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

We study the distribution of colloidal particles confined in drying spherical freestanding 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 (HIs) 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 HIs 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 the radial symmetry of the drying droplet are in excellent agreement with particle-based simulations for free-draining hydrodynamics, but DDFT unexpectedly fails for pairwise HIs 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.