Studying density On earth when 2 immiscible liquids with unequal densities are kept together in a container, one with lower density moves up. But what will happen if we do the same somewhere where gravity is not present?
 A: If the two liquids would sediment separately under gravity, then they must be essentially immiscible. In the absence of gravity, the predominant energy penalty is the existence of a surface or interface between the two liquids. (A surface requires additional energy because some bonds aren't satisfied, as they would be in the bulk.)
Therefore, over time, an emulsion will "ripen" or "coarsen" in a process in which large droplets grow and small droplets shrink and disappear as molecules of liquid A diffuse through liquid B and vice versa. This molecular motion is governed by the fact that small droplets, which contain proportionally more surface, are relatively energetically unfavorable. 
The equilibrium condition is half of the jar consisting of liquid A and half consisting of liquid B (assuming the initial volumes were equal), although the orientation of the interface will be independent of gravity (and will instead likely be governed by the geometry or surface chemistry of the jar).
A: If the liquids are completely still and initially one on top of another, in theory they wouldn't move. However, movements within the liquid (Brownian etc.) would ultimately set inertia into flow, and the whole thing would float away chaotically. 
