Approximating stationary deformation of flat and toroidal drops in compressional viscous flow using generalized Cassini ovals

Lavrenteva, Olga M.; Ee, Bernard K.; Smagin, Irina; Nir, A.

doi:10.1017/jfm.2021.483

Cited by 4 publications

(19 citation statements)

References 27 publications

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“…Generalized Cassini ovals approximation gives similar shapes, yet with some minor deviations, and the normal velocity is of the same order of magnitude as the method of Zabarankin et al (2015). For smaller values of Ca, the accuracy of all the methods improves and the difference in shapes decreases dramatically (see Lavrenteva et al 2021).…”

Section: Conclusion and Discussionmentioning

confidence: 85%

“…In the application to toroidal drops, this approach was discussed in Zabarankin et al (2015). Lavrenteva et al (2021) considered a three-parameters family of axisymmetric bodies, with cross-sections of generalized Cassini ovals, and obtained branches of stationary shapes of singly connected and toroidal drops embedded in axisymmetric biextensional flow. This method requires finding a minimum of a function of several real variables and, thus, it is highly effective.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…The comparison of shapes and interfacial normal velocities obtained by the three methods for Bo = 0, Ca = 0.18 and Ca = 0.19 is presented in figure 11, respectively. Solid, dashed and dashed-dotted lines present the results of the method of this paper, Zabarankin et al (2015) and (Lavrenteva et al 2021), respectively. One can see that the shapes obtained by simulating controlled and uncontrolled dynamics are almost indistinguishable, while the normal velocity obtained by the method of this paper is two to three orders of magnitude lower.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…The 'stationary' circular tori agree satisfactorily with the numerical shapes only for small values of Ca, however, they provide a quite good approximation for the starting point that leads to a stationary shape in numerical simulations. Lavrenteva et al (2021) suggested a generalized Cassini ovals approach for the approximation of both toroidal and simply connected stationary drops in compressional flow (Bo = 0). Zabarankin et al (2015) also presented results of fitting the stationary shapes obtained by using quasidynamic simulations with shapes depending on a higher number of parameters.…”

Section: Dynamic Deformations and Stationary Statesmentioning

confidence: 99%

“…In the application to toroidal drops, this approach was discussed in Zabarankin et al (2015). Lavrenteva et al (2021) considered a three-parameter family of axisymmetric bodies with cross-sections of generalized Cassini ovals and obtained branches of stationary shapes of singly connected and toroidal drops embedded in axisymmetric biextensional flow.…”

Section: Introductionmentioning

confidence: 99%

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Controlled stabilization of rotating toroidal drops in viscous linear flow

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Toroidal drops, embedded in viscous flow, have a large range of stationary shapes that are challenging to compute numerically due to their inherent instability. When both the drop and the outer fluid are Newtonian liquids, the only reported cases of such stable configurations are of highly expanded drops rotating in an axisymmetrical extensional flow. In this study, we propose a method for stabilizing the stationary shapes of inherently unstable rotating toroidal drops, embedded in extensional or biextensional flow, by subjecting the system to feedback control stabilization. The proposed controller is designed using a two-state dynamic model of the system and is tested on a high-order nonlinear dynamic model of the drop deformation. It is demonstrated that, through this simplified feedback-control-centred approach, an extended collection of stabilized stationary solutions is generated, which spans the range from highly expanded drops to almost collapsed ones. In the latter region, that was never obtained in previous studies, multiplicity of solutions is identified. Furthermore, our method is more accurate and more efficient compared with the previously used ones.

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Section: Conclusion and Discussionmentioning

confidence: 85%

Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Dynamic Deformations and Stationary Statesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stationary dimpled drops under linear flow

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Idan

et al. 2024

J. Fluid Mech.

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The axially symmetric deformation of a drop in a viscous fluid, under the influence of an externally imposed flow having simultaneous rotating and compressional or extensional components, is addressed. In the previous studies, two families of stationary drop shapes were constructed by simulating the dynamics of drop deformation: stable singly connected shapes with respect to axisymmetric disturbances, and unstable toroidal shapes. These two branches coexist at the same flow conditions, but were not connected. In this study, we obtain a new family of branches of unstable highly deformed stationary drops connecting with the stable flattened shapes and the toroidal ones. We use a method based on classical control theory. The controller is designed for a two-state dynamic model of the system and is employed on a high-order nonlinear dynamic model of the drop deformation. Through this feedback-control-centred approach, an extended collection of unstable stationary solutions is constructed, which spans the range from the loss of stability to the dimpled shapes almost collapsed at the centre. In the latter region, which was never obtained in previous studies, a multiplicity of solutions is identified.

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Approximating stationary deformation of flat and toroidal drops in compressional viscous flow using generalized Cassini ovals

Abstract: Abstract

Cited by 4 publications

References 27 publications

Controlled stabilization of rotating toroidal drops in viscous linear flow

Controlled stabilization of rotating toroidal drops in viscous linear flow

Dynamic and stationary shapes of rotating toroidal drops in viscous linear flows

Stationary dimpled drops under linear flow

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