A new lattice Boltzmann method for simulating multiphase flows is developed theoretically. The method is adjusted such that its continuum limit is the Navier-Stokes equation, with a driving force derived from the Cahn-Hilliard free energy. In contrast to previous work, however, the bulk and interface terms are decoupled, the former being incorporated into the model through the local equilibrium populations, and the latter through a forcing term. We focus on gas-liquid phase equilibria with the possibility to implement an arbitrary equation of state. The most novel aspect of our approach is a systematic Chapman-Enskog expansion up to the third order. Due to the third-order gradient in the interface forcing term, this is needed for full consistency with both hydrodynamics and thermodynamics. Our construction of a model that satisfies all conditions is based upon previous work by Chen, Goldhirsch, and Orszag (J. Sci. Comp. 34, 87 (2008)), and implies 59 and 21 velocities in three and two dimensions, respectively. Applying the conditions of positivity of weights, existence of a two-phase region in the phase diagram, and positivity of the bulk viscosity, we find substantial restrictions on the permitted equation of state, which can only be lifted by an even more refined model. Moreover, it turns out that it is necessary to solve a self-consistent equation for the hydrodynamic flow velocity, in order to enforce the identity of momentum density and mass current on the lattice. The analysis completely identifies all spurious terms in the Navier-Stokes equation, and thus shows how to systematically eliminate each of them, by constructing a suitable collision operator. (continued - see article PDF)

As variance from standard phospholipids of eubacteria and eukaryotes, archaebacterial diether phospholipids contain branched alcohol chains (phytanol) linked to glycerol exclusively with ether bonds. Giant vesicles (GVs) constituted of different species of archaebacterial diether phospholipids and glycolipids (archaeosomes) were prepared by electroformation and observed under a phase contrast and/or fluorescence microscope. Archaebacterial lipids and different mixtures of archaebacterial and standard lipids formed GVs which were analysed for size, yield and ability to adhere to each other due to the mediating effects of certain plasma proteins. GVs constituted of different proportions of archaeal or standard phosphatidylcholine were compared. In nonarchaebacterial GVs (in form of multilamellar lipid vesicles, MLVs) the main transition was detected at T(m) = 34. 2°C with an enthalpy of ΔH = 0.68 kcal/mol, whereas in archaebacterial GVs (MLVs) we did not observe the main phase transition in the range between 10 and 70°C. GVs constituted of archaebacterial lipids were subject to attractive interaction mediated by beta 2 glycoprotein I and by heparin. The adhesion constant of beta 2 glycoprotein I-mediated adhesion determined from adhesion angle between adhered GVs was in the range of 10(-8) J/m(2). In the course of protein mediated adhesion, lateral segregation of the membrane components and presence of thin tubular membranous structures were observed. The ability of archaebacterial diether lipids to combine with standard lipids in bilayers and their compatibility with adhesion-mediating molecules offer further evidence that archaebacterial lipids are appropriate for the design of drug carriers.

Interaction between similarly charged surfaces can be attractive at high electrostatic coupling constants Ξ = l(B)Z(2)/μ(GC), where l(B) is the Bjerrum length, μ(GC) the Gouy-Chapman length, and Z the valency of counterions. While this effect has been studied previously in detail, as a function of surface charge density and valency of the pointlike counterions, much less is known about the effect of counterion size. We apply the Wang-Landau sampling Monte Carlo (MC) simulation method to compute the free energy F as a function of the scaled distance between the plates D̃=D/μ(GC) for a range of Ξ and scaled counterion radii R̃=R/μ(GC). We find that for large Ξ and small ion radius, there is a global equilibrium distance D̃=D̃(eq)=2(1+R̃), correctly giving the expected value at the point counterion limit. With increasing R̃ the global minimum in F(D̃) changes to a metastable state and finally this minimum vanishes when R̃ reaches a critical value, which depends on Ξ. We present a state diagram indicating approximate boundaries between these three regimes. The Wang-Landau MC method, as it is applied here, offers a possibility to study a wide spectrum of extended problems, which cannot be treated by the use of contact value theorem.

In biological systems, charged membrane surfaces are surrounded by charged molecules such as electrolyte ions and proteins. Our recent experiments in the systems of giant phospholipid vesicles indicated that some of the blood plasma proteins (macro-ions) may promote adhesion between equally charged membrane surfaces. In this work, theory was put forward to describe an IgG antibody-mediated attractive interaction between negatively charged membrane surfaces which was observed in experiments on giant phospholipid vesicles with cardiolipin-containing membranes. The attractive interactions between negatively charged membrane surfaces in the presence of negatively and positively charged spherical macro-ions are explained using functional density theory and Monte Carlo simulations. Both, the rigorous solution of the variational problem within the functional density theory and the Monte Carlo simulations show that spatial and orientational ordering of macro-ions may give rise to an attractive interaction between negatively charged membrane surfaces. It is also shown that the distinctive spatial distribution of the charge within the macro-ions (proteins) is essential in this process.

The interaction between equal, uniformly charged flat surfaces, separated by a solution of spheroidal nanoparticles was studied theoretically. The nanoparticles were assumed to have spatially distributed electric charge. The nonlocal Poisson-Boltzmann (PB) theory for the spheroidal nanoparticles, which play the role of counterions, was developed. In the model the center of the spheroidal nanoparticle could not approach the charged surfaces closer than the radius of the nanoparticle. It was shown that for large enough diameters of nanoparticles and large enough surface charge densities of membrane surfaces, the two equally charged surfaces could experience an attractive force due to the spatially distributed charges within the nanoparticles. The results presented in this chapter may add to a better understanding of the coalescence of negatively charged membrane surfaces induced by positively charged nanoparticles (e.g., proteins) which are proposed to play an important role in the complex vital processes such as blood clot formation.