Viscosity

In a general parallel flow, the shear stress is proportional to the gradient of the velocity.

Viscosity is the material property which relates the viscous stresses in a material to the rate of change of a deformation (the strain rate). Although it applies to general flows, it is easy to visualize and define in a simple shearing flow, such as a planar Couette flow.

The analogy with heat and mass transfer can be made explicit. Just as heat flows from high temperature to low temperature and mass flows from high density to low density, momentum flows from high velocity to low velocity. These behaviors are all described by compact expressions, called constitutive relations, whose one-dimensional forms are given here:

One of the most common instruments for measuring kinematic viscosity is the glass capillary viscometer.

Also used in coatings, a Stormer viscometer employs load-based rotation to determine viscosity. The viscosity is reported in Krebs units (KU), which are unique to Stormer viscometers.

Kinematic viscosity has units of square feet per second (ft2/s) in both the BG and EE systems.

Experiment showing the behavior of a viscous fluid with blue dye for visibility

In contrast with gases, there is no simple yet accurate picture for the molecular origins of viscosity in liquids.

As for pure liquids, the viscosity of a blend of liquids is difficult to predict from molecular principles. One method is to extend the molecular "cage" theory presented above for a pure liquid. This can be done with varying levels of sophistication. One expression resulting from such an analysis is the Lederer–Roegiers equation for a binary mixture:

Because viscosity depends continuously on temperature and pressure, it cannot be fully characterized by a finite number of experimental measurements. Predictive formulas become necessary if experimental values are not available at the temperatures and pressures of interest. This capability is important for thermophysical simulations, in which the temperature and pressure of a fluid can vary continuously with space and time. A similar situation is encountered for mixtures of pure fluids, where the viscosity depends continuously on the concentration ratios of the constituent fluids

The following table illustrates the range of viscosity values observed in common substances. Unless otherwise noted, a temperature of 25 °C and a pressure of 1 atmosphere are assumed.

The values listed are representative estimates only, as they do not account for measurement uncertainties, variability in material definitions, or non-Newtonian behavior.