Solubility of potassium silicate in water
Potassium silicate is synthesized by melting $\ce{KOH}$ above $400$°C, and adding some solid $\ce{SiO2}$. Its composition depends on the amount of silica used. The dissolution process does not look so. But it is a slow chemical reaction with a rather viscous liquid. The result can be cooled down and gives a solid substance practically insoluble in water at room temperature.
However it is possible to dissolve it with boiling water under pressure. Surprisingly enough, the obtained potassium silicate becomes more easily dissolved at $T&gt;80$°C under pressure. The concentrated solution so obtained can be cooled down. It yields an extremely viscous liquid, more viscous than honey. This liquid is usually not really transparent, but it can be diluted with pure water without producing a precipitate. Such solutions are probably colloidal solutions of $\ce{H2SiO3}$ or $\ce{H4SiO4}$ in a concentrated solution of $\ce{KOH}$. As a matter of fact, if such a solution is heavily diluted, neutralized to destroy KOH, washed and evaporated in a vacuum, hydrated silica is obtained and it is made of $\ce{H2SiO3}$ flakes which are extremely light : the density of the stuff is not much bigger that air, as if it was made of rather long chains $\ce{HO -[- Si(OH)2 - O -]_n-H}$ sometimes directed in all directions around a central Silicium atom.
The chemistry of the silicic acid and its salts is extremely complex. The ternary diagram $\ce{Na2O - SiO2 - H2O}$ contains $11$ different phases.
Ref.: J. G. Vial, Soluble silicates, Reinhold, New York, 1952.
N. Greenwood, A. Earnshaw, Chemistry of the Elements, Pergamon, 1986, § 9.3.4. p. 398