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Register a new userFaceting and flattening of emulsion droplets: a mechanical model
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Added by
Ireth Garc\\'ia-Aguilar
Publication date
2020
fields
Physics
and research's language is
English
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When cooled down, emulsion droplets stabilized by a frozen interface of alkane molecules and surfactants have been observed to undergo a spectacular sequence of morphological transformations: from spheres to faceted icosahedra, down to flattened liquid platelets. While generally ascribed to the interplay between the elasticity of the frozen interface and surface tension, the physical mechanisms underpinning these transitions have remained elusive, despite different theoretical pictures having been proposed in recent years. In this article, we introduce a comprehensive mechanical model of morphing emulsion droplets, which quantitatively accounts for various experimental observations, including the scaling behavior of the faceting transition. Our analysis highlights the role of gravity and the spontaneous curvature of the frozen interface in determining the specific transition pathway.
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In their Comment [arXiv:2102.03842], Haas et al. advance two hypotheses on the nature of the shape transformations observed in surfactant-stabilized emulsion droplets, as the theoretical models that us [Phys. Rev. Lett. 126, 038001 (2021)] and others [P. A. Haas et al. Phys. Rev. Lett. 118, 088001 (2017), Phys. Rev. Research 1, 023017 (2019)] have introduced to account for these observations. (1) Because of the different surfactants used in experimental studies, the physical mechanisms underpinning the shape transformations may, in fact, differ in spite of the extraordinary resemblance in the output. (2) The theoretical models are mathematically equivalent by virtue of the small magnitude of the stretching and gravitational energies. In this Reply, we argue that neither of these hypotheses is well justified.
We investigate the mechanical behavior of particle-stabilized droplets using micropipette aspiration. We observe that droplets stabilized with amphiphilic dumbbell-shaped particles exhibit a two-stage response to increasing suction pressure. Droplets first drip, then wrinkle and buckle like an elastic shell. While particles have a dramatic impact on the mechanism of failure, the mechanical strength of the droplets is only modestly increased. On the other hand, droplets coated with the molecular surfactant Sodium Dodecyl Sulfate are even weaker than bare droplets. In all cases, the magnitude of the critical pressure for the onset of instabilities is set by the fluid surface tension.
We use an elastic model to explore faceting of solid-wall vesicles with elastic heterogeneities. We show that faceting occurs in regions where the vesicle wall is softer, such as areas of reduced wall thicknesses or concentrated in crystalline defects. The elastic heterogeneities are modeled as a second component with reduced elastic parameters. Using simulated annealing Monte Carlo simulations we obtain the vesicle shape by optimizing the distributions of facets and boundaries. Our model allows us to reduce the effects of the residual stress generated by crystalline defects, and reveals a robust faceting mechanism into polyhedra other than the icosahedron.
The interplay between geometry, topology and order can lead to geometric frustration that profoundly affects the shape and structure of a curved surface. In this commentary we show how frustration in this context can result in the faceting of elastic vesicles. We show that, under the right conditions, an assortment of regular and irregular polyhedral structures may be the low energy states of elastic membranes with spherical topology. In particular, we show how topological defects, necessarily present in any crystalline lattice confined to spherical topology, naturally lead to the formation of icosahedra in a homogeneous elastic vesicle. Furthermore, we show that introducing heterogeneities in the elastic properties, or allowing for non-linear bending response of a homogeneous system, opens non-trivial pathways to the formation of faceted, yet non-icosahedral, structures.
The effect of a spatially uniform magnetic field on the shear rheology of a dilute emulsion of monodispersed ferrofluid droplets, immersed in a non-magnetizable immiscible fluid, is investigated using direct numerical simulations. The direction of the applied magnetic field is normal to the shear flow direction. The droplets extra stress tensor arising from the presence of interfacial forces of magnetic nature is modeled on the basis of the seminal work of G. K. Batchelor, J. Fluid Mech., 41.3 (1970) under the assumptions of a linearly magnetizable ferrofluid phase and negligible inertia. The results show that even relatively small magnetic fields can have significant consequences on the rheological properties of the emulsion due to the magnetic forces that contribute to deform and orient the droplets towards the direction of the applied magnetic vector. In particular, we have observed an increase of the effective (bulk) viscosity and a reversal of the sign of the two normal stress differences with respect to the case without magnetic field for those conditions where the magnetic force prevails over the shearing force. Comparisons between the results of our model with a direct integration of the viscous stress have provided an indication of its reliability to predict the effective viscosity of the suspension. Moreover, this latter quantity has been found to behave as a monotonic increasing function of the applied magnetic field for constant shearing flows (magneto-thickening behaviour), which allowed us to infer a simple constitutive equation describing the emulsion viscosity.
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