# Molecular Science of Lubricant Additives +
## 1 Introduction
### The Stribeck Lubrication Model  
There are many types of machine elements with different configurations that work under different operating parameters. Lubrication systems are individually designed in most cases. Despite this, we have a versatile model for simulation and explanation of the lubrication performances, the Stribeck curve [4]. The model concept is the dependence of friction coefficient on the operating parameters (load and velocity), the material properties (surface roughness and elastic modulus), and the lubricant properties (viscosity and pressure-viscosity relations). As Figure 1 depicts, the friction coefficient of a lubrication system varies with the Hersey number calculated from viscosity, load, and velocity. When a liquid (lubricating oil) is applied to tribo-contact, it develops a liquid film between the surfaces. The thickness of liquid film \(H_{m}\) (or clearance between the surfaces supported by the liquid) depends both on the properties of the solid and the liquid materials [5]. A viscous liquid tends to provide a thicker liquid film at the contact, while a low viscous liquid tends to provide a thinner film between surfaces. If the thickness of the liquid film is greater than the surface roughness \(R^{1}\) and \(R^{1}\) (more precisely \(\lambda>2\)), the surfaces could be completely separated by the liquid. Therefore, the surfaces can move without contact between solids and this results in low friction. This lubrication regime is defined as \"hydrodynamic lubrication\". Ideally, machine elements are designed to operate in this regime since low friction as well as negligible wear could be achieved. When the Hersey number becomes smaller, the lubrication regime shifts to the boundary regime. Asperities on the surfaces come to interfere with each other. As a result, friction becomes higher and substantial wear occurs. This regime is defined as boundary lubrication. The properties of surfaces are important to achieve lubrication performances in this lubrication regime. Mixed lubrication regime is an intermediate regime between hydrodynamic lubrication and boundary lubrication. Although the phenomena in the real world are more complicated, this simplified model helps us to understand the role of each substance in lubrication systems. Today, the Stribeck model is a consensus model to predict the lubrication performance. Relative importance of three functions varies with individual application. For example, metalworking fluids have to wash out cutting dusts from the contact and have to cool the tool surface simultaneously. High water based fluids are frequently used in metalworking applications. Although the lubricity is inferior to that of petroleum-based fluids, water-based fluids have strong advantages in cleaning and cooling functions together with cost effectiveness. Of course, the lubricity  
Figure 1: The Stribeck curve and lubrication regime. of metalworking fluid is necessary to prevent tool wear, for example, but cooling and cleaning are a technical priority in most cases. On the other hand, friction reduction is the major concern for bearing applications. This is why greases are mostly used in bearing lubrication where cooling and cleaning functions are of secondary importance. The differences in requirements of lubricants for different applications could be understood more clearly if we look at the Stribeck curve [4]. Bearings should be operated under hydrodynamic (precisely under elasto-hydrodynamic) conditions where wear of material and heat generation are trivial. On the other hand, metalworking processes are \"heavily\" influenced by boundary conditions. When we look at the Stribeck curve carefully, friction increases as Hersey number increases under a hydrodynamic lubrication regime. This means that if the operating conditions are constant, friction increases as viscosity of the fluid increases. Since viscosity is defined as \"a measure of the resistance to flow\" [6], increased friction by viscosity could be understood as \"internal friction in fluids\".