Spinning Drop Dynamics in Miscible and Immiscible Environments

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. ,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) ∼ t 2 5 in very good agreement with the dynamics predicted by Lister and Stone (J. Fluid Mech. , ( )) 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. arXiv:1907.02802v1 [cond-mat.soft]

Spinning elastic beads: a route for simultaneous measurements of shear modulus and interfacial energy of soft materials

“…Fluorescent labelling was therefore needed to track the bead deformation. Under the illumination of the blue LED light, fluorescein-rich beads appear as bright green-yellow regions, since the fluorescein adsorption and emission spectra (in polar solvents) are peaked at λ ≈ 485 nm and λ ≈ 511 nm [32,45,46], respectively.…”

“…Though an SDT is usually employed to measure low liquid-liquid interfacial free energies [29][30][31], recently it has been used also for purposes ranging from the study of the relaxation dynamics of liquid drops [32] and the presence of an effective interfacial tension in miscible fluids [32][33][34], to the characterization of the mechanical properties of thin elastic capsules [35] and viscoelastic properties of polymer melts [36,37].…”

Shapes of a rising miscible droplet

“…For instance, one of the most recent experimental study, designed to measure the surface tena) Electronic mail: A.Vorobev@soton.ac.uk sion coefficient at a miscible (glycerol-water) interface by using the spinning drop tensiometry technique, turned out with the conclusion that the correct description of the dynamics of a miscible droplet in a spinning tensiometer does not require the use of the surface tension. 9 The authors even state that the earlier measurements 5,6 that were conducted with the use of the spinning drop tensiometer need revision.…”

Ultra-low effective interfacial tension between miscible molecular fluids

“…Such a transient, out-of-equilibrium interfacial tension has been invoked in literature to rationalize the behaviour of miscible fluids at short times, before they are fully mixed, and several works tried to elucidate the role of stresses at miscible boundaries, both theoretically [7][8][9][10][11][12] and experimentally. Among the strategies adopted to measure the EIT between miscible fluids, the most recent ones leverage on the study of hydrodynamic instabilities [5,13], on light scattering experiments probing capillary waves [6,14] and on the observation of the shape of drops and threads under an external forcing [15][16][17]. Despite of this effort, the magnitude and even the very existence of EIT between simple molecular fluids is still debated and mostly unclear.…”

“…A second possibility is to characterize the time evolution of the drop after a sudden rotational speed jump. Recently, we have employed this technique to study the elongation dynamics of drops, both in miscible and immiscible background fluids [16], showing that the drop dynamics towards an equilibrium state are characterized by a relaxation time fully determined by i) the viscosity of the fluids, ii) the drop size and iii) the interfacial tension. In the past few decades, SDT experiments aiming at measuring equilibrium states have been performed by several groups to investigate the presence of an EIT between miscible fluids, either close [15] or far from a spinodal decomposition of the fluids [21,22].…”