Say I want to separate red blood cells from plasma in blood. How can I use this law to make quantitative predictions on the centrifugation speed I must use to separate into the two phases.
The distance a single particle migrates within a horizontal tube is given by stokes velocity times Relative Centrifugal Acceleration (Centrifugal acceleration/earth acceleration). Dimensionless RCA reads about 5.59 x 10 (exp -7) x RPM x RPM x 2R. R in mm is the distance from centre of revolution.
But if the concentration is higher, lets say about a few % v/v, sedimentation speed will increasingly decrease with increasing concentration. This is described by the hindrance function. It depends also from the behaviour of the particles. For RBC, which are deformable, it is less pronounced as for rigid particles. In addition, stokes low assumes Newtonian liquids.
See:
Acta Mech 201, 83–94 (2008)
DOI 10.1007/s00707-008-0074-y
Torsten Detloff · Dietmar Lerche
Centrifugal separation in tube and disc geometries:
experiments and theoretical models
As it was mentioned before Stokes is for steady state with no interference between particles. However, the separation also depends on the centrifugation time and travel distance; e.g., at low speed and short tube you may need shorter spinning time that long tube and high speed. Also the efficiency is important it may be quick to separate 60 % but take for ever to obtain 99%.
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