We employ a particle-in-cell Monte Carlo collision/particle-particle particle-mesh simulation to study the plasma flow around and the charge distribution of a three-dimensional dust cluster in the sheath of a low-pressure rf argon discharge. The geometry of the cluster and its position in the sheath are fixed to the experimental values, prohibiting a mechanical response of the cluster. Electrically, however, the cluster and the plasma environment, mimicking also the experimental situation, are coupled self-consistently. We find a broad distribution of the charges collected by the grains. The ion flux shows on the scale of the Debye length strong focusing and shadowing inside and outside the cluster due to the attraction of the ions to the negatively charged grains, whereas the electron flux is characterized on this scale only by a weak spatial modulation of its magnitude depending on the rf phase. On the scale of the individual dust potentials, however, the electron flux deviates in the vicinity of the cluster strongly from the laminar flow associated with the plasma sheath. It develops convection patterns to compensate for the depletion of electrons inside the dust cluster.

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