EQUILIBRIUM-STATE DENSITY PROFILES OF CENTRIFUGED CAKES

We have examined the equilibrium-state density profiles of centrifuged cakes both theoretically and experimentally. The theoretical density profiles were obtained by implementing the experimental pressure-density relationship into the general differential equation for centrifugation with appropriate boundary conditions. With a power-law pressure-density relationship, P = beta phi(n), we show that phi(Z)/phi(max) = (1 - Z/Z(m))(1/(n - 1)) where phi(max) is the density at the bottom of the cake, Z the distance measured from the bottom of the cake, and Z(m) the distance at which the cake density vanishes. Experimentally, the density profiles were examined with gamma-ray densitometry. The predicted density profiles are in good agreement with the experimental ones. We also show that form phi(Z)/phi(max) = (1 - Z/Z(m))(1/(n - 1)) applies to sedimentation cakes as well, provided the pressure-density relationship of sedimentation cakes is also a power-law one.