Some rules of thumb:

M in Kdaltons, s in Svedbergs, D in Ficks, Rs in Angstroms,

speed in K rpm, rho=1.000 g/cc, v-bar=0.725 cc/g,  T = 293 K.

Transport

M=91s/D   Rs=215/D20,w    s=2.4 M/Rs       f/fo=4.32M2/3/s (&delta1=0.3)

For the equivalent sphere

&delta1=0.0

Ro=20/3 M1/3        so=M2/3/2.8           M = 5.6 so3/2

&delta1=0.3

Ro=30/4 M1/3        so=M2/3/3.2           M = 4.7 so3/2

For the random coil

&delta1=0.0

Rs = 10.0 M0.56            src = 0.24 M0.44

For a prolate ellipsoid

for a/b > 5.0,    f/fo=(a/b)2/3/ln(2a/b)

For dc/dt analysis

Δt/t = Δln(&omega2t) <  70/(M1/2speed)

D = (σω2trmen)2/2t  (σ= std dev of g(s*)in Svedbergs)

Equilibrium

For σ > 2.0 cm-2 , where &sigma = d(lnc)/d(r2/2)=M(1-v ρ)ω2/RT

teq,5o=40000/(speed)2/s20,w    hours   (τ=0.22) (column height=3mm) (Mason's Rule)

teq,5o=17000 (Rs/M)/(speed)2   hours   (τ=0.22)   &tau=2ω2st=2ln(rb/rm)

tos/teq=0.134(σ)0.58/((ωoseq)2-0.5)  (c.f. D.E. Roark, 1976)

For σ > 0:

Compute time to equilibrium - any speed

speedeq=88[σ/M]1/2;   M=[σ/(speedeq/88)2] and σ = M(speedeq/88)2

Walter Stafford - May 8, 2006