What governs the merging of globs of inmiscible liquid?
Emulsion chemistry is actually rather complicated, but I'll try to give a conceptual description. Whenever you have a surface dividing two phases, there is an energy associated with creating a certain amount of surface, expressed as a surface energy density with dimensions of energy divided by area. This represents the energy cost of disrupting the intermolecular interactions of each phase at the interface, e.g. for your water/chloroform system, water can't hydrogen bond across the interface so it takes energy to break all the bonds required to make the surface. The larger the surface area, the more energy it takes. Logically, you can see that the lowest energy state is the one in which the interfacial area is minimized, which is why in the absence of external forces like gravity, liquids assume spherical shapes which give the smallest surface area for a given volume.

When you have many small droplets, there is a large surface area to volume ratio which is a high energy state, so it is energetically favourable for the droplets to form larger droplets. However, the reason it doesn't occur instantaneously is that an energy barrier can exist between the two states, for various reasons (electrostatic repulsion is a big one). In most cases, smaller droplets are lost first because the energy barrier to coalescing is surface area dependant. Larger droplets are more stable. Depending on the liquids, different separation mechanisms can occur with different kinetics. (coalescence, Ostwald ripening) I can't give a definite answer, but I'm guessing in your system you would not see an exponential decay-type half-life as that assumes a stochastic process where the probability is always the same. Since the stability depends on surface area, this isn't true in this case.