Solving lubrication problems at the nanometer scale

Abstract

Lubrication problems at lengthscales for which the traditional Navier-Stokes description fails can be solved using a modified Reynolds lubrication equation that is based on the following two observations: first, classical Reynolds equation failure at small lengthscales is a result of the failure of the Poiseuille flowrate closure (the Reynolds equation is derived from a statement of mass conservation, which is valid at all scales); second, averaging across the film thickness eliminates the need for a constitutive relation providing spatial resolution of flow profiles in this direction. In other words, the constitutive information required to extend the classical Reynolds lubrication equation to small lengthscales is limited to knowledge of the flowrate as a function of the gap height, which is significantly less complex than a general constitutive relation, and can be obtained by experiments and/or offline molecular simulations of pressure driven flow under fully developed conditions. The proposed methodology, which is an extension of the Generalized Lubrication Equation of Fukui & Kaneko to dense fluids, is demonstrated and validated via comparison to Molecular Dynamics simulations of a model lubrication problem.

Physics of nanoscale immiscible fluid displacement

“…[28] yielding a decorrelation time of 1 ns. Figure 2 shows that parabolic profiles are indeed excellent approximations to the MD data, albeit with substantial slip; this is in general agreement with previous work [26]. Specifically, using the Navier condition (2) with s = αh, we find α w = 0.33 for water and α p = 2.5 for pentane.…”

“…Even though the Navier-Stokes description remains valid at these scales (e.g., see Ref. [26] for discussion), we expect deviations from the Tanner-Voinov law since the above-described separation of scales does not necessarily exist. Particularly important is the presence of slip in these flows [27], which is not compatible with relation (1), since the latter relies on the presence of no-slip conditions at distances d s away from the contact line [3].…”

Transport Behavior of Oil in Mixed Wettability Shale Nanopores

“…In order to validate the proposed model presented in this study, the results of previous experiments/simulations studies are adopted. − Notably, the inorganic surface ratio and other variables (surface coverage, adsorption thickness, and roughness fractal dimension) are difficult to determine. Thus, the proposed model is validated by the simplified formula: …”

Influence of new surface micro-structures on the performance behaviours of fluid film tilting pad thrust bearings

“…72 It is noticed that if characteristic length (of particles and micro-geometries) reaches in the range of nanometre scale leading to K n > 0.001, then need arises to use the modified Reynolds equation or non-classical continuum theory. 73 The literature review reveals that previously major performance exploration on thrust bearings has been carried out employing textures, pockets, and profiles on fixed pads and sliders. Few investigations have also been reported with textured tilting pads, and it is mentioned that the rectangular pocketed pad performed best among all.…”

“…72 It is noticed that if characteristic length (of particles and micro-geometries) reaches in the range of nanometre scale leading to K n > 0.001, then need arises to use the modified Reynolds equation or non-classical continuum theory. 73…”