Surface ageing at drop scale

Surface ageing of a micro-drop populated by surfactants below the critical micellar concentration and subject to evaporation is considered, motivated by our interest in the transport of biomolecules in digital microfluidics. The classical approach based on diffusion–sorption processes is reviewed in order to address a finite-sized system of digital microfluidics. Short-time and long-time asymptotic approximations for a diffusion-limited regime, as well as full analytical expressions for adsorption- and evaporation-limited regimes, are constructed, which help to validate numerical calculations of full coupling between all these kinetics. The impact of the small drop size and the continuous lack of equilibrium induced by evaporation are described by introducing specific dimensionless numbers. By taking into account evaporative mass transfer in the mass balance, the boundary condition for surfactant transport to and from the interface is modified. Furthermore, the small size of the geometry suggests allowing a novel non-dimensionalisation for surface concentration, following from the mass balance of surfactant molecules in thermo-dynamic equilibrium. This order of magnitude quantifies the equilibrium surface concentration for small-sized geometries.