One-dimensional reduction of viscous jets. II. Applications

Pitrou, Cyril

doi:10.1103/physreve.97.043116

Cited by 2 publications

(3 citation statements)

References 20 publications

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“…We have developed all the theoretical tools which are required to obtain a general one-dimensional description of curved fibers. A concrete application for toroidal viscous fibers is presented separately in Pitrou (2018). From a theoretical point of view, our 2 + 1 splitting, our use of fiber adapted coordinates, and more importantly our parametrization of the velocity field in terms of STF tensors allow for a clear discussion about constraints and dynamical equations.…”

Section: Discussionmentioning

confidence: 99%

“…Several technical developments are gathered in the Appendices, among which the symmetric trace-free tensors in Appendix A which we use throughout the article. The formalism is applied to study toroidal viscous fibers in Pitrou (2018).…”

Section: Outlinementioning

confidence: 99%

“…This improved rod model is necessary to compute in Ref. Pitrou (2018) the Rayleigh-Plateau instability of a viscous fibers. The validity of rod models is limited by the fact that we are considering one correction while discarding other sources of corrections, whereas in our approach we systematically consider all corrections of order 2 R .…”

Section: Rod Models and Their Validitymentioning

confidence: 99%

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One-dimensional reduction of viscous jets. I. Theory

Pitrou

2018

Phys. Rev. E

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We build a general formalism to describe thin viscous jets as one-dimensional objects with an internal structure. We present in full generality the steps needed to describe the viscous jets around their central line, and we argue that the Taylor expansion of all fields around that line is conveniently expressed in terms of symmetric trace-free tensors living in the two dimensions of the fiber sections. We recover the standard results of axisymmetric jets and we report the first and second corrections to the lowest order description, also allowing for a rotational component around the axis of symmetry. When applied to generally curved fibers, the lowest order description corresponds to a viscous string model whose sections are circular. However, when including the first corrections, we find that curved jets generically develop elliptic sections. Several subtle effects imply that the first corrections cannot be described by a rod model since it amounts to selectively discard some corrections. However, in a fast rotating frame, we find that the dominant effects induced by inertial and Coriolis forces should be correctly described by rod models. For completeness, we also recover the constitutive relations for forces and torques in rod models and exhibit a missing term in the lowest order expression of viscous torque. Given that our method is based on tensors, the complexity of all computations has been beaten down by using an appropriate tensor algebra package such as xAct, allowing us to obtain a one-dimensional description of curved viscous jets with all the first order corrections consistently included. Finally, we find a description for straight fibers with elliptic sections as a special case of these results, and recover that ellipticity is dynamically damped by surface tension. An application to toroidal viscous fibers is presented in the companion paper [Pitrou, Phys. Rev. E 97, 043116 (2018)10.1103/PhysRevE.97.043116].

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Section: Discussionmentioning

confidence: 99%

Section: Outlinementioning

confidence: 99%

Section: Rod Models and Their Validitymentioning

confidence: 99%

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