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Density-gradient centrifugation uses a liquid whose density varies along the separation direction. A band does not by itself establish which mechanism produced it: rate-zonal centrifugation separates by migration rate before equilibrium, whereas isopycnic centrifugation uses equilibrium positions set by buoyant density.

The distinction is between a moving clock and a restoring balance. In rate-zonal centrifugation, two species may occupy different positions because their sedimentation coefficients differ, even when their buoyant densities agree. In isopycnic centrifugation, two differently sized species can converge to the same band because their buoyant densities agree. Conversely, equal mass does not ensure equal migration velocity: shape affects drag force, and medium density affects buoyancy.^[ref]

The worked finite-time rate-zonal separation and linear-gradient isopycnic focusing examples isolate these mechanisms in chosen mathematical models. The actual DNA experiment described under isopycnic centrifugation illustrates the second mechanism; its initial collection of biological cells into centrifugation pellets is a different operation from the later molecular banding. Collecting liquid fractions from a tube can recover material at different positions, but the position alone does not identify its molecules or establish purity.

Consider two dilute populations of spheres with the same buoyant density and radii $b$ and $2b$. Adopt the fixed linear density gradient and constant local centrifugal acceleration of linear-gradient isopycnic focusing, with constant dynamic viscosity and negligible diffusion. Stokes's law makes $V/f$ proportional to $b^2$, so doubling radius multiplies the migration rate parameter by four, although the mass increases eightfold.

Use $u=z/L$, $\tau =t/T$ and $q=({\rho }_b-{\rho }_0)/(GL)=2$. The liquid occupies $0\le u\le 1$, so the matching density position lies beyond its outer boundary. Both populations begin at $u(0)=0.1$; choose ${\lambda }_A=0.15$ and ${\lambda }_B=0.6$. Their band-center trajectories areAt $\tau =0.5$, they lie at approximately $0.2373$ and $0.5924$; at $\tau =1$, at $0.3647$ and $0.9573$. Equal buoyant density has not prevented a useful finite-time separation. Solving $u_B(\tau )=1$ using the natural logarithm gives first boundary arrival at $\tau =\ln (1.9)/0.6\simeq 1.0698$. The corresponding arrival for A is $\ln (1.9)/0.15\simeq 4.2790$. Trajectories describe migration only until contact with the boundary; subsequent collection into a centrifugation pellet is not represented by extending the curve beyond $u=1$.

This is the useful contrast with isopycnic centrifugation: stopping time helps determine the recovered positions in rate-zonal centrifugation, whereas a stationary matching density position sets the limiting band center in isopycnic centrifugation. Real resolution also depends on initial zone width, diffusion and variations in particle properties; distinct calculated centers alone do not prove that fractions will be pure.