MODELLING OF HIGH-PRESSURE PHASE EQUILIBRIUM IN SYSTEMS OF INTEREST IN THE FOOD ENGINEERING FIELD USING THE PENG-ROBINSON EQUATION OF STATE WITH TWO DIFFERENT MIXING RULES

In this work, thermodynamic models for fitting the phase equilibrium of binary systems were applied, aiming to predict the high pressure phase equilibrium of multicomponent systems of interest in the food engineering field, comparing the results generated by the models with new experimental data and with those from the literature. Two mixing rules were used with the Peng-Robinson equation of state, one with the mixing rule of van der Waals and the other with the composition-dependent mixing rule of Mathias et al. The systems chosen are of fundamental importance in food industries, such as the binary systems CO(2)-limonene, CO(2)-citral and CO(2)-linalool, and the ternary systems CO(2)-Limonene-Citral and CO(2)-Limonene-Linalool, where high pressure phase equilibrium knowledge is important to extract and fractionate citrus fruit essential oils. For the CO(2)-limonene system, some experimental data were also measured in this work. The results showed the high capability of the model using the composition-dependent mixing rule to model the phase equilibrium behavior of these systems.

Tidal friction in close-in satellites and exoplanets: The Darwin theory re-visited

This report is a review of Darwin`s classical theory of bodily tides in which we present the analytical expressions for the orbital and rotational evolution of the bodies and for the energy dissipation rates due to their tidal interaction. General formulas are given which do not depend on any assumption linking the tidal lags to the frequencies of the corresponding tidal waves (except that equal frequency harmonics are assumed to span equal lags). Emphasis is given to the cases of companions having reached one of the two possible final states: (1) the super-synchronous stationary rotation resulting from the vanishing of the average tidal torque; (2) capture into the 1:1 spin-orbit resonance (true synchronization). In these cases, the energy dissipation is controlled by the tidal harmonic with period equal to the orbital period (instead of the semi-diurnal tide) and the singularity due to the vanishing of the geometric phase lag does not exist. It is also shown that the true synchronization with non-zero eccentricity is only possible if an extra torque exists opposite to the tidal torque. The theory is developed assuming that this additional torque is produced by an equatorial permanent asymmetry in the companion. The results are model-dependent and the theory is developed only to the second degree in eccentricity and inclination (obliquity). It can easily be extended to higher orders, but formal accuracy will not be a real improvement as long as the physics of the processes leading to tidal lags is not better known.

Modelling the line variations from the wind-wind shock emissions of WR 30a

The study of Wolf-Rayet stars plays an important role in evolutionary theories of massive stars. Among these objects, similar to 20 per cent are known to be in binary systems and can therefore be used for the mass determination of these stars. Most of these systems are not spatially resolved and spectral lines can be used to constrain the orbital parameters. However, part of the emission may originate in the interaction zone between the stellar winds, modifying the line profiles and thus challenging us to use different models to interpret them. In this work, we analysed the He II lambda 4686 angstrom + C IV lambda 4658 angstrom blended lines of WR 30a (WO4+O5) assuming that part of the emission originate in the wind-wind interaction zone. In fact, this line presents a quiescent base profile, attributed to the WO wind, and a superposed excess, which varies with the orbital phase along the 4.6-d period. Under these assumptions, we were able to fit the excess spectral line profile and central velocity for all phases, except for the longest wavelengths, where a spectral line with constant velocity seems to be present. The fit parameters provide the eccentricity and inclination of the binary orbit, from which it is possible to constrain the stellar masses.

Vegetable Oils Deacidification by Solvent Extraction: Liquid-Liquid Equilibrium Data for Systems Containing Sunflower Seed Oil at 298.2 K

Liquid-liquid equilibrium experimental data for refined sunflower seed oil, artificially acidified with commercial oleic acid or commercial linoleic acid and a solvent (ethanol + water), were determined at 298.2 K. This set of experimental data and the experimental data from Cuevas et al.,(1) which were obtained from (283.2 to 333.2) K, for degummed sunflower seed oil-containing systems were correlated using NRTL and UNIQUAC models with temperature-dependent binary parameters. The deviation between experimental and calculated compositions presented average values of (1.13 and 1.41) % for NRTL and UNIQUAC equations, respectively, indicating that the models were able to correctly describe the behavior of compounds under different temperature and solvent hydration.

Invariants of binary differential equations

In this paper, we study binary differential equations a(x, y)dy (2) + 2b(x, y) dx dy + c(x, y)dx (2) = 0, where a, b, and c are real analytic functions. Following the geometric approach of Bruce and Tari in their work on multiplicity of implicit differential equations, we introduce a definition of the index for this class of equations that coincides with the classical Hopf`s definition for positive binary differential equations. Our results also apply to implicit differential equations F(x, y, p) = 0, where F is an analytic function, p = dy/dx, F (p) = 0, and F (pp) not equal aEuro parts per thousand 0 at the singular point. For these equations, we relate the index of the equation at the singular point with the index of the gradient of F and index of the 1-form omega = dy -aEuro parts per thousand pdx defined on the singular surface F = 0.

Structural Characterization of Photopolymerizable Binary Liposomes Containing Diacetylenic and Saturated Phospholipids

The use of liposomes to encapsulate materials has received widespread attention for drug delivery, transfection, diagnostic reagent, and as immunoadjuvants. Phospholipid polymers form a new class of biomaterials with many potential applications in medicine and research. Of interest are polymeric phospholipids containing a diacetylene moiety along their acyl chain since these kinds of lipids can be polymerized by Ultra-Violet (UV) irradiation to form chains of covalently linked lipids in the bilayer. In particular the diacetylenic phosphatidylcholine 1,2-bis(10,12-tricosadiynoyl)- sn-glycero-3-phosphocholine (DC8,9PC) can form intermolecular cross-linking through the diacetylenic group to produce a conjugated polymer within the hydrocarbon region of the bilayer. As knowledge of liposome structures is certainly fundamental for system design improvement for new and better applications, this work focuses on the structural properties of polymerized DC8,9PC:1,2-dimyristoyl-sn-glycero-3-phusphocholine (DMPC) liposomes. Liposomes containing mixtures of DC8,9PC and DMPC, at different molar ratios, and exposed to different polymerization cycles, were studied through the analysis of the electron spin resonance (ESR) spectra of a spin label incorporated into the bilayer, and the calorimetric data obtained from differential scanning calorimetry (DSC) studies. Upon irradiation, if all lipids had been polymerized, no gel-fluid transition would be expected. However, even samples that went through 20 cycles of UV irradiation presented a DSC band, showing that around 80% of the DC8,9PC molecules were not polymerized. Both DSC and ESR indicated that the two different lipids scarcely mix at low temperatures, however few molecules of DMPC are present in DC8,9PC rich domains and vice versa. UV irradiation was found to affect the gel fluid transition of both DMPC and DC8,9PC rich regions, indicating the presence of polymeric units of DC8,9PC in both areas, A model explaining lipids rearrangement is proposed for this partially polymerized system.