||In this work, the structure of plasma sheaths in presence of dust particles with different sizes is investigated numerically in a multifluid framework, where the dust size distribution is modeled by Gauss' law. For this, we have established a 1D, stationary, unmagnetized, and weakly collisional electronegative dusty plasma sheath model. The electrons and negative ions are considered in a local thermodynamic equilibrium, therefore, described by a Boltzmann distribution. On the other hand, positive ions and dust grains are described by fluid equations. The charging process is described by the orbit motion limited model. It is shown that taking into account dust grains with different sizes reduces considerably the sheath thickness. The behavior of dust surface potential is not affected, but the dust charge number is reduced, as well as the electrostatic force. It results in a decrease of layered structure. The presence of negative ions makes the structure of the electrostatic potential more oscillatory. The other physical parameters are also analyzed and discussed. (C) 2013 American Institute of Physics.