1 Definition and basic concepts

Viscosity is the measure of a fluid’s resistance to deformation and flow. It describes how readily a substance changes shape when a force is applied. Fluids with high viscosity, such as honey or motor oil, move more slowly under the same conditions than fluids with low viscosity, such as water or air.

1.1 Flow resistance

Flow resistance refers to the opposition a fluid offers to motion. In practice, this means that adjacent layers of fluid tend to move at different speeds, and energy is required to overcome this internal resistance. The greater the resistance, the more sluggish the flow.

1.2 Internal friction

Viscosity is often described as internal friction because it arises from interactions within the fluid itself. As one layer slides past another, molecules or particles transfer momentum across the boundary between layers. This transfer dissipates mechanical energy and produces resistance to movement.

1.3 Dynamic and kinematic viscosity

Dynamic viscosity measures the force needed to move one layer of fluid relative to another. It is the most direct expression of viscous behavior. Kinematic viscosity combines dynamic viscosity with density, giving a measure of how a fluid flows under gravity or inertial effects. It is especially useful in engineering calculations.

1.4 Units and dimensions

In the International System of Units, dynamic viscosity is expressed in pascal-seconds. A common older unit is the poise, with centipoise used in many practical contexts. Kinematic viscosity is measured in square meters per second, and the centistokes is widely used in laboratory and industrial settings.

2 Physical interpretation

Viscosity has a molecular origin and becomes visible whenever a fluid resists being sheared. It is not simply a property of how “thick” a substance appears, but a result of microscopic interactions that control momentum transfer.

2.1 Molecular basis

At the molecular level, viscosity reflects collisions, intermolecular attractions, and the structure of the fluid. In liquids, closely packed molecules continually interact, making relative motion more difficult. In gases, momentum transfer between fast-moving and slower-moving molecules creates the effect.

2.2 Shear stress and shear rate

Shear stress is the force per unit area acting parallel to a surface, while shear rate describes how quickly adjacent fluid layers move relative to one another. For many fluids, viscosity links these quantities in a simple proportional relationship. This relationship is central to describing flow in pipes, channels, and open systems.

2.3 Newtonian and non-Newtonian behavior

A Newtonian fluid has a constant viscosity at a given temperature and pressure, regardless of the applied shear rate. Water and many simple gases are typical examples. Non-Newtonian fluids change their effective resistance under stress, so their viscosity depends on how they are stirred, stretched, or compressed.

3 Types of viscosity

Several forms of viscosity are used depending on the physical situation and the method of measurement. Each emphasizes a different aspect of flow behavior.

3.1 Dynamic viscosity

Dynamic viscosity is the fundamental measure used in fluid mechanics. It quantifies the proportionality between shear stress and shear rate in simple flows. Engineers use it when analyzing pumping, lubrication, and fluid motion through narrow passages.

3.2 Kinematic viscosity

Kinematic viscosity is the ratio of dynamic viscosity to density. Because it incorporates mass distribution as well as flow resistance, it is convenient for comparing fluids whose densities differ substantially. It is often used in studies of diffusion-like motion in fluids.

3.3 Apparent viscosity

Apparent viscosity describes the effective viscosity of a fluid whose behavior is not strictly Newtonian. It depends on the conditions of measurement, such as shear rate, time, and history of deformation. This concept is common in suspensions, gels, and biological fluids.

3.4 Extensional viscosity

Extensional viscosity characterizes resistance to stretching rather than simple sliding motion. It is important in processes where fluid elements are drawn apart, such as fiber spinning, atomization, and certain food-processing operations. Some fluids respond very differently to extension than to shear.

4 Measurement of viscosity

Viscosity can be measured by observing the behavior of a fluid under controlled motion. Different instruments are suited to different ranges of viscosity and material types.

4.1 Capillary viscometers

Capillary viscometers determine viscosity by measuring the time a fluid takes to flow through a narrow tube. The method is based on pressure-driven laminar flow and is especially useful for low- to moderate-viscosity liquids. It is valued for simplicity and reproducibility.

