On the Stability of Pickering and Classical Nanoemulsions: Theory and Experiments

Emulsification is a crucial technique for mixing immiscible liquids into droplets in various industries, such as food, cosmetics, biomedicine, agrochemistry, and petrochemistry. Quantitative analysis of the stability is pivotal before the utilization of these emulsions. Differences in X-ray attenuation for emulsion components and surface relaxation of the droplets may contribute to X-ray CT imaging and low-field NMR spectroscopy as viable techniques to quantify emulsion stability. In this study, Pickering (stabilized solely by nanoparticles) and Classical (stabilized solely by low molecular weight polymers) nanoemulsions were prepared with a high-energy method. NMR and X-ray CT were employed to constantly monitor the two types of nanoemulsions until phase separation. The creaming rates calculated from NMR match well with the results obtained from X-ray CT. Furthermore, we show that Stokes' law coupled with the classical Lifshitz-Slyozov-Wagner theory underestimates the creaming rate of the nanoemulsions compared to the experimental results from NMR and X-ray CT imaging. A new theory is proposed by fully incorporating the effects of Pickering nanoparticles, hydrocarbon types, volume fraction, size distribution, and flocculation on the droplet coarsening. The theoretical results agree well with the experimentally measured creaming rates. It reveals that the attachment of nanoparticles onto a droplet surface decreases the mass transfer for hydrocarbon molecules to move from the bulk aqueous phase into other droplets, thus slowing the Ostwald ripening. Therefore, Pickering nanoemulsions show a better stability behavior compared to Classical nanoemulsions. The impacts of hydrocarbon and emulsification energy on the stability of nanoemulsions are reported. These findings demonstrate that the stability of the nanoemulsions can be manipulated and optimized for a specific application, setting the stage for subsequent investigations of these nanodroplets.

Parsimony and goodness-of-fit in multi-dimensional NMR inversion

Multi-dimensional nuclear magnetic resonance (NMR) experiments are often used for study of molecular structure and dynamics of matter in core analysis and reservoir evaluation. Industrial applications of multi-dimensional NMR involve a high-dimensional measurement dataset with complicated correlation structure and require rapid and stable inversion algorithms from the time domain to the relaxation rate and/or diffusion domains. In practice, applying existing inverse algorithms with a large number of parameter values leads to an infinite number of solutions with a reasonable fit to the NMR data. The interpretation of such variability of multiple solutions and selection of the most appropriate solution could be a very complex problem. In most cases the characteristics of materials have sparse signatures, and investigators would like to distinguish the most significant relaxation and diffusion values of the materials. To produce an easy to interpret and unique NMR distribution with the finite number of the principal parameter values, we introduce a new method for NMR inversion. The method is constructed based on the trade-off between the conventional goodness-of-fit approach to multivariate data and the principle of parsimony guaranteeing inversion with the least number of parameter values. We suggest performing the inversion of NMR data using the forward stepwise regression selection algorithm. To account for the trade-off between goodness-of-fit and parsimony, the objective function is selected based on Akaike Information Criterion (AIC). The performance of the developed multi-dimensional NMR inversion method and its comparison with conventional methods are illustrated using real data for samples with bitumen, water and clay.

Species abundance distribution and dynamics in two locally coupled communities

This study considered a model for species abundance dynamics in two local community (or islands) connected to a regional metacommunity. The model was analyzed using continuous probabilistic technique that employs Kolmogorov-Fokker-Planck forward equation to derive the probability density of the species abundance in the two local communities. Using this technique, we proposed a classification for the species abundance dynamics in the local communities. This classification was made based on such characteristics as immigration intensity, species representation in the metacommunity and the size of local communities. We further distinguished several different scenarios for species abundance dynamics using different ecological characteristics such as species persistence, extinction and monodominance in one or both local communities. The similarity of the species abundance distributions between the two local communities was studied using the correlation coefficient between species abundances in two local communities. The correlation is a function of migration rates between local communities and between local and metacommunity. Immigration between local communities drives the homogenization of the local communities, while immigration from the metacommunity will differentiate them. This community subdivision model provides useful insights for studying the effect of landscape fragmentation on species diversity.

Continuous probabilistic approach to species dynamics in Hubbell's zero-sum local community

In this paper a continuous probabilistic approach formulated using Kolmogorov-Fokker-Planck forward and backward models is applied to Hubbell's zero-sum neutral theory for species dynamics in local community. Using this technique the probability density of species abundance, distribution of the first passage time to extinction or fixation and probability of extinction are defined. The resulting values for the distribution of the first passage time to extinction are verified by the simulation study of Hubbell's zero-sum neutral model for the local community. Based on the sensitivity analysis for the continuous probabilistic models, the realistic classification of local communities subject to their diversity and species dynamics is proposed with respect to the immigration probability, the species metacommunity relative abundance, and the size of local community.

Dynamics of group formation in collective motion of organisms

A mathematical description of the collective motion of organisms using a density-velocity model is presented. This model consists of a system of nonlinear parabolic equations, a forced Burgers equation for velocity and a diffusion-convection equation for density. The motion is mainly due to forces resulting from the differences between local density levels and a prescribed density level. The existence of a global attractor for a 1D density-velocity model is proved by asymptotic analysis to demonstrate different patterns in the attractors for density. The theoretical results are supplemented with numerical results. These patterns correspond to movements of collective organized groups of organisms such as fish schools and bird flocks.