Derivation of Sedimentation Coefficient Equation

Derivation of Sedimentation Coefficient Equation

by Andrey K

Formal & Physical Sciences Physics PHDClassical mechanicsPHDFPhysics: Fluid mechanics
🎙 Andrey K 👥 852K 📅 February 3, 2015 ⏱ 15 min 👁 42K 📄 tutorial 🧭 2026-08-17
Available in: English (current) Français

Keywords

sedimentation coefficientcentrifugationSvedberg equationderivationbiochemistry

Summary

This video provides a step-by-step derivation of the sedimentation coefficient equation, a key concept in biochemistry used to describe particle sedimentation in a centrifuge. The presenter begins by defining the sedimentation coefficient (s) as m(1 - v̄ρ)/f, where m is particle mass, v̄ is partial specific volume, ρ is solvent density, and f is the frictional coefficient. He then sets up a physical scenario of a particle in a rotating test tube, identifying three forces: centrifugal force (positive), buoyant force, and frictional force (both negative). Assuming constant velocity (zero acceleration), he applies Newton’s second law to set the sum of forces to zero. He expresses each force: centrifugal force as mω²r, buoyant force as m_displaced ω²r, and frictional force as fv. He then relates the displaced mass to particle mass and densities, using v̄ = 1/ρ_particle, leading to mω²r(1 - v̄ρ) - fv = 0. Rearranging yields v/ω²r = m(1 - v̄ρ)/f, and since s = v/ω²r, he obtains the desired equation. He also shows an alternative form using Avogadro’s number to express molar mass, resulting in s = M(1 - v̄ρ)/(N_A f). The derivation is clear and based on classical physics principles.

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Critical Evaluation

Value of the Information & Strength of the Argument

The video provides a clear and logical derivation of the sedimentation coefficient equation from fundamental physics principles. It systematically identifies the forces acting on a sedimenting particle and applies Newton’s second law under steady-state conditions. The argumentation is solid, with each step justified and explained. The presenter also demonstrates an alternative form using molar mass, which adds practical relevance. However, the video does not discuss the assumptions and limitations of the model, such as the neglect of diffusion or the assumption of spherical particles, which could be important for a complete understanding.

Scientific Rigor, Source Quality, Title Accuracy

The video is a tutorial and does not cite specific scientific sources, but the derivation is based on well-established principles in classical mechanics and fluid dynamics. The title accurately describes the content. The description provides links to the presenter’s website and a donation page, but no direct references to scientific literature. The lack of citations reduces the scientific rigor, but the content itself is mathematically correct and aligns with standard textbook treatments.

179 words

Title / Content Match

The title accurately reflects the content, which is a derivation of the sedimentation coefficient equation.

Quality & Reliability

7/10

The derivation is mathematically sound and follows from classical mechanics and fluid dynamics. The presentation is clear and step-by-step, but lacks citations to primary sources and does not discuss limitations or assumptions in depth.

Key Moments

Markers derived by PSI from the transcript: the creator did not define chapters.

Cited Sources

Concurring Sources

External References

Contribution & Novelties

The video provides a clear and systematic derivation of the sedimentation coefficient equation, which is often presented as a given in biochemistry textbooks. It bridges the gap between physical principles and biochemical applications, making the concept more accessible. The alternative form using molar mass is a useful addition.

Pour aller plus loin :

  • Svedberg equation — Provides background on the equation and its applications.
  • Sedimentation coefficient — Detailed explanation of the coefficient and its measurement.
  • Centrifugation — Overview of the technique and its principles.

84 words

Radar Profile

The radar profile shows high scores in quality of information and technical level, indicating a solid educational resource. The quantity of information is moderate, and the overall reliability is good, though the lack of citations slightly reduces the score.

Reliability 7/10

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