In this letter, we derive entropy functions whose local equilibria are suitable to recover the Navier-Stokes equations in the framework of the Lattice Boltzmann method. For the two-dimensional nine-velocity lattice we demonstrate that such an entropy function is unique, and that the expansion of the corresponding local equilibrium is the well-known local equilibrium of Y. H. Qian et al. (Europhys. Lett., 17 (1992) 479). Based on the knowledge of entropy functions, we introduce a new version of the Lattice Boltzmann method with an H-theorem built in.

We present a systematic, top-down, thermodynamic parametrization scheme for dissipative particle dynamics (DPD) using water-octanol partition coefficients, supplemented by water-octanol phase equilibria and pure liquid phase density data. We demonstrate the feasibility of computing the required partition coefficients in DPD using brute-force simulation, within an adaptive semi-automatic staged optimization scheme. We test the methodology by fitting to experimental partition coefficient data for twenty one small molecules in five classes comprising alcohols and poly-alcohols, amines, ethers and simple aromatics, and alkanes (i.e., hexane). Finally, we illustrate the transferability of a subset of the determined parameters by calculating the critical micelle concentrations and mean aggregation numbers of selected alkyl ethoxylate surfactants, in good agreement with reported experimental values.

We use dissipative particle dynamics (DPD) to study micelle formation in alkyl sulfate surfactants, with alkyl chain lengths ranging from 6 to 12 carbon atoms. We extend our recent DPD force field [ J. Chem. Phys. 2017 , 147 , 094503 ] to include a charged sulfate chemical group and aqueous sodium ions. With this model, we achieve good agreement with the experimentally reported critical micelle concentrations (CMCs) and can match the trend in mean aggregation numbers versus alkyl chain length. We determine the CMC by fitting a charged pseudophase model to the dependence of the free surfactant on the total surfactant concentration above the CMC and compare it with a direct operational definition of the CMC as the point at which half of the surfactant is classed as micellar and half as monomers and submicellar aggregates. We find that the latter provides the best agreement with experimental results. Finally, with the same model, we are able to observe the sphere-to-rod morphological transition for sodium dodecyl sulfate (SDS) micelles and determine that it corresponds to SDS concentrations in the region of 300-500 mM.

The evolution of the microstructure and composition occurring in the aqueous solutions of di-alkyl chain cationic/nonionic surfactant mixtures has been studied in detail using small angle neutron scattering, SANS. For all the systems studied we observe an evolution from a predominantly lamellar phase, for solutions rich in di-alkyl chain cationic surfactant, to mixed cationic/nonionic micelles, for solutions rich in the nonionic surfactant. At intermediate solution compositions there is a region of coexistence of lamellar and micellar phases, where the relative amounts change with solution composition. A number of different di-alkyl chain cationic surfactants, DHDAB, 2HT, DHTAC, DHTA methyl sulfate, and DISDA methyl sulfate, and nonionic surfactants, C12E12 and C12E23, are investigated. For these systems the differences in phase behavior is discussed, and for the mixture DHDAB/C12E12 a direct comparison with theoretical predictions of phase behavior is made. It is shown that the phase separation that can occur in these mixed systems is induced by a depletion force arising from the micellar component, and that the size and volume fraction of the micelles are critical factors.