It depends on the quantity, the type of particles and the size dsitribution.. I guess. If they are crystalline and "not in a very small volume fraction" you can consider x-ray or neutron diffraction. If they are sufficiently diluted you can also consider small angle scattering
I was posing question for natural systems where we can expect different nano-particles in addition to other water constituents.
In synthetic solution, this question still holds. The objective is to understand stability of these NPs in terms of their properties (chemical and physical), applicability and final fate.
sorry, one can not answer such general questions; colloidal systems are very particular, every type of nanoparticle in different systems behave differently; even the same type of nano-particle if available in different particle size or particle size distribution is already different.
As a general answer, I would follow the particle size distribution over time when keeping the colloidal system at room temperature (or whatever temperature you are concerned with, but please keep in mind: temperature has a huge impact on stability! can be positive, can be negative!)