By definition, **viscosity** is a fluid’s resistance to flow or deformation. A fluid with a high viscosity, such as honey, flows as a slower rate than a less viscous fluid, such as water. The word “viscosity” comes from the Latin word for mistletoe, *viscum*. Mistletoe berries yield a viscous glue, also called viscum. Common symbols for viscosity include the Greek letter mu (μ) and the Greek letter eta (η). The reciprocal of viscosity is **fluidity**.

- Viscosity is a fluid’s resistance to flow.
- Liquid viscosity decreases as temperature increases.
- Gas viscosity increases as temperature increases.

### Viscosity Units

The SI unit for viscosity is newton-second per square meter (N·s/m^{2}). However, you’ll often see viscosity expressed in terms of pascal-second (Pa·s), kilogram per meter per second (kg·m^{−1}·s^{−1}), poise (P or g·cm^{−1}·s^{−1} = 0.1 Pa·s) or centipoise (cP). This makes the viscosity of water at 20 °C about 1 cP or 1 mPa·s.

In American and British engineering, another common unit is pound-seconds per square foot (lb·s/ft^{2}). An alternative and equivalent unit is pound-force-seconds per square foot (lbf·s/ft^{2}).

### How Viscosity Works

Viscosity is friction between fluid molecules. As with friction between solids, higher viscosity means it takes more energy to make a fluid flow.

When you pour a liquid from a container, there is friction between the container wall and the molecules. Basically, these molecules stick to the surface to a greater or lesser degree. Meanwhile, molecules further from the surface are more free to flow. They are only inhibited by their interactions with one another. Viscosity looks at the difference in the rate of flow or deformation between between molecules a certain distance from a surface and those at the liquid-surface interface.

Multiple factors influence viscosity. These include temperature, pressure, and the addition of other molecules. The effect of pressure on liquids is small and often ignored. The effect of adding molecules can be significant. For example, adding sugar to water makes it much more viscous.

But, temperature has the greatest effect on viscosity. In a liquid, increasing temperature decreases viscosity because heat gives molecules enough energy to overcome intermolecular attraction. Gases also have viscosity, but the effect of temperature is just the opposite. Increasing gas temperature increases viscosity. This is because intermolecular attraction doesn’t play a significant role in gas viscosity, but increasing temperature leads to more collisions between molecules.

### Dynamic Viscosity vs Kinematic Viscosity

There are two ways to report viscosity. Absolute or **dynamic viscosity** is a measure of a fluid’s resistance to flow while **kinematic viscosity** is the ratio of dynamic viscosity to a fluid’s density. While the relationship is straightforward, it’s important to remember two fluids with the same dynamic viscosity values may have different densities and thus difference kinematic viscosity values. And, of course, dynamic viscosity and kinematic viscosity have different units.

### Table of Viscosity Values

Fluid | Viscosity (mPa·s or cP) | Temperature (°C) |
---|---|---|

Benzene | 0.604 | 25 |

Water | 1.0016 | 20 |

Mercury | 1.526 | 25 |

Whole milk | 2.12 | 20 |

Beer | 2.53 | 20 |

Olive oil | 56.2 | 26 |

Honey | 2000-13000 | 20 |

Ketchup | 5000-20000 | 25 |

Peanut butter | 10^{4}-10^{6} | 20-25 |

Pitch | 2.3 x 10^{11} | 10-30 |

### Viscosity of Water

The dynamic viscosity of water is 1.0016 millipascals⋅second or 1.0 centipoise (cP) at 20 °C. Its kinematic viscosity is 1.0023 cSt, 1.0023×10^{-6} m^{2}/s, or 1.0789×10^{-5} ft^{2}/s.

Liquid water viscosity decreases as temperature increases. The effect is fairly dramatic. For example, water’s viscosity at 80 °C is 0.354 millipascals⋅second. On the other hand, water vapor viscosity increases as temperature increases.

The viscosity of water is low, yet it is higher than that of most other liquids made of comparable-sized molecules. This is due to hydrogen bonding between neighboring water molecules.

### Newtonian and Non-Newtonian Fluids

**Newton’s law of friction** is an important equation relating to viscosity.

*τ = μ dc / dy* = *μ γ*

where

*τ* = shearing stress in fluid (N/m^{2})

*μ* = dynamic viscosity of fluid (N s/m^{2})

*dc *= unit velocity (m/s)

*dy *= unit distance between layers (m)

*γ *= dc / dy = shear rate (s^{-1})

Rearranging the terms, gives the formula for dynamic viscosity:

*μ* = *τ dy / dc * *= τ / γ *

A **Newtonian fluid** is a fluid that obeys Newton’s law of friction, where viscosity is independent of the strain rate. A **non-Newtonian fluid** is one which does not obey Newton’s law of friction. There are different ways non-Newtonian fluids deviate from Newtonian behavior:

- In
**shear-thinning fluids**, viscosity decreases as the rate of shear strain increases. Ketchup is a good example of a shear-thinning fluid. - In
**shear-thickening fluids**, viscosity increases as the rate of shear strain increases. The suspension of silica particles in polyethylene glycol found in body armor and some brake pads is a shear-thickening fluid. - In a
**thixotropic fluid**, shaking or stirring reduces viscosity. Yogurt is an example of a thixotropic fluid. - In a
**rheopectic or dilatant fluid**, shaking or stirring increases viscosity. A mixture of cornstarch or water (oobleck) is a good example of a dilatant. **Bingham plastics**behave as solids normally, but flow as viscous liquid under high stress. Mayonnaise is an example of a Bingham plastic.

### Measuring Viscosity

Instruments for measuring viscosity are viscometers and rheometers. Technically, a rheometer is a special type of viscometer. The devices either measure the flow of a fluid past a stationary object or else the movement of an object through a fluid. The viscosity value is the drag between the fluid and the object surface. These devices work when there is laminar flow and a small Reynold’s number.

### References

- Assael, M. J.; et al. (2018). “Reference Values and Reference Correlations for the Thermal Conductivity and Viscosity of Fluids”.
*Journal of Physical and Chemical Reference Data*. 47 (2): 021501. doi:10.1063/1.5036625 - Balescu, Radu (1975).
*Equilibrium and Non-Equilibrium Statistical Mechanics*. John Wiley & Sons. ISBN 978-0-471-04600-4. - Bird, R. Bryon; Armstrong, Robert C.; Hassager, Ole (1987).
*Dynamics of Polymeric Liquids, Volume 1: Fluid Mechanics*(2nd ed.). John Wiley & Sons. - Cramer, M. S. (2012). “Numerical estimates for the bulk viscosity of ideal gases”.
*Physics of Fluids*. 24 (6): 066102–066102–23. doi:10.1063/1.4729611 - Hildebrand, Joel Henry (1977).
*Viscosity and Diffusivity: A Predictive Treatment*. John Wiley & Sons. ISBN 978-0-471-03072-0.