Chapter 4: Thin Film Lubrication- Theoretical Modeling
Thin-Film Lubrication (TFL) deals with the region wherein the film gap is in the molecular scale. Due to this small scale, researchers rely on molecular dynamic simulation which has the given macroscopic flow of equations in which the experimental approach of this study depends. However, seeing the study in theoretical view is still limited. This viewpoint considers the material to be a continuum one in an ensemble-averaged, rather than a spatial-averaged.

For a material to be continuum, the molecules must be very small in relation to the problem scale that implies a spatial averaging. A small region of space, which contains many particles, but is still much smaller than the problem scale, must be chosen. Here, quantities which smoothly vary from spatial averaging can be defined using limits. On the other hand, ensemble averaging is used to determine the value of an expected parameter. From a large number of trials in a certain point of space, average quantities are determined at this point for the trials.

From a schematic diagram, researchers had found that the thick film region varies linearly with the line from Elasto-hydrodynamic Lubrication (EHL) predictions, while the thin film region levels off progressively as the thickness decreases. The thinner the film is, the more the difference can be seen. Decreasing the thickness in TFL leads to a failure region which kills the lubricant’s mobility. Thus, TFL is the last of the lubrication regimes where the Reynolds equation can be applied.

In TFL, lubricating performances can be determined by its ordered layers. This state can be achieved by the surface guiding effects and anchoring potential of the solid walls which can be described by a director, in contrast to vector in nematics. However, director and vector are different. The nematic is quite ordered leading to the existence of director in the conventional state. In TFL, the alignments and orientation of molecules are hindered by external sources, that the parameters are strongly dependent on the surface force field of the walls and other conditions. Molecular orientations can be rearranged in both of them. This similarity makes it possible to use the nematic theories in analyzing the flow in TFL. Here, Leslie coefficients are determined by combining the property of solid walls with that of the lubricants in TFL.

Discrepancy of TFL from EHL results from the elasticity of lubricants. The viscosity-to-elasticity ratio is introduced to account for the effects of the elasticity. If the viscosity plays a dominant role, it keeps constant, but if the elasticity prevails, the angle of the director varies linearly; consequently the viscosity varies.

Based from the experimental results, the variation of the films thickness with its rolling velocity is continuous, that validates a continuum mechanism, that some extent in TFL. Because is it describe that the state if the film thickness is at its molecular scale of the lubricants. An example is a nanometer size, that most common lubricants may exhibits microstructures in thin films. And to use the continuum theory is to consider its effect of spinning molecular that was confined by the solid-liquid interface. The micropolar theory will account for this behavior. When the molecular dimension is reached the inner spinning of the molecules will contribute to its performance and we should bear in mind that it is not considered in the conventional theory of lubrication. The general properties of micropolar fluids are they a subclass of microfluids, is a viscous media whose properties and behavior are affect by the local motion of particles in its micro-volume. It allows the particle micro-motion to take place, but also prevents the deformation of microelements. The point contact thin film lubrication problem with micropolar fluids. That requires simultaneous solution of several governing equations like Reynolds equation for a micropolar model. Under its usual assumptions made for lubricating films, and through a detailed order of magnitude analysis. Singh et al. derived a generalized Reynolds eqation. Based on the lubrication equation, having incorporating a cavitation algorithm, Lin studied the performances of finite journal bearing with micropolar fluids. The viscosity-pressure relation equation talks about the viscosity of the lubricant which is assumed to be dependent on pressure. The film thickness and load balance equation must be a balanced integral of pressure over its entire solution domain and was used to determine the reference film thickness in the equation of film thickness. The system equations including the Reynolds, film thickness, load balance, viscosity-pressure, and viscosity modification equations is simultaneously solved with the help of a multilevel technique described by Venner and Lubrecht with modifications to take account of the variations in viscosity.

In micropolar theory, the fluid particles are rigid and randomly distributed in a viscous medium. If the micro-polarity is taken into account, the motion will be affected by the viscous action, the effect of coupled stress, and the direct coupling of the microstructure to the velocity field. In non-polar case, the motion will only be affected by the viscous action and the other factors are ignored. They are accounted for in the present model by introducing a characteristic length and a coupling number that reveals a particular feature in the film lubrication.