4.2 Rotational viscometers

Rotational viscometers measure the torque needed to rotate a spindle, cone, or cylinder within a fluid. The resistance to rotation provides an estimate of viscosity. These instruments are widely used because they can handle a broad range of liquids and can also assess non-Newtonian behavior.

4.3 Falling-ball viscometers

Falling-ball viscometers determine viscosity by timing how quickly a ball descends through a fluid. The balance between gravitational pull, buoyancy, and drag reveals the fluid’s resistance to motion. This technique is common in laboratories and for selected quality-control applications.

4.4 Oscillatory methods

Oscillatory methods examine how a fluid responds to small periodic deformations. They are useful for complex materials that have both liquid-like and elastic features. Such methods provide insight into viscoelastic properties as well as viscosity itself.

4.5 Standard units and calibration

Reliable measurement depends on standardized units and careful calibration. Instruments are checked against reference fluids with known viscosities to ensure accuracy. Temperature control is especially important, since even small thermal changes can alter results significantly.

5 Factors affecting viscosity

Viscosity is sensitive to physical conditions and molecular structure. Changes in temperature, pressure, composition, and particle arrangement can all alter a fluid’s resistance to flow.

5.1 Temperature

Temperature has a strong influence on viscosity. In liquids, viscosity usually decreases as temperature rises because molecules move more freely and intermolecular forces are easier to overcome. In gases, the opposite trend often occurs because faster molecular motion increases momentum transfer.

5.2 Pressure

Pressure can affect viscosity, especially in dense fluids and liquids. Higher pressure often increases resistance to flow by bringing molecules closer together. For many everyday conditions, however, the effect is modest compared with temperature.

5.3 Composition and concentration

A fluid’s composition strongly shapes its viscosity. Dissolved substances, suspended particles, and added polymers can make a fluid thicker or more resistant to motion. Concentration changes often produce large shifts in flow properties, particularly in mixtures and colloids.

5.4 Molecular shape and interactions

Long, irregular, or strongly interacting molecules tend to increase viscosity. Linear polymers, for example, can entangle and resist motion more than compact molecules. Attractive forces, hydrogen bonding, and structural organization also influence the ease with which layers slide past one another.

6 Viscosity in fluids

Different classes of fluids show distinct viscous behavior depending on their internal structure and thermal state. These differences are important in both natural phenomena and industrial design.

6.1 Liquids

Liquids usually have much higher viscosity than gases because their molecules are close together and interact strongly. Their viscosity typically falls with increasing temperature. Many familiar liquids show a wide range of behavior, from very mobile solvents to highly resistive syrups and oils.

6.2 Gases

Gases generally have low viscosity, but their resistance to flow is still significant in aerodynamics and combustion. Gas viscosity is mainly governed by molecular collisions and momentum transfer. Unlike liquids, gaseous viscosity often rises with temperature.

6.3 Suspensions and emulsions

Suspensions contain solid particles dispersed in a fluid, while emulsions contain droplets of one liquid distributed in another. Both can show viscosities much higher than the base fluid alone. Their behavior depends on particle size, droplet interactions, packing, and stability over time.

6.4 Polymer solutions

Polymer solutions often display complex viscous behavior because long chains interact with the surrounding fluid and with one another. Their viscosity can increase sharply with concentration and may vary with flow history. These solutions are important in textiles, coatings, and many biological systems.

7 Non-Newtonian fluids

Non-Newtonian fluids do not maintain a constant relationship between shear stress and shear rate. Their response can vary with deformation, time, or even the direction of applied force.

7.1 Shear-thinning fluids

Shear-thinning fluids become less viscous as they are stirred or stressed more strongly. Common examples include many paints, sauces, and polymer-rich mixtures. This behavior can make a material easy to pour yet stable at rest.

