The special-function expansion method is used to solve the sedimentation problem of polydisperse colloid particles with thin double layer. The pair-distribution function is expanded into Legendre polynomials. The recurrence formulas for calculating the coefficients of the Legendre polynomials and the expressions for calculating the sedimentation coefficient are deduced analytically. Then, the sedimentation of polydisperse particles with thin double layer at small Peclet number is analyzed numerically by the perturbation method. Results indicate that the sedimentation of potential interacting particles is more complex than that of the hard spheres, and the existence of the thin double layer affects the particles settling heavily. Critical double-layer thickness exists, without which a colloid system may change from a stable one into an unstable one and the hindered settling may change into accelerated settling.
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