Assembling Ellipsoidal Particles at Fluid Interfaces using Switchable Dipolar Capillary Interactions
• Detachment Energies of Spheroidal Particles from Fluid-Fluid Interfaces
• Colloidal gels assembled via a temporary interfacial scaffold
• Crossover from fast relaxation to physical aging in colloidal adsorption at fluid interfaces
• Stratification in Drying Films Containing Bidisperse Mixtures of Nanoparticles
• Shape and effective spring constant of liquid interfaces probed at the nanometer scale: finite size effects
• Capillary Adhesion at the Nanometer Scale
• Nanocapillary adhesion between parallel plates
• Influence of hydrodynamic interactions on stratification in drying mixtures
• The Meniscus on the Outside of a Circular Cylinder: from Microscopic to Macroscopic Scales

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