Water treatment is part of sanitary engineering. Chemists and civil engineers have some knowledge in this field. But it can be said that this is a multi-faceted field for which knowledge about biology, microbilogy, hydraulics and many others is needed. It is not a full specialty of chemistry or civil engineering. It is rather the sanitary engineering.
Water treatment is an important subject in environmental engineering departments today. In addition, the main topic of many researchers in environmental engineering is water treatment. On the other hand, environmental engineering is a multidisciplinary discipline. Civil engineers, chemists, chemical engineers, biologists are usually science branches that give the most researchers to environmental engineering science branches. So, yes, research topics of water treatment can be related to area of chemical and civil enginnering discipline.
Depending on the type of water pollution to be treated, the application field will probably defer. Water treatment may be for industrial effluents; domestic sewerage; drinking water; etc. The main specialization one looks upto is a scientist with chemistry background, if it for chemical analysis & treatment. However if the function of water treatment is towards developing treatment plants or network designing or instruments itself, then one needs specialists in the field of Chemical Eng; Public Health Eng; Environmental Eng; Instrumental Eng; Industrial Engineering; Water Supply & Sanitation Eng; Some of these specialized topics are of course covered in the Civil Eng. Any way now a days one solves the problem involving multiple specialization, giving equal importance to all fields of science (including social science) and engineering.
Water treatment is part of general engineering. Chemists, civil engineers, hydraulic engineers, biology engineers, food engineers, agriculture engineers and so on. All these engineers types have knowledge in one of the following fields related to water industry: Physic- chemical Treatment methods, analysis and characterization, Biological treatments, transport, diffusion, maintenance, and so on. So the question of water is a multi-faceted field. All engineering types cited can contribute in water management.
The treatment of both types of water (drinking water, waste water) depends on the overlap of many sciences, not limited to civil engineering and chemistry. I agree with what Dr. Emad Kamil explained on that point.
Nature of waste water is playing a sole role in treatment procedure, means, medical waste water in totally different from domestic waste water, and so on, so that means, it is important to add more expertise persons to the above mentioned list in all posts based on the source of the waste water.