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In trying to understand some fluid-dynamic principles, I am trying to discern between a couple water droplet interactions. This droplet video demonstrates the scenarios properly, but unfortunately doesn’t afford a ton of explanation related to the supporting math.

Combining Droplets
Somewhere around 00:15 two droplets combine in the bottom corner of the screen.

two droplets combining

Cohabiting Droplets
Whereas the video seems a bit more interested in droplets chasing each other.

a droplet chasing another

Forces related to surface tension are definitely at play - and perhaps density as well. But I'm trying to understand what exactly would determine whether two droplets combine or maintain some level of independence. For ex, if we were to track two colliding droplets that were to combine, what threshold in the formula would need to be crossed to convert from colliding to unionized droplets.

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A kind soul on Reddit found the study from the video in question. From what I understand, droplets in contact with each other will eventually combine, but that process is slowed depending on the concentration of each liquid. In the source video, those concentrations refer to varying mixtures of propylene glycol and water. Two droplets of differing concentrations will take longer to coalesce, which creates an extended 'chase sequence.' Here's the related quote from the study:

Droplets of sufficiently different concentrations can undergo a prolonged ‘chasing phase’26 as explained by Riegler and Lazar30 (Fig. 1b). Fluid is directly exchanged between the droplets, as visualized by a fluorescent dye (Supplementary Video 7). This exchange of fluid leads to a surface tension gradient across both the droplets, where the droplet of lower surface tension ‘chases’ the droplet of higher surface tension, which in turn ‘flees’ away30. Additional subtleties of short-range interactions can be obtained by adjusting concentrations and volumes (Supplementary Information, Extended Data Fig. 7).

And one of the provided figures:

supplemental figure from study

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