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Phase stacking diagram of colloidal mixtures under gravity
The observation of stacks of distinct layers in a colloidal or liquid mixture
in sedimentation-diffusion equilibrium is a striking consequence of bulk phase
separation. Drawing quantitative conclusions about the phase diagram is,
however, very delicate. Here we introduce the Legendre transform of the
chemical potential representation of the bulk phase diagram to obtain a unique
stacking diagram of all possible stacks under gravity. Simple bulk phase
diagrams generically lead to complex stacking diagrams. We apply the theory to
a binary hard core platelet mixture with only two-phase bulk coexistence, and
find that the stacking diagram contains six types of stacks with up to four
distinct layers. These results can be tested experimentally in colloidal
platelet mixtures. In general, an extended Gibbs phase rule determines the
maximum number of sedimented layers to be , where is the
number of binodals and is the number of their inflection points
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