What Is Viscosity? A Liquid's Reluctance to Be Sheared

Imagine a fluid between two plates, one fixed and one dragged sideways. The fluid immediately touching each plate moves with it, which is the no-slip condition and is an experimental fact rather than an assumption, so the fluid in between is sheared, with each layer sliding over the one below at a slightly different speed. Viscosity is the ratio of the force per unit area required to the rate at which the layers are shearing, and a fluid needing more force for the same shear rate is more viscous. The physical origin differs between liquids and gases in an instructive way. In a liquid it comes from intermolecular attraction, so heating a liquid, which gives molecules enough energy to escape each other's attraction, lowers its viscosity, which is why engine oil thins when hot and why warm honey pours. In a gas it comes from molecules carrying momentum between layers as they move randomly, so heating a gas, which speeds that transfer, raises its viscosity. The two behave oppositely with temperature, which surprises most people.

A Newtonian fluid has a viscosity that does not depend on how hard it is being sheared, which water, air and most simple liquids obey. Many everyday materials do not:

• •Shear thinning fluids get less viscous the harder they are sheared, which is why paint spreads under a brush and then stops running, why ketchup flows once shaken and why blood thins in narrow vessels
• •Shear thickening fluids get more viscous, the classic demonstration being cornflour in water, which can be walked on and which is being explored for flexible body armour
• •Bingham plastics behave as a solid until a threshold stress is exceeded and then flow, which describes toothpaste, mayonnaise and wet concrete, and is why toothpaste sits on a brush
• •Thixotropic materials thin over time under constant shear and recover when left alone, which is how non-drip paint and drilling mud work
• •Viscoelastic materials show both viscous and elastic behaviour, which is what makes silicone putty bounce when thrown and puddle when left
• •Extensional viscosity, the resistance to being stretched rather than sheared, behaves differently again and is what makes some liquids form long strings

Viscosity determines how fluid behaves at every scale. In pipes and blood vessels, flow rate for a given pressure depends on viscosity and, dramatically, on the fourth power of the radius, so halving a vessel's diameter cuts the flow to a sixteenth, which is why small changes in arterial narrowing matter so much medically. The ratio of inertial to viscous forces, the Reynolds number, determines whether flow is smooth or turbulent, and it explains why swimming is a completely different physical problem for a bacterium, which lives in a world where viscosity dominates entirely and coasting is impossible, than for a person. Lubrication is viscosity used deliberately, maintaining a film that keeps surfaces apart, and engine oil grades describe viscosity at low and high temperature precisely because the requirement changes between a cold start and a hot engine. Volcanic behaviour depends on magma viscosity, with runny basaltic lava producing gentle effusive eruptions and viscous silica-rich magma trapping gas until it explodes.

Several instruments exist because different fluids and industries need different information. A capillary viscometer times how long a fixed volume takes to flow through a narrow tube under gravity, which is simple and accurate for Newtonian liquids. A falling-ball viscometer times a sphere sinking through the fluid. A rotational viscometer or rheometer turns a spindle or cone in the sample and measures the torque, which allows viscosity to be measured across a range of shear rates and is therefore the only way to characterise a non-Newtonian material properly. Industrial shortcuts include flow cups that time drainage through an orifice, which are crude and adequate for quality control. The most famous measurement of all is the pitch drop experiment begun in 1927 at the University of Queensland, in which a sample of tar pitch drips roughly once a decade, demonstrating that a substance brittle enough to shatter with a hammer is a liquid of enormous viscosity, and holding a record for the longest-running laboratory experiment.

Viscosity measures how much force is needed to slide one layer of a fluid past another, arising from molecular attraction in liquids and momentum transfer in gases, which is why heating thins a liquid and thickens a gas. Many everyday materials are not Newtonian: paint and blood thin under shear, cornflour suspension thickens, and toothpaste stays put until a threshold is passed. Flow through a tube depends on the fourth power of its radius, which is why small arterial narrowing matters so much.