RU Seminar - 21.07.21 Andrea Codrignani "Validity of continuum lubrication equations in the nanoscale"

Validity of continuum lubrication equations in the nanoscale

The fluid dynamics of lubricant oils needs to be described in a continuum framework, which allows to study and design whole machine elements. However, in very thin gaps, which occur due to high local pressure, the lubricant behavior is mostly governed by the atomic interactions between lubricant molecules and solid surfaces. Thus, the continuum models need to be formulated with constitutive laws that correctly describe the nanoscale fluid dynamics [1].

Among the continuous methods, the most used one is the Reynolds equation, which stems from a simplification of the Navier-Stokes equations valid for thin lubricant films. In its original formulation, we can use this equation down to few tenths of nanometer gap only under mild operating conditions (i.e. at low pressure). Under more severe conditions, the thin lubricant flow experiences more complicated behaviors whose numerical description requires some extensions to the original Reynolds formulation [2].

In this work we aim to extend the validity of the traditional Reynolds equation in order to analyze one typical aspect of nanoscale lubricant flows, namely the total or partial slip of the first layer of lubricant at the liquid/solid interface. This velocity discrepancy can be observed through molecular dynamics simulations and modeled into the continuum Reynolds equation through an additional term, which is referred to as the slip length. To achieve a proper description of this term, we analyzed the flow of a typical mineral oil base (hexadecane C16H34) in a representative geometry of a lubricated contact (i.e. a converging-diverging channel) and we carried out a comprehensive parametric molecular dynamics study in order to analyze the influence of mild to severe operating conditions on the occurring of slip phenomena.

In this study, we observed a complex relationship between the local slip velocities and tangential stresses at the wall, which strongly deviates from the expected linear relationship as seen, for example, in carbon nanotubes [3]. We discuss how the Reynolds equation could be extended in order to match the onset of slip while switching from a mild to a severe operating condition.

In conclusion, we find that a correct model, which describes the slip velocity, could be crucial in order to extend the applicability of continuous method such as the Reynolds equation. This can lead to an easier and more efficient modelling of lubricant flows in narrow gaps in the nanoscale.

References:

[1] Hamrock, Bernard J., Bernard J. Schmid, and Bo O. Jacobson. Fundamentals of fluid film lubrication. Vol. 169. CRC press, 2004.

[2] Savio, Daniele, Kerstin Falk, and Michael Moseler. "Slipping domains in water-lubricated microsystems for improved load support." Tribology international 120 (2018): 269-279.

[3] Falk, Kerstin, et al. "Ultralow liquid/solid friction in carbon nanotubes: Comprehensive theory for alcohols, alkanes, OMCTS, and water." Langmuir 28.40 (2012): 14261-14272.