# Spinning drop dynamics in miscible and immiscible environments

## TL;DR

This study investigates the spinning drop dynamics in miscible and immiscible fluids, revealing distinct relaxation behaviors and confirming theoretical models for each case, with implications for interfacial tension measurement.

## Contribution

It provides experimental validation of existing models for drop relaxation in immiscible fluids and uncovers indefinite elongation in miscible fluids, challenging assumptions about interfacial tension.

## Key findings

- Immiscible drops relax exponentially to equilibrium shape.
- Relaxation time matches predictions by Stone and Bush.
- Miscible drops elongate indefinitely with a power-law growth.

## Abstract

We report on the extensional dynamics of spinning drops in miscible and immiscible background fluids following a rotation speed jump. Two radically different behaviours are observed. Drops in immiscible environments relax exponentially to their equilibrium shape, with a relaxation time that does not depend on the centrifugal forcing. We find an excellent quantitative agreement with the relaxation time predicted for quasi-spherical drops by Stone and Bush (Q. Appl. Math. 54, 551 (1996)), while other models proposed in the literature fail to capture our data. By contrast, drops immersed in a miscible background fluid do not relax to a steady shape: they elongate indefinitely, their length following a power-law $l(t)\sim t^{\frac{2}{5}}$ in very good agreement with the dynamics predicted by Lister and Stone (J. Fluid Mech. 317, 275 (1996)) for inviscid drops. Our results strongly suggest that low compositional gradients in miscible fluids do not give rise to an effective interfacial tension measurable by spinning drop tensiometry.