Dynamics of Irreversible Particle Adsorption to Fluid Interfaces

TL;DR

This paper develops a unified model for particle adsorption at fluid interfaces that transitions from diffusion-limited to kinetically limited regimes, validated by experiments measuring interfacial tension changes.

Contribution

It introduces a coupled diffusion and RSA-based model capturing irreversible adsorption and particle blocking, extending beyond traditional equilibrium models.

Findings

Adsorption flux decreases with surface coverage, matching RSA predictions.

A critical surface coverage marks the transition to kinetically controlled adsorption.

The Thiele modulus quantifies the shift from diffusion to reaction-limited regimes.

Abstract

Understanding the dynamic adsorption of colloidal particles at fluid interfaces is essential for applications ranging from emulsion stabilization to interfacial assembly of functional materials. Adsorption dynamics is often described through diffusion-limited models (such as the Ward-Tordai framework) along with assuming dynamic equilibrium between the adsorbed and dispersed particles. However, most experiments show that particle adsorption is irreversible, and diffusion-limited models fail as the surface coverage goes beyond the dilute limit where particle crowding limits further adsorption. Here, we present a unified model that captures the transition from diffusion-limited to kinetic-limited regimes by coupling diffusion with a Random Sequential Adsorption (RSA)-based boundary condition that accounts for irreversible adsorption and particle blocking for a spherical droplet. Using both a microtensiometer and pendant drop tensiometry, we measure dynamic interfacial tension changes for 3-(Trimethoxysilyl)propyl methacrylate (TPM) particles at the toluene/water interface across a range of bulk concentrations, drop sizes, and particle functionalization. Our analysis shows that the adsorption flux becomes increasingly hindered as the surface area fills, in agreement with RSA predictions. Furthermore, we calculate the Thiele modulus as a dimensionless number that quantifies the relative importance of adsorption kinetics to diffusion. We find that above a critical surface coverage, adsorption becomes reaction-limited, marking a transition to kinetically controlled dynamics. This approach provides a predictive framework for particle adsorption at fluid interfaces and highlights the necessity of moving beyond equilibrium diffusion-limited models.