Asphaltenes are a solubility class of crude oils comprising polyaromatic and heterocyclic molecules with different interfacial activities. The previously neglected effects of compositional mixture on dilatational rheology are discussed in the light of diffusional relaxation models. It is demonstrated that the reported deviations from the Lucassen-van den Tempel model for a single-component solution could largely originate from a distribution in adsorption coefficients within the asphaltenes class. This particularly applies to the peculiar gel point rheology previously ascribed to asphaltenes cross-linking at the interface. Furthermore, an extensive bibliographical review shows that asphaltenes dilatational rheology data always verify the main features of diffusional relaxation, including a decrease in modulus at high bulk concentrations and phase shift values always lower than 45°. Using diffusional relaxation concepts, the reanalysis of the most extensive dataset so far confirmed recently published studies, showing that asphaltenes exhibit a unique equation of state (EOS) irrespective of adsorption conditions. This EOS proves to be very similar for bitumen and petroleum asphaltenes. Finally, a numerical application of a binary diffusional model proved efficient to capture both dynamic interfacial tension and dilatational rheology, with the same parameters. It appears that a minority of asphaltenes (less than 10%) have a much stronger interfacial activity than the bulk of them, as previously demonstrated by fractionation. These results open up the need for a reinterpretation of the physical mechanisms of asphaltenes adsorption in terms of classical amphiphilic behavior, with a potential impact on emulsion breaking and enhanced oil recovery strategies.

An alternative approach for deriving the equation of state for a two-dimensional lattice gas is proposed, based on arguments similar to those used in the derivation of the Langmuir-Szyszkowski equation of state for localized adsorption. The relationship between surface coverage and excluded area is first extracted from random sequential adsorption simulations incorporating surface diffusion (RSAD). The adsorption isotherm is then obtained using kinetic arguments, and the Gibbs equation gives the relation between surface pressure and coverage. Provided surface diffusion is fast enough to ensure internal equilibrium within the monolayer during the RSAD simulations, the resulting equations of state are very close to the most accurate equivalents obtained by cumbersome thermodynamic methods. An internal test of the accuracy of the method is obtained by noting that adsorption RSAD simulations starting from an empty lattice and desorption simulations starting from a full lattice provide convergent upper and lower bounds on the surface pressure.

The determination of phase behavior and, in particular, the nature of phase transitions in twodimensional systems is often clouded by finite size effects and by access to the appropriate thermodynamic regime. We address these issues using an alternative route to deriving the equation of state of a two-dimensional hard-core particle system, based on kinetic arguments and the Gibbs adsorption isotherm, by use of the random sequential adsorption with surface diffusion (RSAD) model. Insight into coexistence regions and phase transitions is obtained through direct visualization of the system at any fractional surface coverage via local bond orientation order. The analysis of the bond orientation correlation function for each individual configuration confirms that first-order phase transition occurs in a two-step liquid-hexatic-solid transition at high surface coverage. arXiv:1908.05555v1 [cond-mat.soft]