# Using the Stokes Law in Oil-Water Separators

Initially developed by George Gabriel Stokes in 1851, the Stokes law is a mathematical theory of frictional force. It describes the relationship between the viscosity of a fluid and the frictional force between a spherical object and a surface. It applies to viscous liquids with a small Reynolds number.

**Gravitational force**

Observing the settling of small spherical particles in a fluid medium, Sir George Gabriel Stokes devised a law relating the velocity of a solid sphere to its viscosity. This law has since proven to be a valuable tool in sedimentation analysis.

The law states that the viscous force of a spherical object is directly proportional to the size of the sphere. This force is also known as the drag force. It acts on the body because of the motion and opposes the gravitational force.

The law is helpful in centrifuges, hydro cyclones, and settling pits. In addition, it is useful in determining the charge of an electron. In a famous experiment performed by the British scientist Sir Millikan, he used this law to calculate the cost of an electron.

The law is derived from a simple mathematical formula. The formula uses a constant, F, and the derivation of the equation is straightforward.

This law is essential in explaining cloud formation. It also has applications in sediment settlement in freshwater.

**The viscosity of a fluid**

Developed by Anglo-Irish physicist and mathematician Sir George Gabriel Stokes, Stokes’s law is a mathematical equation that relates the drag force to the velocity of a sphere in a viscous fluid. The drag force is a function of the sphere’s length, mass, and speed.

The equation has two main parts, the terminal velocity and the frictional force. The terminal velocity is the velocity at which the combination of gravity and frictional drag is balanced.

The terminal velocity can be calculated by using the following formula. To calculate the frictional force, multiply the terminal velocity by the number of kilograms per square centimeter of the sphere. For example, a sphere of radius one centimeter has a mass of about one hundred and fifty kilograms per square meter. Therefore, the frictional force is about one kilogram per square meter.

The other important point to remember about Stokes’s law is that it is only valid for spherical objects that are smooth and uniform in density. This means that a falling raindrop or fog droplet falling through the air can not be considered a sphere.

**Brownian movement**

During the nineteenth century, physicists began to study Brownian motion, also called stochastic signal. Initially, the phenomenon was thought to be caused by the movement of living organisms. Eventually, however, scientists realized that it was random fluctuations in the position of particles.

In 1906, Marian Smoluchowski developed a method to solve the Brownian motion problem. Her results proved that the motions of tiny, uniform spheres were the same as those of larger, irregularly shaped particles in large quantities.

Brownian motion is a type of uncontrolled fluctuation, which is a consequence of collisions between molecules. It is a process that can be used to study the diffusion of pollutants through the atmosphere and holes through semiconductors.

In addition to its microscopic characteristics, Brownian motion can also be found in the movement of calcium through bone tissue in living organisms. In these cases, the sedimentation process is responsible for the displacement of large particles.

In the late nineteenth century, the French experimentalist Leon Gouy discovered that the motion of microscopic particles in liquids was not dependent on thermal convection. Instead, he believed thermal molecular collisions caused the phenomenon.

**Application in oil-water separator**

Using Stokes’ law in an oil-water separator has several advantages. One significant advantage is that it separates a very high oil concentration from water. It also helps prevent pollution. Another advantage is that it requires little space.

The basic design of an oil/water separator involves three components: an oil separator unit, a collecting chamber, and a coalescing stage. The three components are designed in different ways. The separation efficiency is affected by the size of the separator, the amount of oil,, and the viscosity of the primary fluid.

An oil/water separator is a filtration device that separates oil from wastewater. It is used in several applications. For instance, it is commonly found in commercial kitchens, service stations, and mining workshops. It is also used in ships.

To ensure proper separation, the vessel should be sized to fit the application. It should also have siphon breaks. This helps stop the oil and water from entering the separator when it is low-flowing.