One-dimensional dynamics of nearly unstable axisymmetric liquid bridges

Perales, José Manuel Perales; Vega, José M.

doi:10.1063/1.3516640

Cited by 4 publications

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References 36 publications

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“…The breakup of inviscid liquid bridges at the minimum-volume stability limit was first analyzed from the slice model [22]. The nonlinear oscillations and the breakup of liquid bridges in this parameter region have recently been examined using both a one-dimensional viscous model [23] and the inviscid Navier-Stokes equations [24]. Neither the linearized nor the full viscous Navier-Stokes equations have been solved to analyze the liquid bridge dynamics at the minimum-volume stability limit.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of an axisymmetric liquid bridge close to the minimum-volume stability limit

et al. 2014

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We analyze both theoretically and experimentally the dynamical behavior of an isothermal axisymmetric liquid bridge close to the minimum-volume stability limit. First, the nature of this stability limit is investigated experimentally by determining the liquid bridge response to a mass force pulse for volumes just above that limit. In our experiments, the liquid bridge breakup takes place only when the critical volume is surpassed and is never triggered by the mass force pulse. Second, the growth of the small-amplitude perturbation mode initiating the liquid bridge breakage is measured experimentally and calculated from the linearized Navier-Stokes equations. The results of the linear stability analysis allow one to explain why liquid bridges with volumes just above the stability limit are so robust. Finally, the nonlinear process leading to the liquid bridge breakup is described from both experimental data and the solution of the full Navier-Stokes equations. Special attention is paid to the free-surface pinchoff. The results show that the flow becomes universal (independent of both the initial and boundary conditions) sufficiently close to that singularity and suggest that the transition from the inviscid to the viscous regime is about to take place in the final stage of both the experiments and numerical simulations.

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Section: Introductionmentioning

confidence: 99%

Dynamics of an axisymmetric liquid bridge close to the minimum-volume stability limit

et al. 2014

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“…The validity of these methods has been studied in details in the subsequent literature, e.g. in Perales and Vega (2010), , or Vincent et al (2014). In § VI, we recover the standard lowest order results plus first corrections using the radial expansion method.…”

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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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