An experimental and theoretical study is proposed for low temperature plasmas that contain particulates. A plasma is an ionized gas, and in this work we will concentrate on weakly- ionized plasmas of the kind that are used widely in industry for manufacturing semiconductors, optical materials, and magnetic media. In a plasma, particulates (i.e. micron-size dust particles) become electrically charged. They also may grow in size by collecting sputtered atoms in the plasma. Particulates are a costly problem industrial uses of plasma processing because they can fall to a substrate and contaminate it. This is the motivation for this work. Experiments will be carried out to observe the time and density dependence of electrical charging of dust grains. These measurements will employ optical detection of grains in parallel-plate radio-frequency plasmas, and the results will be used to test theories of particulate charging in plasmas. Theoretical modeling will be performed to simulate the trapping of ions by charged grains. Negatively charged grains can trap positive ions in confined orbits, and this cause a reduction in the net electric forces that the charged grains experience. This modeling will employ numerical simulations of the motion of ions, including collisions with neutral atoms as well as the electric force created by charged grains.