Stokes Settling Formula
Definition
The equation v = 2r²g(ρₛ - ρ_f) / 9η relating the settling velocity of a spherical particle to its radius, the density difference between particle and fluid, and the fluid viscosity; governs equilibration time in density-gradient columns.
- Equation
- v = 2r2g(rho_s - rho_f) / 9(eta)
- Variables
- Particle radius, density difference, fluid viscosity
- Application
- Density-gradient column equilibration time
Common questions
Why does particle size matter so much for how quickly a density-gradient column reaches equilibrium?+
The formula shows settling velocity scales with the square of the particle radius, so a small change in particle size produces a much larger change in settling speed, meaning finely ground samples equilibrate far faster than coarser ones for the same density difference.
What happens to Stokes' law accuracy for very small or irregularly shaped particles?+
The formula assumes a smooth, rigid sphere settling under laminar flow, so it becomes less accurate for irregularly shaped fragments or particles small enough that Brownian motion competes with gravitational settling, both of which are practical limitations in forensic density-gradient work.
Related terms
- ASTM E2365
- The American Society for Testing and Materials standard for forensic comparison of glass by density; specifies temperature control, calibration, and precision requirements...
- Bromoform-Bromobenzene System
- The reference liquid mixture used in forensic density-gradient columns and sink-float tests; bromoform (2.890 g/cm³) and bromobenzene (1.495 g/cm³) mix in variable...
- Density
- Mass per unit volume (ρ = m/V), expressed in g/cm³ or kg/m³; a physical property used to compare and discriminate glass, mineral,...
- Density-Gradient Column
- Glass column filled with stepwise layers of liquids of decreasing density (commonly bromoform 2.89 g/cm3 and bromobenzene 1.50 g/cm3 mixed in known...
- DFSS
- Directorate of Forensic Science Services, India; issues the Forensic Laboratory Manual that governs glass and soil examination procedures, including the bromoform-based density...
- ENFSI ENG3-2013
- The ENFSI Glass Expert Working Group guideline for glass comparison casework; specifies the examination sequence, within-source variation requirements, statistical comparison framework, and...
- Hydrostatic Weighing
- Density measurement exploiting Archimedes' principle; the apparent weight loss of a solid submerged in a liquid of known density equals the weight...
- Neutral Buoyancy
- The condition in which a solid object's density exactly matches the density of the surrounding liquid; the object neither sinks nor rises...
- Oscillating-U-Tube Densitometer
- An instrument that measures liquid density from the resonant frequency of a liquid-filled U-shaped tube; precision of ±0.0001 g/cm³, widely used for...
- Pycnometry
- Absolute density measurement using a calibrated-volume flask; the density of a solid is calculated from the mass of liquid displaced when the...
- Sink-Float Test
- Qualitative density screening in which a solid fragment is immersed in a liquid of adjustable density until neutral buoyancy is achieved; the...