What Is Viscosity?

Viscosity is a physical property of fluids that quantifies their internal resistance to flow, arising from intermolecular friction between adjacent layers of fluid moving at different velocities. It was formally defined by Isaac Newton in the seventeenth century for idealized fluids in which shear stress is directly proportional to the rate of strain, a class now called Newtonian fluids. Dynamic viscosity, measured in pascal-seconds (Pa·s), describes the ratio of shear stress to shear rate, while kinematic viscosity, measured in square meters per second (m²/s), expresses dynamic viscosity divided by fluid density. Water at 20°C has a dynamic viscosity of approximately 1 mPa·s, whereas heavy fuel oils and polymer melts can be many orders of magnitude higher. Viscosity is temperature-dependent in all fluids and, in gases, increases with temperature, while in liquids it decreases with temperature, a distinction of practical importance in engineering design.

Viscosity is a central variable in process engineering, tribology, food technology, and biomedical science. Accurate measurement and control of fluid viscosity is required to ensure product quality, equipment longevity, and safe operating conditions across many industries.

Fluid Flow Modeling and the Navier-Stokes Framework

The Navier-Stokes equations govern the motion of viscous fluids by coupling conservation of momentum and mass with the viscous stress tensor. For incompressible Newtonian fluids, viscosity enters as a constant coefficient multiplying the velocity gradient terms, yielding a set of partial differential equations that describe laminar and turbulent flow regimes. The NIST Rheology program supports the development of measurement science and standard reference materials that underpin the calibration of computational fluid dynamics models. For non-Newtonian fluids, including polymer solutions, biological fluids like blood, and dense suspensions such as cement slurries, the constitutive relationship between stress and strain rate is nonlinear, requiring more complex rheological models such as the power-law, Carreau, or Bingham formulations.

Rheology and Measurement Techniques

Rheology is the branch of mechanics concerned with the flow and deformation of matter, of which viscosity is the most commonly measured property. Rotational rheometers measure dynamic viscosity by shearing a fluid sample between two surfaces, one stationary and one rotating, and recording the torque required to maintain a prescribed shear rate. Capillary viscometers use the Hagen-Poiseuille equation to derive viscosity from the time for a fluid to flow through a calibrated tube under gravity or applied pressure. The NIST Technical Note on rheological measurement of cement documents standardized procedures for complex non-Newtonian fluids, illustrating how measurement methodology must be tailored to the fluid class under study. Falling-sphere and rolling-ball viscometers offer alternative approaches suited to transparent liquids in laboratory settings.

Viscosity Sensors and Industrial Measurement

Inline and online viscosity sensors allow continuous monitoring of fluid viscosity during manufacturing processes without extracting samples for laboratory analysis. Vibrating-element sensors immerse a probe resonating at a defined frequency and measure the damping effect of the surrounding fluid, from which viscosity is inferred. Acoustic-wave devices, including quartz crystal microbalances and surface acoustic wave sensors, detect viscosity-correlated changes in resonant frequency and dissipation with high sensitivity at small sample volumes. Microfluidic viscometers integrate measurement channels on a chip and require only microliter sample volumes, which is advantageous for biological assays. IEEE Xplore research on non-Newtonian fluid viscosity measurement using inertial viscometers demonstrates how computer vision systems can automate viscosity determination for complex fluids in real-time laboratory workflows.

Applications

Viscosity has applications in a wide range of engineering and scientific disciplines, including:

• Industrial process control for polymer extrusion, mixing, and coating operations
• Lubricant selection and tribology in engines, bearings, and hydraulic systems
• Biomedical analysis of blood rheology for cardiovascular disease diagnosis
• Food and beverage manufacturing quality control of sauces, creams, and emulsions
• Petroleum refining to characterize crude oil and fuel oil fractions for pipeline transport