Exploring the role of hydrodynamic interactions in spherically-confined drying colloidal suspensions

TL;DR

This study investigates how hydrodynamic interactions influence particle distribution during the drying of colloidal droplets, revealing that pairwise hydrodynamics significantly affect concentration gradients and challenge existing theoretical models.

Contribution

It demonstrates the impact of hydrodynamic interactions on drying colloidal droplets and highlights limitations of current DDFT approaches in modeling these effects.

Findings

Hydrodynamic interactions increase particle accumulation at the droplet interface.

DDFT agrees with simulations for free-draining hydrodynamics but fails with pairwise interactions.

Boundary conditions at the droplet interface have minimal effect on particle distribution.

Abstract

We study the distribution of colloidal particles confined in drying spherical droplets using both dynamic density functional theory (DDFT) and particle-based simulations. In particular, we focus on the advection-dominated regime typical of aqueous droplets drying at room temperature and systematically investigate the role of hydrodynamic interactions during this nonequilibrium process. In general, drying produces transient particle concentration gradients within the droplet in this regime, with a considerable accumulation of particles at the droplet's liquid-vapor interface. We find that these gradients become significantly larger with pairwise hydrodynamic interactions between colloidal particles instead of a free-draining hydrodynamic approximation; however, the solvent's boundary conditions at the droplet's interface (unbounded, slip, or no-slip) do not have a significant effect on the particle distribution. DDFT calculations leveraging radial symmetry of the drying droplet are in excellent agreement with particle-based simulations for free-draining hydrodynamics, but DDFT unexpectedly fails for pairwise hydrodynamic interactions after the particle concentration increases during drying, manifesting as an ejection of particles from the droplet. We hypothesize that this unphysical behavior originates from an inaccurate approximation of the two-body density correlations based on the bulk pair correlation function, which we support by measuring the confined equilibrium two-body density correlations using particle-based simulations. We identify some potential strategies for addressing this issue in DDFT.