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A thermal model to describe kinetic dispersion in rubber nanocomposites: The effect of mixing time on dispersion
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Abstract A multivariate adiabatic connection (MAC) framework for describing dispersion interactions in a system consisting of N non-overlapping monomers is presented. By constraining the density to the physical ground-state density of the supersystem, the MAC enables a rigorous separation of induction and dispersion effects. The exact dispersion energy is obtained from the zero-temperature fluctuation–dissipation theorem and partitioned into increments corresponding to the interaction energy gained when an additional monomer is added to a K -monomer system. The total dispersion energy of an N -monomer system is independent of any partitioning into subsystems. This statement of dispersion size consistency is shown to be an exact constraint. The resulting additive separability of the dispersion energy results from multiplicative separability of the generalized screening factor defined as the inverse generalized dielectric function. Many-body perturbation theory (MBPT) is found to violate dispersion size-consistency because perturbative approximations to the generalized screening factor are nonseparable; on the other hand, random phase approximation-type methods produce separable generalized screening factors and therefore preserve dispersion size-consistency. This result further explains the previously observed increase in relative errors of MBPT for dispersion interactions as the system size increases. Implications for electronic structure theory and applications to supramolecular materials and condensed matter are discussed.more » « less
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Diffusiophoresis refers to the movement of colloidal particles in the presence of a concentration gradient of a solute and enables directed motion of colloidal particles in geometries that are inaccessible, such as dead-end pores, without imposing an external field. Previous experimental reports on dead-end pore geometries show that, even in the absence of mean flow, colloidal particles moving through diffusiophoresis exhibit significant dispersion. Existing models of diffusiophoresis are not able to predict the dispersion and thus the comparison between the experiments and the models is largely qualitative. To address these quantitative differences between the experiments and models, we derive an effective one-dimensional equation, similar to a Taylor dispersion analysis, that accounts for the dispersion created by diffusioosmotic flow from the channel sidewalls. We derive the effective dispersion coefficient and validate our results by comparing them with direct numerical simulations. We also compare our model with experiments and obtain quantitative agreement for a wide range of colloidal particle sizes. Our analysis reveals two important conclusions. First, in the absence of mean flow, dispersion is driven by the flow created by diffusioosmotic wall slip such that spreading can be reduced by decreasing the channel wall diffusioosmotic mobility. Second, the model can explain the spreading of colloids in a dead-end pore for a wide range of particle sizes. We note that, while the analysis presented here focuses on a dead-end pore geometry with no mean flow, our theoretical framework is general and can be adapted to other geometries and other background flows.more » « less
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Abstract The salinity distribution of an estuary depends on the balance between the river outflow, which is seaward, and a dispersive salt flux, which is landward. The dispersive salt flux at a fixed cross‐section can be divided into shear dispersion, which is caused by spatial correlations of the cross‐sectionally varying velocity and salinity, and the tidal oscillatory salt flux, which results from the tidal correlation between the cross‐section averaged, tidally varying components of velocity and salinity. The theoretical moving plane analysis of Dronkers and van de Kreeke (1986) indicates that the oscillatory salt flux is exactly equal to the difference between the “local” shear dispersion at a fixed location and the shear dispersion which occurred elsewhere within a tidal excursion; therefore, they refer to the oscillatory salt flux as “nonlocal” dispersion. We apply their moving plane analysis to a numerical model of a short, tidally dominated estuary and provide the first quantitative confirmation of the theoretical result that the spatiotemporal variability of shear dispersion accounts for the oscillatory salt flux. Shear dispersion is localized in space and time due to the tidal variation of currents and the position of the along‐channel salinity distribution with respect to topographic features. We find that dispersion near the mouth contributes strongly to the salt balance, especially under strong river and tidal forcing. Additionally, while vertical shear dispersion produces the majority of dispersive salt flux during neap tide and high flow, lateral mechanisms provide the dominant mode of dispersion during spring tide and low flow.more » « less
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1016/j.polymer.2019.03.044
