An oscillating droplet of oil becomes unstable when the kinetic energy is sufficient to make up for the difference in the surface energy between the single droplet and the two smaller droplets formed from it. At the same time that this process is occurring, the motion of the smaller oil particles is causing coalescence to occur. Therefore, it should be possible to define statistically a maximum droplet size for a given energy input per unit mass and time at which the rate of coalescence equals the rate of dispersion.
One relationship for the maximum particle size that can exist at equilibrium was proposed by Hinze as follows:
It can be seen that the greater the pressure drop and thus the shear forces that the fluid experiences in a given period of time while flowing through the treating system, the smaller the maximum oil droplet diameter will be. That is, large pressure drops that occur in small distances through chokes, control valves, desanders, etc., result in smaller droplets.
The dispersion process is theoretically not instantaneous. However, it appears from field experience to occur very rapidly. For design purposes, it could be assumed that whenever large pressure drops occur, all droplets larger than dmax will instantaneously disperse. This is, of course, a conservative approximation.