Density gradient theory (DGT) allows fast and accurate determination of surface tension and density profile through a phase interface. Several algorithms have been developed to apply this theory in practical calculations. While the conventional algorithm requires a reference substance of the system, a modified "stabilized density gradient theory" (SDGT) algorithm is introduced in our work to solve DGT equations for multiphase pure and mixed systems. This algorithm makes it possible to calculate interfacial properties accurately at any domain size larger than the interface thickness without choosing a reference substance or assuming the functional form of the density profile. As part of DGT inputs, the perturbed chain statistical associating fluid theory (PC-SAFT) equation of state (EoS) was employed for the first time with the SDGT algorithm. PC-SAFT has excellent performance in predicting liquid phase properties as well as phase behaviors. The SDGT algorithm with the PC-SAFT EoS was tested and compared with experimental data for several systems. Numerical stability analyses were also included in each calculation to verify the reliability of this approach for future applications. List of symbols Symbol Units DescriptionA 0 J Homogeneous Helmholtz free energy A id 0 J Ideal gas contribution to A 0 A hs 0 J Hard sphere contribution to A 0 A hc 0 J Hard chain contribution to A 0 A disp 0

For more than a century, density gradient theory (DGT) has been developed and applied for interfacial property calculations of pure and mixed fluid systems. However, due to the local density approximation, DGT has not been applicable to amphiphilic molecules. By developing a modified DGT model with the chain contribution to the free energy, this paper extends the application of the DGT model to heteronuclear chain molecules, such as surfactants. The chain contribution term is derived based on the work from the iSAFT model. With the help of the Stabilized Density Gradient Theory (SDGT) algorithm developed in our previous work and the PC-SAFT equation of state (EoS), the modified DGT model is tested in water/oil/surfactant mixture systems, the results of which have been qualitatively verified with other theories and experimental data.

Based on insulin potentiating activity of cinnamon, effects of a water extract of cinnamon were tested in a 2‐mo double‐blind placebo trial with 137 participants in China. Mean±SEM age was 61.3 ± 0.8 years, BMI was 25.3 ± 0.3 and M/F ratio was 65/72. A placebo capsule or a 250 mg dried water‐extract cinnamon (CinSulin) capsule was given twice per day. At baseline, homeostasis model assessment‐estimated insulin resistance (HOMA‐IR) was significantly correlated with diastolic blood pressure (r=0.23) postprandial glucose (r=0.45) and insulin (r=0.42), triglycerides (r=0.29), fructosamine (0.23), BMI (r=0.29) and negatively correlated with HDLC (r=0.37). After 2 mo, fasting glucose decreased (p<0.001) in the aqua‐cinnamon‐supplemented group (8.85 ± 0.36 to 8.19 ± 0.29 mmol/L) compared with 8.57 ± 0.32 to 8.44 ± 0.34 mmol/L in the placebo group (p=0.45). Glucose 2 h after a 75 g carbohydrate load also decreased (p<0.0001) with CinSulin (15.09 ± 0.57 to 13.30 ± 0.55 mmol/L) compared to 14.18 ± 0.60 to 13.74 ± 0.58 mmol/L with placebo. Insulin concentrations and HOMA‐IR tended to be improved by aqua‐cinnamon supplements but differences were not significant. In summary, supplementation of a water extract of cinnamon had beneficial effects in subjects with hyperglycemia. (Supported by USDA‐ARS, Tang‐An Medical & Oklahoma State Univ).

Modeling droplet nucleation processes requires a molecular-scale approach to describe the interfacial tension (IFT) of spherical interfaces. Density gradient theory (DGT), also referred to as square gradient theory in some publications, has been widely used to compute the IFT of many pure and mixed systems at the molecular scale. However, the application of DGT to droplet interfaces is limited by its setup in open systems in which a stable droplet cannot be achieved. In this paper, we propose a mass-conserved DGT model in a closed system, i.e., with no-flux boundary conditions, where no mass exchange is allowed with the outside environment. As opposed to the traditional approach, this model enforces a canonical ensemble and guarantees energy dissipation. The proposed model has been successfully applied to systems with planar interfaces as well as spherical interfaces, especially for IFT calculation for droplets in the nucleation process. By extending the DGT model from open to closed systems, we demonstrate the potential of DGT as an inhomogeneous model for a wider range of academic and industrial applications.

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