My experiment of injecting radial conductive flow (no rotation) of a less viscous fluid into a more viscous one was unique in that the fluids were highly viscous to start with. That high viscosity dropped out the rotational, time-based terms on the left side of the Energy Equation. Since the video camera used captured only 35 frames per second, slowing the behavior was paramount and this was done by raising the viscosity, thus slowing the droplet’s oscillatory frequency.

During my experiments that covered injecting a less viscous fluid into a more viscous fluid, I chose three different (equally spaced) viscosity contrasts and three different (equally spaced) flow rates. But I also had some fun in attempting to see what would happen as one fluid expanded into another when the inner water-based fluid was injected into an outer oil-based fluid that had a nearly equal viscosity to the inner fluid.

Surprisingly the expanding interface between the two fluids began growing inward as if it were cleaving the inner fluid.

The first step in the unsteady process of the inner fluid expansion is always the circular interface shifting to one side of the injection hole. When plotting the amplitude of the interface about the average radius (equipotential flow field), we see that the shift, or offset, is the first sine wave incident on the interface.

The smaller the difference in viscosities across the interface, the later the wave troughs begin to form, the more waves are incident on the interface, and the greater the resulting curvature.

When the inner and outer fluids have the same viscosities then the interface is relatively stable. But when the inner fluid is a very small amount less in viscousity, then there is still the problem of the outer fluid not being forced out of the way fast enough. The expanding droplet offsets from its injection hole (source) when the first random perturbation is encountered.

But the interface or circular inner fluid is stable enough to disallow a disturbance by any further perturbations.

So, in this case of one offset wave, initially the curvature of the interface is extremely low and constant. That is consistent with what was seen in other tests, that the smaller number of waves form early and have low curvature. However, as time proceeds, the one trough formed from the first wave superimposing on the interface takes on an extremely high curvature and appears to burrow into and equally divide the circular inner fluid.

Upon further observation, the flow field has appeared to change from pure conduction. Because the boundary of the inner water-based fluid becomes stable (impervious to perturbations attempting to cross it) instead of the flow continuing its radial conduction of fluid, the inner fluid is forced around the inside of the stable interface and grows the inner fluid into the wave crest.

Since all wave troughs when they initiate are stable localities at certain radial distances from the original centroid of the flow, the inner fluid appears to cleave itself. The inner fluid flows around its own narrow trough appearing to cut itself in two equal parts.

A primitive cell resting on a hot surface made up of comparable fluids would expand just enough to produce such a trough and complete its cell division amoebalike by cytoplasmic flow away from the trough initiation site.

[I will endeavor to find the video of this event which has been sent to an archeo bacteriologist, who offered me a position where I could further this research, but could not accept while building my family]

Following is another, more complex theory from a physicist that posits other motivations for the further evolutionary succession of life:

A new analog is developing in the theory of life, showing how it can be a ubiquitous phenomenon. link: https://www.quantamagazine.org/20140122-a-new-physics-theory-of-life/