An effective diffusion model for particle-laden interfaces*

Nanoparticles can stabilize the interface of emulsion droplets, forming so-called Pickering emulsions. Their long-term stability makes them promising candidates for sustainable chemical conversion processes. However, the step towards industry-scale applications is currently hampered by our limited fundamental understanding of diffusive transport in multi-phase systems with particle-laden interfaces.

Recent experiments in various multi-phase systems have led to counterintuitive observations that solute diffusion is barely hindered by particles forming a steric barrier at the interface, with the total net transport similar to that of a bare interface. 

To explain these observations, we developed an effective unsteady diffusion model where the particle-laden interface is described as a heterogeneous material with varying diffusivity. Our numerical results include the transient fluxes at various positions across the interface and total diffused mass. We distinguish two regimes separated by a timescale set by the interfacial properties, including its thickness and effective diffusivity. At short times, the layer's properties determine the diffusive transport. In contrast, only the bulk characteristics govern the transport at long times.

Finally, we reconcile the contradictory observations in various physical systems, including Pickering droplets, where the transition between regimes is typically inaccessible in experiments because it occurs well below the millisecond range.