Hybrid particle-phase field model and renormalized surface tension in dilute suspensions of nanoparticles

TL;DR

This paper introduces a hybrid particle-phase field model for simulating dilute nanoparticle suspensions near interfaces, revealing how particle dynamics influence interfacial tension and providing analytical and numerical insights.

Contribution

The study develops a novel coupled particle-phase field model and analytical solutions to explore interfacial phenomena in dilute nanoparticle suspensions, highlighting the impact on surface tension.

Findings

Renormalized surface tension decreases with higher particle concentration.

Strong coupling alters the liquid-gas interface significantly.

Analytical solutions agree well with numerical simulations.

Abstract

We present a two-phase field model and a hybrid particle-phase field model to simulate dilute colloidal sedimentation and flotation near a liquid-gas interface (or fluid-fluid interface in general). Both models are coupled to the incompressible Stokes equation, which is solved numerically using a combination of sine and regular Fourier transforms to account for the no-slip boundary conditions at the boundaries. The continuum two-phase field model allows us to analytically solve the equilibrium interfacial profile using a perturbative approach, demonstrating excellent agreement with numerical simulations. Notably, we show that strong coupling to particle dynamics can significantly alter the liquid-gas interface, thereby modifying the liquid-gas interfacial tension. In particular, we show that the renormalized surface tension is monotonically decreasing with increasing colloidal particle concentration and decreasing buoyant mass.