Diffusion across particle-laden interfaces in Pickering droplets

Emulsions stabilized by nanoparticles, known as Pickering emulsions, exhibit remarkable stability, which enables applications ranging from encapsulation, to advanced materials, to chemical conversion. The layer of nanoparticles at the interface of Pickering droplets is a semi-permeable barrier between the two liquid phases, which can affect the rate of release of encapsulates, and the interfacial transfer of reactants and products in biphasic chemical conversion. A gap in our fundamental understanding of diffusion in multiphase systems with particle-laden interfaces currently limits the optimal development of these applications. To address this gap, we developed an experimental approach for in situ, real-time quantification of concentration fields in Pickering droplets in a Hele-Shaw geometry and investigated the effect of the layer of nanoparticles on diffusion of solute across a liquid-liquid interface. The experiments did not reveal a significant hindrance on the diffusion of solute across an interface densely covered by nanoparticles. We interpret this result using an unsteady diffusion model to predict the spatio-temporal evolution of the concentration of solute with a particle-laden interface. We find that the concentration field is only affected in the immediate vicinity of the layer of particles, where the area available for diffusion is affected by the particles. This defines a characteristic time scale for the problem, which is the time for diffusion across the layer of particles. The far-field concentration profile evolves towards that of a bare interface. This localized effect of the particle hindrance is not measurable in our experiments, which take place over a much longer time scale. Our model also predicts that the hindrance by particles can be more pronounced depending on the particle size and physicochemical properties of the liquids and can ultimately affect performance in applications.