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 R_s=215/D_20,w    s=2.4 M/R_s       f/f_o=4.32M^2/3/s (&delta₁=0.3)

For the equivalent sphere

&delta₁=0.0

R_o=20/3 M^1/3 s_o=M^2/3/2.8 M = 5.6 s_o^3/2

&delta₁=0.3

R_o=30/4 M^1/3 s_o=M^2/3/3.2 M = 4.7 s_o^3/2

For the random coil

&delta₁=0.0

R_s = 10.0 M^0.56 s_rc = 0.24 M^0.44

For a prolate ellipsoid

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

For dc/dt analysis

  Δt/t = Δln(&omega²t) < 70/(M^1/2speed)

  D = (σω²tr_men)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

t_eq,5^o=40000/(speed)²/s_20,w hours (τ=0.22) (column height=3mm) (Mason's Rule)

t_eq,5^o=17000 (R_s/M)/(speed)² hours (τ=0.22)   &tau=2ω²st=2ln(r_b/r_m)

t_os/t_eq=0.134(σ)^0.58/((ω_os/ω_eq)²-0.5)  (c.f. D.E. Roark, 1976)

For σ > 0:

Compute time to equilibrium - any speed

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

Walter Stafford - May 8, 2006