In Rheology and Viscosity Modification, a proposed function is described the viscosity distribution to attain the predictive results and to described the characteristics of Thin Film Lubrication in the viewpoint of engineering. An experiment was done and a new postulation based on the ordered model and ensemble average was put forward to describe viscosity in the nano-scale gap. The lubricant used in this experiment is polyglycol oil. It is expected that the main imposing the greatest influence on lubrication properties is velocity, which is consistent with the EHL theory of film profiles versus the relation of the lubricant.
Based on the experiment done, it tells that if the film is as thin as 15nm the centreline along the film direction is flat while the film becomes thicker, it shows a typical EHL earlobe shape. From the film thickness versus the velocity relation, if the velocity is higher than 100 mm·s−1 the film is thicker than 50 nm, all the results from EHL, TFL, and experimental data are very close to each other, which indicate that when in the EHL lubrication regime, bulk viscosity plays the main role. When the velocity decreases to a low value, the EHL results are much lower than that of experimental data. Thus, it cannot be regarded as in the EHL lubrication regime. In EHL, the film thickness varies with the velocity in an exponential relation. In the case of thin film lubrication, the thinner the film is the less correlation between velocity and bulk viscosity will be. From the film thickness that varies with lubricant atmosphere viscosity, it shows that when the film thickness decrease with 15nm, the EHL result is much less than of the experimental data and the result coming from the model proposed is very closed to experimental data. The film thickness is varies with the bulk viscosity which is not true in thin film lubrication. Showing the film thickness varies with the load, the film thickness obtained from TFL solution is higher than that of EHL. The film thickness decreases slightly with load in both cases.
In the application of Solvation Pressure in thin film Lubrication, calculations are made and the advantage of calculating is that laborious and difficult experiments are not required in order to obtain unknown parameters. Calculating solvation pressure agrees well with the experiments for the liquids that have strong solvation force. Applying this theory to the liquids with weak solvation force is more difficult.
In the experiment of couple stress and its application to two-phase flows tells that, the larger the characteristic length is, the greater the enhancement effect is. In the case of thick film thickness, the volume ratio of ordered molecules is small, and the lubrication is characterized by conventional fluid sand can thus be regarded as EHL. With the decrease of the film thickness, couple stress does have an increasing effect, which leads to an increased volume ratio of the ordered fluids molecules, and subsequently the lubrication transfers gradually into the TFL regime. In TFL modeling, two factors to be addressed are the microstructure of the fluids and the surface effects due to the very small clearance between two solid walls in relative motion.

Good Comments:
This journal explained all of its concepts down to the smallest detail. All of the figures were properly tagged and precise to the text. These figures proved the concepts visually to let the readers understand in terms of coordinate plane versus plots and schematic diagrams. The introduction part provides a complete overview of what can be seen in this chapter, and the conclusion part summarizes the concepts discussed.

The topic about simulations via micropolar theory is an interesting topic that is discussed in this chapter because we learned new things and values. Also the topic about viscosity is really interesting because by using the system equations we can improve or change the viscosity of a certain samples that may help in their lubrication process. Also, it is good that there are a lot of comparisons about the thickness of the film on the experiments.

Bad Comments:

The text is unfriendly to its readers. Some equations and some part of this chapter are hard to understand. The authors use words that aren’t familiar to some of the readers. I think it would be helpful if the authors would put some meaning of the words used or use words that have generalized meaning that the public can relate.

Also, the concepts involved and the way on how these were explained are quite difficult to understand. Thus, a normal people (which are not in the field of this journal) would reject reading the text. In addition, the text is wordy and is unpleasing to read. Too many words can mislead its readers, an excess of words also increase the complication of the concepts involved.

Suggestions:

Words should be decreased to reduce the reader’s boredom while reading the text. Explanation should be clear and easy so that other people can understand the concepts involved. Although the figures used are precise in the text, an increase in the figures will also help the readers understand the topic more. For the mathematical equations used in the journal which is totally complicated, a step-by-step derivation of the equations used is also a great help for the readers. All in all, the journal should be friendly meaning, enjoyable, clear, precise, visually-presentable and easy to understand.

Also, the authors must improve some of their results because some of the results are noted to have some problem like that are not clear enough due to some errors occurred. And some of the formulas are not well explained or how they arrived in that form.