A fluid is a substance that continuously deforms under an applied force, encompassing both liquids and gases. Viscosity measures a fluid’s resistance to this flow or deformation. A central question in fluid dynamics is how a fluid’s viscosity behaves when it is forced to move or change shape. This distinction is crucial for accurately predicting the movement of air in everything from weather patterns to aircraft design.
Defining Newtonian and Non-Newtonian Fluids
Fluids are categorized based on the relationship between the applied force and their resulting rate of movement. When a fluid is sheared, a tangential force (shear stress) is exerted, and the speed at which layers slide past each other is the shear rate. The ratio between shear stress and shear rate defines the fluid’s viscosity.
A fluid is classified as Newtonian if its viscosity remains constant regardless of how quickly it is being sheared. For these fluids, plotting shear stress against shear rate yields a straight line, with the slope representing the constant viscosity value. Water, simple oils, and gasoline are common examples that exhibit this predictable, linear behavior.
In contrast, non-Newtonian fluids have a viscosity that changes when a force is applied. Some fluids, like ketchup or paint, become thinner when stirred (shear-thinning). Others, such as cornstarch and water, become thicker when a rapid force is applied (shear-thickening).
Air’s Behavior Under Normal Conditions
Air, like water, is generally considered a Newtonian fluid under most everyday circumstances. This means that the resistance air offers to flow is directly proportional to how fast it is being forced to flow. The viscosity of air does not change whether it is moving slowly, like a gentle breeze, or quickly, such as air flowing around a car at highway speeds.
The ratio of shear stress to shear rate for air remains constant at a given temperature and pressure, satisfying the defining characteristic of a Newtonian fluid. This predictable behavior allows engineers to use simplified equations, such as the Navier-Stokes equations, to model air movement and aerodynamic forces with high accuracy. The dynamic viscosity of air at standard temperature and pressure is extremely small, approximately \(1.8 \times 10^{-5}\) Pascal-seconds.
How Temperature and Pressure Influence Air’s Viscosity
Air is Newtonian because its viscosity is independent of the shear rate, but its actual viscosity value is highly dependent on thermodynamic conditions. This distinction is a common point of confusion, as the Newtonian classification only describes the relationship between stress and strain rate, not the influence of temperature and pressure on the viscosity coefficient itself. Air’s viscosity, like that of all gases, increases as its temperature rises, which is opposite to the behavior of most liquids.
This relationship is due to the molecular mechanisms that cause viscosity in gases. Viscosity arises primarily from the transfer of momentum between molecules as they collide. As the temperature increases, the molecules move faster and collide more frequently, leading to a greater transfer of momentum between the layers of flowing gas, resulting in higher internal friction and increased viscosity.
Pressure has a minimal effect on the viscosity of air under standard conditions. Viscosity in a gas depends on the molecular motion and collision rate, which remain relatively constant even if the pressure changes, provided the gas is not highly compressed. Only at extremely high pressures does pressure begin to notably influence the viscosity. An increase in altitude, which significantly lowers pressure, does not change the viscosity of air as much as a corresponding change in temperature would.
When Air Deviates from the Newtonian Model
Despite its general Newtonian nature, air can deviate from this simple model under specialized and extreme conditions. The Newtonian model assumes a continuum, where the fluid can be treated as a continuous medium without gaps. In extremely low-density environments, such as the upper atmosphere or a high vacuum, the distance between air molecules becomes very large, and the continuum assumption breaks down.
When the air density is low, the mean free path—the average distance a molecule travels before colliding with another—can become comparable to the size of the object moving through it. In this non-continuum regime, specialized models of molecular flow are required instead of the standard fluid mechanics equations. Deviation also occurs during extremely high-speed airflow, such as in hypersonic flight, where air velocity exceeds Mach 5. The intense shockwaves generated create massive, rapid temperature and pressure variations, complicating the simple linear relationship between shear stress and shear rate.