Dissemination of IT for the Promotion of Materials Science (DoITPoMS)

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Viscosity

Kinematic viscosity, ν, is the ratio of dynamic viscosity to the density of the fluid at the same temperature. Dynamic viscosity, η, is related to shear stress, τ, and rate of strain, d\(\gamma\)/d\(t\) through the formula

\[\tau  = \eta \frac{{{\rm{d}}\gamma }}{{{\rm{d}}t}}\]

Kinematic viscosity is relevant to the dynamics of real fluids; for example, the non-dimensional parameter known as the Reynolds number, \(R\), is defined by the expression

\[R = \frac{{UL}}{\nu } = \frac{{UL\rho }}{\eta }\]

where \(U\) is a typical velocity and \(L\) is a typical length, ρ is the fluid density and ν the kinematic viscosity. \(R\) is the ratio of inertial forces per unit area ρ \(U\)2 to viscous forces per unit area, η \(U\)/\(L\).

For the flow of viscous fluids (e.g., lubricants) around solid objects, \(R\) is low, in which case flow is laminar. For values of \(R\) relevant to the flow of water in narrow pipes, \(R\) can be very large, resulting in turbulent flow.

The SI unit of dynamic viscosity is the Pa s. The unit of kinematic viscosity most commonly used is the centistoke, cSt: 1 cSt = 10-6 m2 s-1.

The viscosity of liquids decreases as temperature increases since the increased thermal energy makes it easier to break intermolecular forces and for molecules to uncoil. A schematic variation of the viscosity of a viscous material such as a glass or lubricant as a function of temperature is shown above. Note the sense of curvature.

The viscosity of a lubricant is closely related to its ability to reduce friction. Generally, the least viscous lubricant which still forces the two moving surfaces apart is desired. If the lubricant is too viscous it will require a large amount of energy to move the two surfaces relative to one another and if it is too thin then many asperities will form and friction and wear will increase.

Viscosity Index:

Viscosity index (VI) is a measure of the change of kinematic viscosity with temperature. The higher the VI, the lower the rate of change of kinematic viscosity with temperature.

Many applications require a lubricant to perform across a wide range of temperature conditions e.g. lubricants between engine components must work when the engine is started from cold up to approximately 200°C when it is running.

The best oils will remain stable and not vary much in viscosity over the temperature range experienced for consistent performance within the working conditions, so a high VI is desired.

VI improving additives (see next section) are widely used which increase the VIs attainable.