= Rate-zonal centrifugation
<Rate-zonal centrifugation> resolves an initially narrow sample zone by differences in <sedimentation coefficient> during a finite interval. Its bands remain transient: extending the interval can carry material into a <centrifugation pellet>. Thus a <density gradient> need not imply an equilibrium <buoyant density> measurement.https://www.beckman.com/resources/technologies/centrifugation/density-gradient-centrifugation/[Types of Density Gradients, Rate Zonal Centrifugation and Table 1: migration rates before equilibrium or complete sedimentation]{ref}
A typical preparation layers a narrow sample above a preformed <density gradient>, often containing <sucrose>. The initial zone must be narrow enough that differences in starting position do not overwhelm the later separation. The run ends while useful bands remain inside the liquid. In the simple case where all particles are denser than every part of the column, none has an interior <isopycnic centrifugation> position.<An Introduction to Ultracentrifugation by Beckman Coulter Life Sciences>[Rate Zonal Centrifugation: top loading, preformed gradient, starting-zone width and stopping before pelleting]{ref}<Density Gradient Centrifugation by Beckman Coulter Life Sciences>[Types of Density Gradients: rate-zonal preformed sucrose gradients]{ref}
The <sedimentation coefficient> $s=(m-\rho_fV)/f$ explains why separation is not an ordering by <mass> alone. At fixed local <centrifugal acceleration>, increasing displaced <volume> can increase <buoyancy>, while a less compact shape can increase the <linear friction coefficient> and reduce <velocity>. Even for a <sphere>, <Stokes's law> gives $s=2b^2(\rho_p-\rho_f)/(9\eta)$, so both the <density> difference and the dynamic <viscosity> matter. The resulting <sedimentation coefficient> can change along a <density gradient>.
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