## Viscosity or Resistance to Flow

The term 'viscosity' describes a material's property from a physicist's point of view. It is a fluid's thickness. Scientifically speaking, it is the measure of a fluid's internal flow resistance, the resistance to being deformed. The two-plates model mathematically describes this definition.

A fluid's viscosity is determined by viscometry, which is part of a wider science called rheometry. Rheometry again is part of rheology, the science of materials' flow behavior and deformation. All materials range on an imaginary scale from solid to liquid. In scientific terms, solid materials are specified as elastic, while liquids are viscous. However, most materials are not purely elastic, nor entirely viscous, but viscoelastic. Depending on their properties, substances can be classified as viscoelastic solids (like e.g. gels) or viscoelastic liquids (like e.g. hair shampoo).

Viscometry deals with ideally viscous fluids, and - with certain limitations - also with viscoelastic liquids, i.e. viscous substances with an elastic portion. If a fluid flows easily, its resistance to deformation is low. It is a low-viscosity fluid. Fluids with greater resistance to deformation do not flow easily. They are highly viscous.

## The Two-plates Model

This model consists of two imaginary plates with the fluid in-between. Two conditions must be met to allow for accurate calculation of the viscosity-related variables.

- The fluid adheres to both plates and does not slip or slide along them.
- There are laminar flow conditions. That means the flow takes the shape of infinitesimally thin layers, no turbulence - i.e. vortices - occurs. A stack of beer mats gives a good idea of how laminar flow works.

### Shear Stress

While the lower plate stands still, the upper plate very slowly moves along. Even the slow movement causes stress that is parallel to the fluid's surface and which is called shear stress.

The shear stress is defined as the force F applied to the upper plate divided by this plate's area A. The force is measured in newton, the area in square meters. The shear stress tau is force divided by area. This calculation results in the unit N/m^{2}, which is called pascal [Pa] after Blaise Pascal.

### Shear Rate

A second variable that can be derived from the two-plates model is the shear rate gamma-dot. In older literature the shear rate is sometimes given as D.

To obtain the shear rate, the velocity v of the upper plate, in meters per second, is divided by the distance h between the two plates in meters. This gives the unit [1/s] or reciprocal second [s^{-1}].

### Newton's Law and Dynamic Viscosity

Newton's Law states that shear stress is shear rate times viscosity. Consequently, shear stress divided by shear rate is viscosity, which is given the variable η 'eta'. This simple relation applies to Newtonian liquids only.

From Newton's Law we obtain the dynamic viscosity, but this is only one of several types of viscosity.

## Typical Substances and Their Viscosity Values

Dynamic viscosity values - data from Thomas G. Mezger 'The Rheology Handbook', 3^{rd} Revised Edition, p. 28, Table 2.3 - with references

Material | Temp. [°C] | Dynamic Viscosity η [mPa.s] |
---|---|---|

Gasoline / petrol (octane) | 20 | 0.538 |

Water | 20 | 1.00 |

Ethanol | 20 | 1.20 |

Glycol | 20 | 20 |

Olive oils | 20 | approx. 100 |

Motor oil SAE 10W-30 | 23 | 175 |

Gear oils | 20 | 300 to 800 |

Glycerine | 20 | 1480 |

Honey / concentrated syrups | 20 | approx. 10 Pa.s |

Bitumen | 20 | 0.5 MPa.s |

Find detailed viscosity tables of various substances...