The Non-Unicity of the Film Thickness in the Hydrodynamic Lubrication: Novel Approach Generating Equivalent Micro-Grooves and Roughness

Since the 1960s, all studies have assumed that a film thickness “h” provides a unique pressure field “p” by resolving the Reynolds equation. However, it is relevant to investigate the film thickness unicity under a given hydrodynamic pressure within the inverse theory. This paper presents a new approach to deduce from an initial film thickness a widespread number of thicknesses providing the same hydrodynamic pressure under a specific condition of gradient pressure. For this purpose, three steps were presented: 1) computing the hydrodynamic pressure from an initial film thickness by resolving the Reynolds equation with Gümbel’s cavitation model, 2) using a new algorithm to generate a second film thickness, 3) comparing and validating the hydrodynamic pressure produced by both thicknesses with the modified Reynolds equation. Throughout three surface finishes: the macro-shaped, micro-textured, and rough surfaces, it has been demonstrated that under a specific hydrodynamic pressure gradient, several film thicknesses could generate the same pressure field with a slight difference by considering cavitation. Besides, this paper confirms also that with different ratios of the averaged film thickness to the root mean square (RMS) similar hydrodynamic pressure could be generated, thereby the deficiency of this ratio to define the lubrication regime as commonly known from Patir and Cheng theory.

Revealing the structure and evolution of entrained oxide film in Mg–Y alloy castings

The structure and evolution of oxide film in Mg alloys have been a research objective for a long time but are still unclear up to now. In the present work, the structure of the entrained oxide film (which is also known as bifilm) in Mg–Y alloy castings protected by SF6/air cover gas was characterized. It was found that the entrained oxide film can be divided into two typical types: (1) single-layered F-rich films and (2) double-layered films with a F-rich inner layer and a F-poor outer layer. Based on the experimental phenomena and thermodynamic calculation, the evolution mechanism of the oxide film was also revealed. It was found that F element from the cover gas reacted with the melt firstly to form the initial F-rich single-layered film. Then, O and S were also involved in the reaction, transforming the initial film to be a (F, O, S)-rich single-layered film. Finally, when the F element was depleted, the newly formed layer on the existing oxide film is characteristically F-poor but (O, S)-enriched, leading to a double-layered oxide film. It was also found that the oxide film grew faster in SF6/air cover gas than in SF6/CO2 cover gas, resulting in a higher repeatability of mechanical properties of Mg–Y alloy castings.

About the Inverse Theory and the Non-Unicity of the Film Thickness: Novel Approach Generating Equivalent Micro-Grooves and Roughness

Since the 1960s, all studies have assumed that a film thickness “h” provides a unique pressure field “p” by resolving the Reynolds equation. However, it is relevant to investigate the film thickness unicity under a given hydrodynamic pressure within the inverse theory. This paper presents a new approach to deduce from an initial film thickness a widespread number of thicknesses providing the same hydrodynamic pressure under a specific condition of gradient pressure. For this purpose, three steps were presented: 1) computing the hydrodynamic pressure from an initial film thickness by resolving the Reynolds equation with Gümbel’s cavitation model, 2) using a new algorithm to generate a second film thickness, 3) comparing and validating the hydrodynamic pressure produced by both thicknesses with the modified Reynolds equation. Throughout three surface finishes: the macro-shaped, micro-textured, and rough surfaces, it has been demonstrated that under a specific hydrodynamic pressure gradient, several film thicknesses could generate the same pressure field with a slight difference by considering cavitation. Besides, this paper confirms also that different ratios of the averaged film thickness by the root mean square (RMS) similar hydrodynamic pressure could be generated, thereby the deficiency of this ratio to define the lubrication regime as commonly known with Patir and Cheng theory.

Molecular Dynamics Simulation on Thin-Film Lubrication of a Mixture of Three Alkanes

We used the COMPASS forcefield to perform molecular dynamics (MD) simulation of a mixture composed of three alkanes as the lubricant for the thin-film lubrication. The viscosity of the lubrication film in the non-working state, the final film thickness, and density distribution were investigated. The results reveal that the viscosity error among different initial film thicknesses in the non-working state is within 5%, which confirms the applicability of the model and the forcefield. The viscosity decreases oscillating as temperature increases. Whatever the initial film thickness is, the film thickness change rate with respect to pressure load is almost the same. When pressure increases, the density peaks increase. As the initial film thickness increases, the normalized thicknesses of adsorption and ordered layers decrease. In nanoscale, the density predicted by the MD simulation is higher than the prediction of the Tait equation, even if the adsorption layers is excluded.

Fingering instability on curved substrates: optimal initial film and substrate perturbations

We investigate the stability of a thin Newtonian fluid spreading on a horizontal cylinder under the action of gravity. The capillary ridge forming at the advancing front is known to be unstable with respect to spanwise perturbations, resulting in the formation of fingers. In contrast to the classic case of a flow over an inclined plane, the gravity components along a cylindrical substrate vary in space and the draining flow is time-dependent, making a modal stability analysis inappropriate. A linear optimal transient growth analysis is instead performed to find the optimal spanwise wavenumber. We not only consider the optimal perturbations of the initial film thickness, as commonly done in the literature, but also the optimal topographical perturbations of the substrate, which are of significant practical relevance. We found that, in both cases, the optimal gains are obtained when the perturbation structures are the least affected by the time horizon. The optimal spanwise wavenumber is found to be dependent on the front location, due to the dependence of the characteristic length of the capillary ridge on its polar location.

Crystallization kinetics of water on graphite

The nucleation and growth of water crystallites on a graphite substrate are discussed in terms of the initial film thickness, deposition temperature, and effects of adspecies.