Entropy Influence on the Dependence of the Nanofluids Viscosity on Temperature and Shear Rate

Abstract

A Brookfield DV-II + Pro rotational viscometer was used to study the viscosity of 7 samples of concentrated nanodispersed systems (nanofluids) with a similar viscosity (6-22 mPa ∙ s), the particles of the dispersed phase in which are nanosized surfactant micelles and conglomerates from them. It was found that for 5 out of 7 studied reagents, there is a decrease in viscosity typical for dispersed systems with an increase in the shear rate, and their flow curves, that is, the dependence of the shear stress on the shear rate, correspond to the ideal plastic flow of non-Newtonian fluids. Moreover, with high reliability, R2 ≥ 0.999 is described by the Bingham equation with a small value of the limiting shear stress (less than 0.2 Pa). It is shown that all the studied reagents are also characterized by an increase in the activation energy of a viscous flow Е with an increase in the shear rate. As a result, a decrease in viscosity with an increase in shear rate, typical for disperse systems, including nanofluids, is provided by a more significant increase in entropy changes ΔS compared to Е. It has been substantiated that, depending on the ratio between the activation energy of viscous flow Е and the change in entropy ΔS, the viscosity of concentrated micellar dispersed systems with an increase in the shear rate can decrease, remain unchanged, and increase. The last two cases, not typical for disperse systems and nanofluids, were identified and studied using the example of two demulsifiers, RIK-1 and RIK-2, with a maximum of a very narrow particle size distribution at 160 ± 5 nm, corresponding to the size of a special type of very stable micelles Surfactant — vesicle.

Entropy change at viscous flow of dispersive systems with a phase transition in their particles

“…It turned out that two thermodynamic functions (enthalpy and entropy) governing the viscosity of ODSs and MDSs are affected by shear strain in such a way that the effect of an H increase on viscosity is offset by a proportional S increase. This conclusion was drawn in [6][7][8] for S values determined using formula (2) up to an undefined constant. Expression (5) for S = βR H obtained in the present study allows one to establish that H at T = T * = T * * is compensated fully by S; i.e., G = 0.…”

“…The obtained data highlight the importance of compensation effect for the viscosity of ODSs and MDSs. The compensation effect is the only one that provides an explanation for the reduction in viscosity at higher shear velocities, which is typical of ODSs and MDSs in spite of the accompanying increase in the values of H due to the breakdown of dispersed phase particles into smaller agglomerates [6][7][8]. It turned out that two thermodynamic functions (enthalpy and entropy) governing the viscosity of ODSs and MDSs are affected by shear strain in such a way that the effect of an H increase on viscosity is offset by a proportional S increase.…”

“…where f ≈ 6 • 10 12 Hz is the frequency with which, according to the Eyring hypothesis, liquid molecules shift to new equilibrium positions; h is the Planck constant; N a is the Avogadro number; and V M is the molar liquid volume. However, it was demonstrated in [8], that the viscosity of ODSs and MDSs is governed by relaxation processes with their characteristic frequencies being 5-7 orders of magnitude lower than those assumed by Eyring. Therefore, one needs to find a way to calculate constant B in (1), ( 2) in order to correctly use the thermodynamic method for DS investigation.…”

“…However, the values of E for ODSs and MDSs determined this way typically increase with shear velocity due to the breakdown of their particles induced by shear strain. This does not agree with a reduction in their viscosity that is observed under these conditions [6][7][8]. This contradiction is resolved only if the influence of entropy on the DS viscosity is taken into account by introducing the following expression into the Eyring equation: G = H − T S, where H and S are the variations of enthalpy and entropy.…”

“…Liquid DSs with a liquid-like state of particles, the size of which may be changed by temperature, shear strain, and phase transitions, are even less well understood. Oil dispersed systems (ODSs) with dispersed phase particles taking the form of nanoaggregates of asphaltene, resin, and paraffin molecules [2][3][4][5][6][7][8] are the examples of such systems. It has been demonstrated in [7,8] that liquid concentrated micellar dispersed systems (MDSs) with dispersed phase particles taking the form of micelles of surfactants and their aggregates are similar to ODSs in their viscous properties.…”