Asymmetric binary mixtures of hard-spheres exhibit several interesting thermodynamic phenomena, such as multiple kinds of glassy states. When the degrees of freedom of the small spheres are integrated out from the description, their effects are incorporated into an effective pair interaction between large spheres known as the depletion potential. The latter has been widely used to study both the phase behavior and dynamic arrest of the big particles. Depletion forces can be accounted for by a contraction of the description in the multicomponent Ornstein-Zernike equation [R. Castañeda-Priego, A. Rodríguez-López, and J. M. Méndez-Alcaraz, Phys. Rev. E 73, 051404 (2006)]. Within this theoretical scheme, an approximation for the difference between the effective and bare bridge functions is needed. In the limit of infinite dilution, this difference is irrelevant and the typical Asakura-Osawa depletion potential is recovered. At higher particle concentrations, however, this difference becomes important, especially where the shell of first neighbors is formed, and, as shown here, cannot be simply neglected. In this work, we use a variant of the Verlet expression for the bridge functions to highlight their importance in the calculation of the depletion potential at high densities and close to the spinodal decomposition. We demonstrate that the modified Verlet closure predicts demixing in binary mixtures of hard spheres for different size ratios and compare its predictions with both liquid state and density functional theories, computer simulations, and experiments. We also show that it provides accurate correlation functions even near the thermodynamic instability; this is explicitly corroborated with results of molecular dynamics simulations of the whole mixture. Particularly, our findings point toward a possible universal behavior of the depletion potential around the spinodal line.
In this work, we studied the chain dimensions, shape, and thermodynamic characteristics of poly(ε-caprolactone) diols (HO-PCL-OH) in solution. PCL diol samples of different molecular weights and architectures were synthesized using immobilized Yarrowia lipolytica lipase as catalyst. Gel permeation chromatography (GPC) with online right-angle laser-light scattering (RALLS), differential viscometer (DV), and interferometric refractometer IRS detectors offered a proper way to obtain information on thermodynamic characteristics and chain flexibility. The weight-average molecular weights of the PCL diol samples (M w ) ranged from 2, 750 to 13,120 uma. The z-average radius of hydrodynamic volume (
An analytical solution for moisture dynamic during freeze-drying based in non-ideal Darcy's law that resolves the singularity at zero time was deducted. The non-ideal Darcy's law is represented by a Darcy's pseudo permeability (K �) and a deviation index (n). The analytical solution must be complemented with a numerical solution of Fourier's equations for heat transfer in the two product zones. The model was fitted to experimental freeze-drying dynamics of an orange juice-based cake. The Darcy's pseudo permeability obtained was K � ¼ 2.0X10 −12 m 2.5 with an ideal deviation index of n ¼ 0.5. The proposed equations, solved with fitted Darcy pseudo permeability and ideal deviation index, reproduced other experimental freeze-drying dynamics of the same product at different temperatures. Solución analítica de un modelo matemático de liofilización basado en la ley de Darcy: aplicación a una torta con base de jugo naranja RESUMEN Se dedujo una solución analítica para la dinámica de la humedad durante la liofilización basada en la ley de Darcy no ideal que resuelve la singularidad en el tiempo cero. La solución analítica debe complementarse con una solución numérica de las ecuaciones de Fourier mediante la transferencia de calor en las dos zonas de producto. El modelo se ajustó a la dinámica experimental de liofilización de un producto a base de naranja. La pseudo-permeabilidad de Darcy obtenida fue de K*=2.0X10 −12 m 2.5 con un índice de desviación de la conducta ideal de n=0.5. Las ecuaciones propuestas, resueltas con la pseudo-permeabilidad de Darcy ajustada y el índice de desviación ideal, reprodujeron la dinámica de liofilización experimental del mismo producto a diferentes temperaturas.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.