Terminal Velocity in Fluids
When a sediment grain falls through water, gravity pulls it down while fluid drag pushes up. Within milliseconds, these forces balance and the grain reaches terminal (settling) velocity. For small particles in the Stokes regime, drag is proportional to velocity and diameter, giving the famous result v = (rhos-rhof)gd²/(18mu). This elegant equation, derived by George Gabriel Stokes in 1851, remains the foundation of sediment transport theory.
The Reynolds Number Boundary
Stokes law assumes laminar flow around the particle — fluid streamlines smoothly part and rejoin. This holds only when the particle Reynolds number Re = rhof*v*d/mu is below about 0.5, corresponding roughly to silt-sized particles (d < 0.1 mm). For sand and gravel, turbulent wake formation increases drag, and empirical drag laws or the Ferguson-Church universal equation must replace simple Stokes theory.
Sediment Sorting and Graded Bedding
The strong dependence of settling velocity on grain size creates natural sorting. In a turbidity current carrying mixed-size sediment, cobbles settle first, then sand, then silt, then clay — producing the characteristic upward-fining graded beds that geologists use to identify ancient submarine fan deposits in the rock record. This gravitational sorting is the physical basis of sedimentary grain-size analysis.
Applications in Engineering and Environment
Stokes settling governs water treatment plant design (settling tanks must be large enough for particles to reach the bottom), dredging operations, volcanic ash dispersal modeling, and microplastic fate in oceans. Understanding how particle properties affect settling velocity is essential for predicting where sediment accumulates in rivers, lakes, and the deep sea.