Bingham plastic fluids.The Bingham plastic theory assumes that a fluid has a rheology where the relationship between shear stress and shear rate is linear
but the line does not cross the origin of the graph.It looks something like the graph below in figure.
This type of rheology exhibits a yield point.Before the fluid will flow, a certain threshold pressure must be applied and any pressure lower than this will not initiate flow.When the fluid is static, a structure builds up which connects particles in the fluid due to electrostatic attractions between them and forms a gel. For a drilling fluid, this is desirable property because when circulation stops and a gel forms, drilled solids are suspended within the gel and do not sink down through the mud. When sufficient shear stress is applied the fluid starts to move and gel structure breaks down again.The slope of the graph(which a straightline in the mathematical model) is given the term 'plastic viscosity'.Therefore to define the behaviour of a Bingham plastic type fluid,the yield point and plastic viscosity are sufficient to predict the shear stress for a given shear rate.
(Steve Devereux,Drilling for oil & gas: a nontechnical guide,p.157)
Rheology
Rheology is a physical method of charecterization of the structure of matter.Rheology gives unambiguous,physically meaningful,quantative parameters of metarials. These paremeters can be correlated with the structure of matter, either chemical(monecular structure of a compound,length and architecture of a molecule, and so on) or physical (physical intermolecular interactions, phase state, size and distrubution of components in multi-component systems, and so on) structure.Rheological parameters correlate with the structure of material and can be used for structure characterization.
(Aleksandr IAkovlevich Malkin,Alexander Ya Malkin,Avraam I. Isayev,Rheology: concepts, methods & applications,p.351)
Hydrodynamic lubrication
Even in an exclusively hydrodynamic state, the complex physical,hydrodynamic,thermal,elastici and plastic phenomena described in 3.1 exist.Therefore, some hypoteses will have have to be introduced to simplify and permit further treatment of the problem.Two hydrodynamic states can be distinguished:
1.Real hydrodynamic lubrication , in whichall parameters are considered to be interdependent: e.g., variation viscosity with pressure, temperature,and velocity gradien; heat transfer; roughness and deformations.
2. Ideal hydrodynamic lubrication, in which viscosity is constant in time and space; surfaces are perfectly smooth, rigid and without deformations;and thermal equilibrium is established.Further external forces and velocities are often considered to be constant in time.
(Nicolae Tipei,Theory of lubrication: with applications to liquid- and gas-film lubrication, p.39)
Elastohydrodynamic lubrication
The term elastohydrodynamic lubrication (EHL) is reserved for hydrodynamic lubrication applied to lubricantfilms between elastically deforming solids.The principles of EHL are readily applicable to such diverse objects as gears, rolling-element bearings, and human animal joints. In general bearingsthat are lubricated in EHL mode are of low geometric conformity, and, in the absence of lubricant film and of elastic deformation, the opposing surfaces would contact in a point (ball bearings) or along a line (gears or roller bearings).
If the solid surfaces that are lubricated in the EHL mode have large elastic modulus,the contact pressures will be largei perhaps of the order of 1GPa.The film thickness will be correspondingly small, of the order of 1μm. Under such conditions the material properties of the lubricant will be distinctly different from its properties in bulk.This change in lubricant properties, when coupled with the effects of elastic deformation of the solid surfaces, yields film thicknesses one or two orders of magnitude larger than those estimated from constant viscosity theory applied to nondeforming surfaces.
EHL theory may be viewed as a combination of hydrodynamic lubrication, allowance for the pressure dependence of viscosity, and elatic deformation of bounding surfaces.
(Andras Z. Szeri,Fluid Film Lubrication,p.37)
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