viscosity

# tag · @ author · ! scientist

Viscosity is a measure of the resistance of a liquid or gas to shear deformation. It characterizes internal friction between layers moving at different speeds. There are dynamic (absolute) viscosity and kinematic viscosity (dynamic divided by density).

History

Studies of fluids in the 17th century led to the understanding that the friction force between layers is proportional to the speed of sliding. Later, scientists found ways to measure and calculate viscosity, which helped build pipes and lubricate mechanisms.

How it works

Imagine passing books from shelf to shelf: if you hand them from person to person, it goes quickly. But if each book gets stuck in hands, movement slows. Similarly, in a fluid, molecules exchange momentum, as if passing 'sticky books', creating resistance.

💡 In some liquids, viscosity increases when stirred — this is dilatancy, like a mixture of cornstarch and water: you can run on its surface, but if you stop, you sink.

For Newtonian fluids, the dynamic viscosity coefficient η relates shear stress τ and velocity gradient du/dy linearly: τ = η du/dy. Kinematic viscosity ν = η/ρ, where ρ is density. In gases, viscosity increases with temperature (due to more intensive momentum transfer); in liquids, it usually decreases (weakening of intermolecular bonds). Non-Newtonian fluids show dependence of η on shear rate, described by rheological models (power-law, Bingham model). Viscosity plays a key role in hydrodynamics, forming the Reynolds number and determining laminar or turbulent regime.

History

The concept of viscosity evolved from empirical observations to molecular kinetic theory. Isaac Newton in his 'Principia Mathematica' (1687) formulated the law of internal friction. In the 19th century, Claude-Louis Navier and George Stokes generalized it in the equations of fluid dynamics. The kinetic theory of gases (James Clerk Maxwell) connected viscosity with momentum transfer by molecules. Later, Ludwig Boltzmann (not from the list, but a key figure) derived an equation for the distribution function allowing calculation of viscosity; his work was continued by Maxwell and others.

How it works

In liquids and gases, viscosity arises from momentum transfer between layers moving at different speeds. In gases, molecules fly freely from layer to layer, carrying momentum and equalizing speeds; in liquids, intermolecular forces dominate, making shear difficult. According to Newton's law of viscosity, shear stress is directly proportional to the transverse velocity gradient. In a microscopic picture, the viscosity of a gas can be expressed in terms of the mean free path and average molecular speed.

\tau = \eta \frac{du}{dy}

τ — shear stress (Pa), η — dynamic viscosity (N·s/m²), du/dy — velocity gradient (s⁻¹)

\nu = \frac{\eta}{\rho}

ν — kinematic viscosity (m²/s), η — dynamic viscosity, ρ — density (kg/m³)

Open problems & fun facts

Accurate prediction of the viscosity of complex fluids (petroleum, biological media) remains a computationally complex task requiring multiscale modeling.

💡 Glass is a liquid with enormous viscosity, but medieval windows are thicker at the bottom not because of flow, but because of imperfect blowing.

No articles yet

viscosity

History

How it works

History

How it works

History

How it works

Open problems & fun facts

Related articles