Yea! There is a state of matter called "superfluid"

A superfluid is a liquid of zero viscosity (think superconductors, which have zero resistance). It can flow without loss of kinetic energy. If you put it in a container, it creeps up the walls and flows out. It cannot be contained! Superfluids have no entropy and have infinite thermal conductivity. Therefore, it is impossible to define a temperature gradient in a superfluid.

One of the most fascinating results of these characteristics is the thermomechanical effect: if a capillary tube is placed in a tank of superfluid helium, and this is heated (even by a light), the superfluid will rise along the tube until it leaves the other leader, as result of the Clausius-Clapeyron reaction.

An important application of superfluids is in dilution chillers:

What determines whether two liquids are “mixable”?

The technical term you refer to in this question is miscibility or solubility, which actually refers to the ability of one liquid to mix with another. In fact, the most important aspect that determines the possibility of one being soluble or not in another depends on the type of chemical bond of its molecules and the forces involved, something that classifies compounds from polar to non-polar.

When a liquid is polar, it means that it has established charges, the poles so to speak, and so it can only mix with other liquids that also have charges and so opposites attract. Polar liquids are well characterized by having very electronegative atoms in their composition and good examples of this are water and ethanol, both endowed with oxygen that generates a negative extreme (by the attraction of electrons from adjacent atoms) and a positive one (by the deficiency of electrons) – the poles that give them the definition.

Examples of polar (top) and non-polar (bottom) molecules. Note that in polars there is an electronic attraction that generates a charge and so your liquids can only be mixed with other equally polar liquids.

In the case of non-polar liquids, there is no “formal” electrical charge, either because they do not contain electronegative atoms, because they contain them in very small numbers compared to others that are not electronically charged, or because they have electronegative atoms but whose chemical spatial arrangement generates a zero vector of forces. That’s why liquids like this are called non-polar and can only mix with others with the same lack of electronic charges, examples of which are oils, hexane, benzene and carbon tetrachloride.

An example of apolarity in which fluorine atoms create a zero vector of forces as they have the same electronegativity. In this way a boron trifluoride liquid can only be mixed with other non-polar liquids.

Finally, it is important to point out that there are compounds that compose “median polarity” liquids, as they are able to partially mix in polar or nonpolar compounds. This fact is possible due to the weak character of one or the other, being a well-established parameter in organic chemistry and that can be checked in different databases. Among some good examples of this is Ethyl Acetate and Butanol.