Diffusivity and hydrodynamic drag of nanoparticles at a vapor-liquid interface

Abstract

Measurements of the surface diffusivity of colloidal spheres translating along a vapor/liquid interface show an unexpected decrease in diffusivity, or increase in surface drag (from the Stokes-Einstein relation) when the particles situate further into the vapor phase. However, direct measurements of the surface drag from the colloid velocity due to an external force find the expected decrease with deeper immersion into the vapor. The paradoxical drag increase observed in diffusion experiments has been attributed to the attachment of the fluid interface to heterogeneities on the colloid surface, which causes the interface, in response to thermal fluctuations, to either jump or remain pinned, creating added drag. We have performed molecular dynamics simulations of the diffusivity and force experiments for a nanoparticle with a rough surface at a vapor/liquid interface to examine the effect of contact line fluctuations. The drag calculated from both experiments agree and decrease as the particle positions further into the vapor. The surface drag is smaller than the bulk liquid drag due to the partial submersion into the liquid, and the finite thickness of the interfacial zone relative to the nanoparticle size. Contact line fluctuations do not give rise to an anomalous increase in drag.When a colloid particle breaches the interfacial zone between two adjoining immiscible fluid phases the interfacial energy of the particle changes, because the area of the fluid interface decreases and the contact areas of the particle with the bounding fluid phases are altered. For a particle which only partially wets both adjoining fluids, the change in interfacial energy is at a minimum when the colloid partially straddles both adjoining phases. For example, for a spherical colloid of radius R at a vapor/liquid interface of interfacial tension γ (Fig. 1a), the minimum free energy relative to the vapor phase is [1] ∆F = −πγR 2 (1 + cos θ) 2 where the contact angle θ is measured through the liquid. For particles of large enough size, ∆F can overwhelm the typical thermal energy k B T and the particle becomes trapped, as thermal fluctuations cannot dislodge the particle from the interface. Monolayers of strongly adsorbed colloids at the fluid interfaces of foams and emulsions provide steric barriers to coalescence of the dispersed phase, and find applications as foam and emulsion stabilizers (e.g. Pickering emulsions). Particle stabilized foams and emulsions are also used for the fabrication of colloid-based solid foams, gels, and bijels, and crystalline monolayers find applications as superhydrophobic or antireflection coatings, and templates for micro and nanostructured materials [2]. Central to these applications is the surface organization of the colloids, which is a balance between interparticle attractive and repulsive forces, external forces applied parallel to the interface, and the viscous resistance or surface drag due to the hydrodynamic motion of the colloids along the fluid surface. As we explain, the surface drag is not w...

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