7.2 Shear-thickening fluids

Shear-thickening fluids become more resistant to flow when the applied shear rate increases. Some concentrated suspensions show this effect clearly. Under sudden force, they may seem firm or stiff, then return to a more fluid state when the stress is removed.

7.3 Bingham plastics

Bingham plastics behave like solids until a minimum yield stress is exceeded. After this threshold, they flow with a roughly linear relation between stress and shear rate. Toothpaste and some drilling muds are common examples.

7.4 Viscoelasticity

Viscoelastic materials combine viscous flow with elastic recovery. They can deform like fluids under sustained stress but also store part of the energy and spring back when the force is removed. This dual behavior is characteristic of many polymers, gels, and biological tissues.

8 Theoretical models

Theoretical descriptions of viscosity connect macroscopic flow to microscopic behavior. These models range from simple laws to more detailed statistical treatments.

8.1 Newton’s law of viscosity

Newton’s law of viscosity states that shear stress is proportional to shear rate for Newtonian fluids. The proportionality constant is the dynamic viscosity. This law provides the foundation for many elementary analyses in fluid mechanics.

8.2 Kinetic theory of gases

Kinetic theory explains gas viscosity in terms of molecular motion and collisions. Molecules moving between layers transport momentum and create resistance to relative motion. This viewpoint helps explain why gas viscosity depends on temperature in a different way from liquid viscosity.

8.3 Molecular and statistical approaches

More advanced models use molecular interactions and statistical mechanics to describe viscosity. These approaches consider how molecular size, shape, and bonding affect flow. They are useful for dense fluids, complex mixtures, and materials near phase transitions.

8.4 Empirical and semi-empirical equations

Many practical formulas estimate viscosity from temperature, composition, or molecular characteristics. Empirical and semi-empirical equations are often developed from experimental data and then applied within a limited range. They are especially valuable in engineering design when exact microscopic modeling is impractical.

9 Applications

Viscosity is central to the design, control, and interpretation of many processes. It affects how materials are transported, mixed, stored, and processed.

9.1 Lubrication

In lubrication, viscosity determines whether a fluid film can separate moving surfaces effectively. If the lubricant is too thin, contact and wear may increase; if too thick, frictional losses may rise. Proper viscosity selection is therefore essential in machinery and engines.

9.2 Transport and pipeline design

Pipeline systems rely on viscosity to predict pressure drop, pumping requirements, and flow regime. Fluids with higher viscosity generally require more energy to move. Accurate viscosity data improve efficiency and help prevent operational problems.

9.3 Food and pharmaceutical processing

Many food products and pharmaceutical formulations depend on viscosity for texture, stability, and ease of use. It influences how a sauce pours, how a cream spreads, and how a medicine is administered. Manufacturers often tailor viscosity to achieve consistent product performance.

9.4 Geophysical and atmospheric flows

Viscosity affects the motion of lava, glaciers, clouds, and air currents at small scales. In geophysical systems, it helps determine how materials deform over long periods. In the atmosphere, viscous effects are usually subtle but become important near surfaces and in fine-scale flow patterns.

Viscosity is closely connected to several other physical ideas that shape fluid behavior and transport phenomena.

10.1 Density

Density is mass per unit volume and influences kinematic viscosity. Two fluids with the same dynamic viscosity may behave differently if their densities differ. The relationship between density and viscosity is important in buoyancy and flow analysis.

10.2 Surface tension

Surface tension governs the behavior of fluid interfaces, while viscosity governs internal resistance to motion. Together they affect droplet formation, wetting, and capillary flow. Their combined action is often seen in sprays, bubbles, and thin films.

10.3 Rheology

Rheology is the broader study of how materials deform and flow. Viscosity is one of its core concepts, but rheology also covers elasticity, yield stress, and time-dependent effects. It is especially important for complex fluids and soft matter.

10.4 Diffusion

Diffusion is the transport of particles from regions of high concentration to low concentration. In fluids, viscous forces can influence how quickly mixing occurs and how particles move. The two processes are distinct, but both are central to transport in liquids and gases.