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Rheology is the study of the deformation and flow of matter (1929). A brief description is given of the rheology of steadily shearing materials, including shear and normal stresses. Some difficulties with the measurement of yield stresses are mentioned. Application of these classical ideas to lubrication in very thin films occasionally gives results at variance with observation. It is suggested, from evidence obtained from nonequilibrium molecular dynamics calculations, that very thin films (nanometre scale thickness) have rheological properties different from thick films-their viscosity is bigger, and they may also slip at solid walls. Wall slip is a feature of non-Newtonian flow in polymers not usually seen in classical fluid mechanics when dealing with small molecule liquids. We show examples of slip under certain conditions. Transient phenomena, especially stress overshoot, are shown to explain some paradoxical results in squeeze-film lubrication. Finally, the main differences between elongational and shear flows are pointed out.

Molecular dynamics simulation has been employed to get an insight into the lubrication process between two parallel plates. We studied the effects of the structure of the confining walls on the behaviour of these thin lubricant films. It is revealed by these simulations that changing the structure of the wall from an atomically smooth crystalline bcc structure to an amorphous wall has a determinant effect on the confined film structure, its solidification and its response to shearing.

Molecular dynamics simulation has been employed to get an insight into the lubrication process between two parallel plates. We studied the effects of molecular architecture in the behaviour of these thin lubricant films. In this work the effect of branching on rheological properties and behaviour of lubricant film is examined. Our study shows viscosity and normal stress effects depend on the degree of branching. A weaker layering near the wall is observed for branched molecules. The results obtained here are useful in designing new lubricants at the molecular level.

An efficient implicit finite volume formulation with third order accuracy is developed and reported for fully three-dimensional, time-dependent viscoelastic fluid flow problems. To verify the code, time-dependent calculations were carried out here for Newtonian flow between two coaxial disks with a finite domain with one of the disks impulsively started from rest. By directly solving the Navier-Stokes equations without the infinite domain assumption, a unique solution is obtained at high values of Reynolds number R e (up to 1000 based on nondimensional gap width 10 - 2 between disks). The calculated data match experimental measurements taken in a finite domain very well, which indicates the influence of edge effects. When inertia is negligible ( R e ≤ 0.5), the Stokes solution is the unique solution. In our calculated range of R e , there is an unique steady state and axisymmetric solution for a given R e , and von Karman’s hypothesis is still valid over increasing portions of the flow domain with increasing values of R e (up to 50% to 70%, depending on R e ), except near the side wall where secondary flows are formed due to no flow condition through the air/fluid interface. The state of steady motion could be reached in a nondimensional time of O ( R e ) for R e 100 , and less than O ( R e ) for R e ≥ 100. At R e = 1000 ; if the time step used is not small enough, a time-dependent, periodic solution is in evidence, which indicates that there may exist multiple solutions if a steady state method is used without strong enough relaxation.

Molecular dynamics simulation has been employed to get an insight into the lubrication process in the vicinity of asperities of a rough wall. The lubrication process in aboundary lubrication regime in ultra-thin films is studied with the purpose of obtaining lubricant film local properties. In particular we would like to study the effect of molecular size of lubricant on those properties. Simulations were conducted for two sizes of linear chain molecules. The larger molecule has 100 segments on its backbone. Results reveal enhanced shear stress and first normal stress difference near the tips of asperities. Molecular size plays important role in quantitative results for lubricant films.

The term ‘rheo-optics’ seems to have been coined in the 1960s.1 It designates the use of optical methods to study flow and deformation in materials. The methods used include birefringence, X-ray diffraction, dichroism and light scattering; all these techniques are older than the collective terminology. Thus, in all cases to be considered the light (or X-ray) is affected by the flow; we shall not consider the reverse effect, where, for example, intense light might be used to affect the flow.

Publisher Summary This chapter discusses some of the precautions required while choosing a constitutive equation when setting out to do computing. Depending on the kinematic problem in hand, one of the several mathematical representations of the material can be chosen. The chapter discusses the behavior of (1) rate-type equations; (2) Green–Rivlin or integral type expansions, and (3) differential constitutive equations. The rate-type equations include the Criminale–Ericksen-Filbey equation, which is an exact representation of isotropic fluid behavior in viscometric flows. The chapter describes the stability of the rheological problem. Sometimes, there might be genuine flow instability, which is observable experimentally. Another cause of problems is lack of convergence because of inadequate numerical schemes. However, assuming that these problems have been avoided, there still remains the possibility that the description of the material, constitutive equation, chosen is the cause of lack of convergence.