Why does density increases when adding nanoparticles in a mixture of water and some clay?
If your question is why density increases with the addition of nanoparticle then i have to recommend this quora post.


  If the attractive forces between the constituent particles of the
  solid with the water molecules are high enough, the total amount of
  intermolecular space is reduced and the total volume of the solution
  can be smaller that the combined volume of its components, leading to
  an extra increase in density....


Surface of silica nanoparticles have siloxane($Si-O-Si$) and silanol ($Si-OH$) groups. Because of the presence of these functional groups silica nanoparticles tend to form hydrogen bonds between themselves and/or with other polar molecules such as water. Its these interactions which reduces the intermoleculr space which further reduces the volume thus increase in density.

If the silica nanoparticles interect with themselves and form a linked three dimensional networks then it will also increase the viscosity of the solution.