Lubrication theory

About: Lubrication theory is a research topic. Over the lifetime, 1713 publications have been published within this topic receiving 50261 citations. The topic is also known as: Fluid bearing.

Film flow for power-law fluids: Modeling and linear stability

Abstract: The paper deals with modeling of a power-law fluid film flowing down an inclined plane for small to moderate Reynolds numbers. A model, accurate up to second order [first order] for dilatant [pseudoplastic] fluids is proposed to describe the nonlinear behavior of the flow. The modeling procedure consists of a combination of the lubrication theory and the weighted residual approach using an appropriate projection basis. A suitable choice of weighting functions allows a significant reduction of the dimension of the problem. The resulting model is naturally unique, i.e., independent of the particular form of the trial functions. Reduced models are proposed for the evolution of the local film thickness and flow rate; their linear spectra are compared to that obtained from the full Orr–Sommerfeld numerical solution. To obtain the latter, a new formulation of the eigenvalue problem is proposed to overcome the classical divergence of the apparent viscosity at the free surface. The full model and its reduced forms all have the advantage of the Benney like model close to criticality. Far from the instability threshold the full model continues to follow the Orr–Sommerfeld solution up to sufficiently large Reynolds numbers and gives better predictions than the depth averaging model. An incomplete regularization procedure is performed to cure the rapid divergence of the reduced two-equation model. Due to its relative simplicity the latter might be preferred in practice to the full model, at least at the initial stage of the nonlinear regime. It is also shown that the convective nature of the instability is not affected by the variation of the power law index.

On the asymptotic analysis of surface-stress-driven thin-layer flow

Abstract: It has been demonstrated experimentally that thin liquid layers may be applied to a solid surface or substrate if a temperature gradient is applied which results in a surface tension gradient and surface traction. Two related problems are considered here by means of the long-wave or lubrication theory. In the first problem, an improved estimate of the applied liquid coating thickness for a liquid being drawn from a bath is found through asymptotic and numerical matching. Secondly, the theory is extended to consider substrates that are not perfectly wetted but exhibit a finite equilibrium contact angle for the coating liquid. This extension incorporates the substrate energetics using a disjoining pressure functional. Unsteady flows are calculated on a substrate of nonuniform wettability. The finite contact angle value required to stop stress-driven flow is predicted and the resulting steady profiles are compared with experimental results for several values of the applied stress.

Highly transient squeeze-film flows

Abstract: The aim of this work was to investigate the flow evolution with time of fluid between two parallel disks and the corresponding pressure variations at the centre of the lower disk that occur subsequent to an impact-loading situation arising from dropping a mass onto the upper disk from a chosen height. During the event a fixed amount of energy is dissipated in the fluid between the disks through the action of friction. Therefore, this fundamental system may be regarded as a constant energy one, as distinct from one in which the upper disk is moving at a constant velocity, or is acted upon by a constant force. A test cell was set up to conduct the investigation, for which the separation between the disks was monitored, together with the pressure at the centre of the lower disk, over the duration of the experiment (about 8–10 ms). Glycerine was used as the test fluid. The equation of motion, based on a self-similarity approach, was reduced to a simpler (quasi-steady linear or QSL) form. Measured values of disk separation, velocity and acceleration were substituted as inputs into the full QSL model and two limiting cases, namely an inviscid and a viscous model. The QSL model provided excellent comparisons between the pressure measurements and data generated by a commercial computational fluid dynamics software package, throughout the duration of a typical experiment. The inviscid and viscous models achieved good correlations with measurements for the initial impact (during which disk accelerations exceeding 2 km s−2 occurred) and towards the end of the event, that were characterized by a small and much larger pressure rise, respectively. The former feature appears not to have been previously reported and is likely to typify that which would be observed in impact systems involving squeeze films.