Equilibrium‐State Density Profiles of Centrifuged Cakes

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Abstract
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 =βφn, we show that where φmax is the density at the bottom of the cake, z the distance measured from the bottom of the cake, and zm the distance at which the cake density vanishes. Experimentally, the density profiles were examined with γ‐ray densitometry. The predicted density profiles are in good agreement with the experimental ones. We also show that the form applies to sedimentation cakes as well, provided the pressure‐density relationship of sedimentation cakes is also a power‐law one.

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