Stokes’ Law describes the drag force experienced by small, spherical objects moving through a viscous fluid. This principle explains why objects fall at a constant rate in liquids or gases, rather than continuously accelerating. It quantifies the resistance an object encounters, a fundamental concept in fluid dynamics.
The Science Behind Falling Objects in Fluids
When an object moves through a fluid, it encounters resistance known as drag. This drag force is influenced by the fluid’s viscosity, a measure of its internal resistance to flow. For instance, water has lower viscosity than honey, so objects move through water with less resistance. The greater the viscosity, the more the fluid resists the object’s movement, increasing drag.
The drag force also depends on the object’s size, shape, and speed. Larger objects, less streamlined shapes, and higher speeds generally experience more drag.
As an object falls through a fluid, gravity pulls it downward, causing acceleration. However, as its speed increases, the upward drag force from the fluid also grows. Eventually, this upward drag force, combined with any buoyant force, balances the downward force of gravity. At this equilibrium, the net force on the object becomes zero, and it stops accelerating, continuing its fall at a constant speed known as terminal velocity.
Where Stokes’ Law Appears in Our World
Stokes’ Law has many practical applications across various fields. One common example is the settling of sediment in water bodies. In rivers or treatment plants, smaller particles settle more slowly than larger ones, a process utilized in designing sedimentation tanks for water purification.
The movement of tiny particles in the air, such as dust, aerosols, and raindrops, also follows this principle. Small water droplets in clouds have low terminal velocities, allowing them to remain suspended until they combine and grow large enough to fall as rain. The law also helps explain why pollutants like smog particles stay suspended in the atmosphere or settle over time.
In medical diagnostics, Stokes’ Law is applied to understand the sedimentation rate of blood cells. This rate, known as the erythrocyte sedimentation rate (ESR), can indicate inflammation or disease, as changes in red blood cell aggregation affect their settling speed in plasma. Industrially, the law is fundamental in processes like centrifugation, separating components in mixtures, and in the oil industry for refining crude oil by separating solid particles. It is also used in falling-sphere viscometers to measure the viscosity of liquids by observing how quickly a sphere falls through them.
When Does Stokes’ Law Apply?
Stokes’ Law is a powerful tool, but its accuracy depends on specific conditions. For the law to apply, the object moving through the fluid must be spherical. While it can offer approximations for other shapes, the precise calculations are for perfect spheres, as object geometry significantly influences fluid flow.
Additionally, the fluid itself must be viscous and incompressible, meaning its density remains constant under pressure. The flow around the object must also be laminar, characterized by smooth, parallel layers of fluid without turbulence. This laminar flow, often associated with low velocities, is crucial because turbulent flow introduces additional forces not accounted for by Stokes’ Law.
The object’s velocity must be low, specifically leading to a small Reynolds number, typically less than one. A low Reynolds number indicates that viscous forces dominate over inertial forces, ensuring laminar flow and that the assumptions of Stokes’ Law hold true. When these conditions are not met, such as with high velocities or irregularly shaped particles, the drag force deviates significantly from what Stokes’ Law predicts.