Forces in Centrifugation: From Classical Physics to Modern Mechanics
Juan José Manotas Mazario
Engineering and Innovation Manager @ RIERA NADEU, S.A. | Project Planning, Business Management
Centrifugation is an essential technique in numerous scientific and technical fields, used to separate particles based on their density and size through the application of centrifugal forces. This post will explore the fundamental forces that drive centrifugation, from the principles of classical physics to advances in modern mechanics, and how these forces have been understood and applied over time.
Fundamental Principles
1. Centrifugal force
Centrifugal force is a fictitious force that appears in a rotating reference frame. Although it is not a real force in the sense that it does not exist in an inertial reference frame, it is useful in describing the behavior of rotating objects. This force tends to move objects away from the axis of rotation and can be calculated using the formula:
where m is the mass of the object, ω is the angular velocity, and r is the distance to the axis of rotation.
The calculation of centrifugal force dates back to the mid-17th century. One of the first records of the term "centrifugal force" appears in the notes and letters of Christiaan Huygens beginning in 1659. Huygens, a prominent Dutch physicist, mathematician, and astronomer, is known for his work in mechanics and his formulation of the theory on centrifugal force.
Huygens improved existing technology by inventing the pendulum clock in 1656, with an accuracy of about 15 seconds per day. The pendulum clock was the most precise mechanism for measuring time until the first quartz clock was built in 1927, at Bell Telephone Laboratories.
In 1673, Huygens summarized his work in the work Horologium oscillatorium ("The Pendulum Clock"). This work is considered one of the three most important works of the 17th century on mechanics, along with "Two New Sciences" (1638) by Galilei and "Mathematical Principles of Natural Philosophy" (1687) by Isaac Newton.
In his work "Horologium Oscillatorium" (1673), Huygens provided one of the first detailed mathematical descriptions of centrifugal force, based on his studies of rotating bodies.
The centrifugal force for uniform circular motion was one of Huygens' greatest discoveries. The readings he did on Galileo Galilei and René Descartes motivated him, but we must not forget that this work derived from his research on the conical pendulum clock.
The pendulum clock was the idea of Galileo Galilei in 1637, and his son began construction in 1649, but did not finish it.
Huygens had discussed centrifugal force in his work Horologium oscillatorium ("The Pendulum Clock") of 1673. However, he had already written it up in his treatise De vi centrifugal ("On the Centrifugal Force") of 1659; but this work was not published until 1703, years after he had died.
The formula that Huygens found for the centrifugal force for uniform circular motion is the same one that is still used today:
This work marked an important milestone in classical physics, providing a theoretical foundation that has been used and refined in subsequent centuries for various scientific and technical applications.
2. Gravitational Force
The gravitational force is one of the four fundamental forces of nature, first described by Isaac Newton in his Law of Universal Gravitation:
where G is the universal gravitation constant, m1 and m2 are the masses of the two bodies, and r is the distance between them. This force plays a crucial role in the natural sedimentation of particles, a principle that is accelerated in centrifugation.
Newton's main achievement was to mathematically demonstrate Johannes Kepler's three laws of planetary motion. In physical language, he deduced that the force with which two bodies attract each other must be proportional to the product of their masses divided by the distance between them squared.
Although many astronomers did not use Kepler's laws, Newton had sensed that they were of great importance, so he magnified them through his law of universal gravitation.
Practical applications
Separation of Biological Components
In molecular biology, centrifugation is used to separate cellular components and macromolecules. For example, in DNA extraction, samples are centrifuged to separate DNA fragments from other cellular components. This process is carried out using high-speed centrifuges, which apply high centrifugal forces to achieve efficient separation.
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Pharmaceutical industry
In the pharmaceutical industry, centrifugation is essential for the purification of biological and pharmaceutical products. Ultra-high-speed centrifuges allow the separation of proteins and other active compounds from impurities and other unwanted materials.
History and Development
Isaac Newton and Gravitation
Isaac Newton, with his formulation of the Law of Universal Gravitation, laid the foundations for understanding the forces that act in rotating systems. His famous anecdote of the falling apple inspired his ideas about gravity, a force that would later be understood as a crucial component in the dynamics of centrifugation.
Jean Perrin and Sedimentation
In the early 20th century, Jean Perrin used centrifugation principles to study Brownian motions and particle sedimentation. His experiments were crucial in demonstrating the existence of atoms and molecules, and earned him the Nobel Prize in Physics in 1926.
Modern Advances
Ultracentrifuges and Advanced Techniques
With the advancement of technology, ultracentrifuges have been developed that can reach extremely high speeds, allowing the separation of particles at the molecular level. These tools are essential in structural biology research and in the biotechnology industry for the purification of viruses, ribosomes and other macromolecular complexes.
Introduction to Ultracentrifuges
Ultracentrifuges are devices used to separate components of a sample based on their density, applying extremely high centrifugal forces. This equipment is essential in fields such as molecular biology, biochemistry and medicine, as it allows the separation and analysis of macromolecules such as proteins, nucleic acids and cellular organelles.
Operating principle
The basic principle of ultracentrifuges is based on centrifugal force, which is generated when a sample is subjected to rapid rotation. The centrifugal force Fc is defined by the formula previously described.
Angular Speed and RPM
Angular velocity (ω) is related to revolutions per minute (RPM) by the formula:
Force Relative to the Earth (g)
Centrifugal force can also be expressed in terms of the force of gravity g (9.81 m/s2):
where RCF is the Relative Centrifugal Force.
Applications
Ultracentrifuges are crucial tools in biomedical and biotechnology research. Understanding how they work and the advanced techniques they use allows you to optimize separation and molecular analysis processes.
Centrifugation is a powerful technique that is based on fundamental principles of classical and modern physics. From Isaac Newton's initial formulations of the gravitational force to today's technological advances, the fundamental forces that drive centrifugation remain essential to scientific and technological progress. The understanding and application of these forces have allowed significant developments in research and industry, consolidating centrifugation as an indispensable tool in numerous fields.
How have the principles of classical physics influenced modern techniques in centrifugation?
In what ways has centrifugation impacted scientific research and industrial applications?
Feel free to share your thoughts and experiences in the comments below!
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