That is way cool. I wonder what would happen if one were to embed a non-Newtonian fluid droplet - whether that would lead to different behavior (slow force application vs. shock)

I seem to remember that for some liuquids surface tension can be switched with an electric field. Adding that could create something like an 'integrity field' like in SciFi novels/series. That would be neat for earthquake-proofing buildings, as individual parts could be strengthened depending on the exact position of the shockwave.

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The interior of droplets is not a subject of flow or even sheer,

With deformation you get shear forces.