In Chemistry, What is Miscibility? Article from Frostburg University
Miscibility is the ability of two liquids to mix with each to form a homogeneous solution. Water and ethanol, for example, are miscible. They can be mixed in any proportion, and the resulting solution will be clear and show only one phase. Oil and water, on the other hand, are immiscible. A mixture of vegetable oil and water will always separate into two layers, and won't dissolve in each other.
Other solvents are only partially miscible, meaning that only some portion will dissolve in water.
Most of the liquids encountered in everyday life are either water-based, called aqueous, or organic, which in the chemical sense means they contain carbon atoms. These can generally be divided into two broad classes. They're either polar or nonpolar. Polar molecules are molecules that have a positive end and a negative end. Nonpolar molecules do not have positive and negative ends. They have the same charge or no charge throughout the molecule.
Why don’t they dissolve? Like dissolves Like!
Polar solvents are miscible with polar solutes. Nonpolar solvents are miscible with nonpolar solutes.
Polar solutes like salt, NaCl, is easily dissolved by polar solvents like water. The figure to the left shows how water molecules dissolve a salt crystal because of the polarity. The positive end of water molecules are attracted to the negative chlorine ions and the negative end of the water molecules are attracted to positive sodium ions.
Immiscible solvents are those that do not mix. Water and oil are immiscible because water is polar and oil is nonpolar.