Centrifugation in liquids with spatially varying densities is used to purify cell components and viruses. This problem concerns simple gravitational settling in such a system. One way to vary the liquid density is with a gradient in sucrose concentration. Suppose that a rod-like virus or other particle of radius R, length L, and density ρp is submerged in a tube of height H, as shown in Fig. P4.6. (The particle dimensions are greatly exaggerated.) A sucrose gradient causes the solution density to vary as

where z = 0 at the tube bottom and ρ = ρ₀ at the top. If the rod settles end-on, what will be its final height h?

Transcribed Image Text:

ρο (1.23 – 0.237) ρ(z) = ρο (1.23 (P4.6-1)