One-dimensional reduction of viscous jets. I. Theory.

@article{Pitrou2015OnedimensionalRO,
  title={One-dimensional reduction of viscous jets. I. Theory.},
  author={Cyril Pitrou},
  journal={Physical review. E},
  year={2015},
  volume={97 4-1},
  pages={
          043115
        }
}
  • C. Pitrou
  • Published 7 November 2015
  • Physics
  • Physical review. E
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… 

Figures and Tables from this paper

One-dimensional reduction of viscous jets. II. Applications.

The Rayleigh-Plateau instability is studied for periodic deformations around the perfect torus, and it is shown that the instability is not sufficient to lead to the torus breakup in several droplets before it collapses to a single spherical drop.

Formation of twisted liquid jets

Liquid jets issued from a non-circular orifice exhibit oscillation owing to the surface tension. When the orifice has an $n$-fold rotational symmetry, a material cross section of the jet interchanges

References

SHOWING 1-10 OF 35 REFERENCES

One-dimensional reduction of viscous jets. II. Applications.

The Rayleigh-Plateau instability is studied for periodic deformations around the perfect torus, and it is shown that the instability is not sufficient to lead to the torus breakup in several droplets before it collapses to a single spherical drop.

Torsional Effects in High-Order Viscoelastic Thin-Filament Models

An approximation theory for thin filaments, fibers or jets which yields families of transient 1-D models (time-dependent, one-dimensional, closed systems of PDEs) and allows torsional flow effects, which are usually ignored, in a general Johnson–Segalman constitutive law.

One-dimensional closure models for three-dimensional incompressible viscoelastic free jets: von Kármán flow geometry and elliptical cross-section

In this paper we derive one-space-dimensional, reduced systems of equations (one-dimensional closure models) for viscoelastic free jets. We begin with the three-dimensional system of conservation

Radiative gravitational fields in general relativity I. General structure of the field outside the source

  • L. BlanchetT. Damour
  • Mathematics, Physics
    Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
  • 1986
We present a well-defined formal framework, together with appropriate mathematical tools, which allow us to implement in a constructive way, and to investigate in full mathematical details, the

On the evolution of non-axisymmetric viscous fibres with surface tension, inertia and gravity

We consider the free boundary problem for the evolution of a nearly straight slender fibre of viscous fluid. The motion is driven by prescribing the velocity of the ends of the fibre, and the free

One-dimensional approximation of viscous flows

Attention has been paid to the similarity and duality between the Gregory-Laflamme instability of black strings and the Rayleigh-Plateau instability of extended fluids. In this paper, we derive a set

The radiative transfer at second order: a full treatment of the Boltzmann equation with polarization

This paper investigates the full Boltzmann equation up to second order in the cosmological perturbations. Describing the distribution of polarized radiation by a tensor-valued distribution function,