Reply to the “Comment on ‘Rheology of an Ionic Liquid with Variable Carreau Exponent: A Full Picture by Molecular Simulation with Experimental Contribution,’ by N. Voeltzel, P. Vergne, N. Fillot, N. Bouscharain, L. Joly, Tribology Letters (2016) 64:25” by H. A. Spikes

Excerpt

We are grateful to H. A. Spikes for giving us the opportunity to provide additional details on our work concerning the prediction of the rheological behavior of an ionic liquid by molecular simulation with experimental contribution [1]. We believe that our paper presents an objective research at the forefront of the current computational possibilities in that matter and sheds light on a rather unusual but with high-potential type of lubricant. In this study, the time–temperature–pressure superposition principle was applied to nearly 200 (\(\eta ,\dot{\gamma })\) cases to end up with a single master curve, which we tentatively proposed to represent by a regression to the Carreau expression whose coefficient of correlation, \(R^{2}\), was equal to 0.86. We thereafter identified a clear dependency of the Carreau exponent with pressure and temperature which was characterized by separate regressions on each series of results (obtained at constant \(T\) and \(p\), see Sect. 4 in [1]) to the same model. These results could explain, to a large extent, the rather low value of the coefficient of correlation obtained for the regression carried out on the entire data set. Finally, we showed that the Carreau exponent variations could be correlated with those of the relaxation time, while inviting for further works to analyze more into details the physical phenomena behind this new question. In his comment [2], Spikes suggests that the so-called discrepancies and the correlation mentioned above could result from our choice of the Carreau equation. He proposes to employ the Eyring model, in accordance with the position he has been advocating for decades—on the question of the more relevant rheological model to represent the shear-thinning response of lubricants—and which he tried to assert again recently [3, 4]. By comparison with the published regression in [1], which results from the Carreau equation, he claims that an equal or even better fit to our reduced data can be obtained with the Eyring expression (see his Figs. 3 and 4 [2]). However, he realized his fit simply keeping our \(\eta_{0}\) value—which results from a Carreau regression—and adjusting \(t_{relE}\), the Eyring relaxation time, to match our rescaled data by eye. Obviously this procedure might be improved and, more importantly, mathematically quantified by new calculations based on the original data. This is indeed one of the major objectives of this reply to present an unbiased additional analysis based on quantitative data, while making available as much as possible the results from our molecular dynamics (MD) simulations that are now included in an electronic supplementary file, published along with our response. We do hope that our reply will help the reader to avoid any misunderstanding and to achieve a balanced view of the points raised both by Spikes and in our response to his comment. The former is organized in three parts: the comparison of the regressions obtained by different models, the consideration of a stress–shear rate dependence and the choice of an appropriate rheological model. …