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The curvature of the drop is influenced by the liquid-solid, solid-air and liquid-air interface forces. It can be determined by the Young-Laplace equation. For more details see this article


Turbulence is well defined in the bulk of the flow, hence in 3D in the examples you quote, while surface tension acts, well, at the surface! I believe a good reformulation of your question would be "will a flow be less chaotic with larger surface tension?" Surface tension is highly dependent on geometry. It stabilizes some flows (e.g. a not-too-shallow ...

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