Osmosis is fundamental to many processes, such as in the function of biological cells and in industrial desalination to obtain clean drinking water. The choice of solute in industrial applications of osmosis is highly important in maximizing efficiency and minimizing costs. The macroscale process of osmosis originates from the nanoscale properties of the solvent, and therefore an understanding of the mechanisms of how these properties determine osmotic strength can be highly useful. For this reason, we have undertaken molecular dynamics simulations to systematically study the influence of ion size and charge on the strength of osmosis of water through carbon nanotube membranes. Our results show that strong osmosis occurs under optimum conditions of ion placement near the region of high water density near the membrane wall and of maintenance of a strong water hydration shell around the ions. The results in turn allow greater insight into the origin of the strong osmotic strength of real ions such as NaCl. Finally, in terms of practical simulation, we highlight the importance of avoiding size effects that can occur if the simulation cell is too small.