**2. Background on Emulsions and Droplet Interfacial Properties**

The relationship between the interfacial properties of adsorbed layers at liquid-liquid interfaces and the process of emulsification and emulsion stability is well-recognized [19,20].

Emulsification is the production of small droplets by fragmentation of the oil phase with a consequent large increase of the surface area. For energetic reasons, it is favored by low surface tensions and fast adsorption processes. In fact, for a given energy provided to the system, smaller droplets are generated with surfactants that are more efficient to adsorb and reduce the interfacial tension. The aging of emulsions is governed by various processes influenced by the bulk and adsorption properties of surfactants, both at equilibrium and in dynamic conditions. These are creaming or sedimentation, which is the gravity-driven phase separation due to the density difference between the two liquids, Ostwald ripening and droplet coalescence [21]. Ostwald ripening consists in a partial dissolution of the dispersed liquid phase induced by the capillary pressure, which results in a net mass transfer from small to big droplets. This process mainly involves small droplets, because of their higher capillary pressure, and, for oils with low solubility in water, as it is case of long-chain alkanes [22,23], presents very long characteristic times. The emulsions reported here are obtained by a low-energy method and are therefore characterized by relatively big droplet sizes, for which Ostwald ripening has a negligible relevance for the emulsion ageing as compared to creaming and coalescence. Coalescence consists on the merging of two droplets into a single larger one, due to the complex hydrodynamic process of thinning and rupture of the liquid film between them. As a consequence of coalescence the droplet size distribution tends to be enlarged and moves towards larger sizes, eventually favoring creaming and destabilization of the emulsion. Among the most important effects relevant for the hindering of droplet coalescence, it is worth to mention the repulsive interaction between adsorbed layers, the interfacial coverage, the steric effects and the high dilational viscoelasticity of the interfacial layers [24,25]. The repulsive interactions are particularly relevant when ionic surfactants are concerned. In that case, it has been shown that a small amount of adsorbed molecules at the drop surface is sufficient to avoid coalescence [25] and improve remarkably the stability of emulsions. The interfacial coverage is the relative area of the interface occupied by the surfactant. High values of this parameter represent another stabilizing factor against coalescence due to the short range interactions of the surfactant molecules adsorbed at the two sides of the film between droplets. Since the total area of the droplet interfaces decreases with droplet coalescence, the surface coverage increases and, when high values of it are achieved through this process, the coalescence eventually stops. Thus surface coverage is implied in determining the droplet size of stable emulsions. Steric effects are especially concerned with composite surface layers, such as surfactant-nanoparticle mixtures or surfactant aggregates but also with large surfactant molecules at high adsorption coverage.

The dilational viscoelasticity, *E*, is the dynamic response of the interfacial tension, γ, to extensional perturbations of the surface area, *A*. For small amplitude harmonic perturbations, *E* is a frequency dependent complex quantity, defined as:

$$E = \frac{\Delta \gamma}{\Delta A / A\_0} \mathbf{e}^{i\varphi} \tag{1}$$

where Δγ and Δ*A* are the amplitudes of the oscillating surface tension and surface area, respectively, *A*<sup>0</sup> is the reference area and ϕ is the phase shift between the oscillating surface tension and surface area. According to its definition, high values of the dilational viscoelasticity tend to make the liquid films between drops in emulsions more stable and, in particular, to hinder their local thinning for Marangoni effects.

From these considerations it is clear that a deep characterization of the surfactants used for stabilizing emulsions, at liquid-liquid interfaces, is of fundamental importance to understand the stabilizing mechanisms and the role of the different features of the used surfactants.
