The buckling and stretching of a viscida

Buckmaster, J.; Nachman, A.; Ting, Lu

doi:10.1017/s0022112075001279

Cited by 77 publications

(88 citation statements)

References 3 publications

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“…We may also neglect inertia and hence use the Stokes equations, except under extreme conditions of very low viscosity and thin walls. Equations governing the evolution of a viscida were previously derived by Buckmaster et al (1975) and Buckmaster & Nachman (1978). We follow a more systematic approach based on asymptotic analysis of the governing Stokes equations and boundary conditions, without using any ad hoc kinematic assumptions.…”

Section: ) Radiusmentioning

confidence: 99%

The surface-tension-driven evolution of a two-dimensional annular viscous tube

Griffiths¹,

Howell²

2007

J. Fluid Mech.

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We consider the evolution of an annular two-dimensional region occupied by viscous fluid driven by surface tension and applied pressure at the free surfaces. We assume that the thickness of the domain is small compared with its circumference so that it may be described as a thin viscous sheet whose ends are joined to form a closed loop. Analytical and numerical solutions of the resulting model are obtained and we show that it is well posed whether run forwards or backwards in time. This enables us to determine, in many cases explicitly, which initial shapes will evolve into a desired final shape. We also show how the application of an internal pressure may be used to control the evolution.This work is motivated by the production of non-axisymmetric capillary tubing via the Vello process. Molten glass is fed through a die and drawn off vertically, while the shape of the cross-section evolves under surface tension and any applied pressure as it flows downstream. Here the goal is to determine the die shape required to achieve a given desired final shape, typically square or rectangular. We conclude by discussing the role of our two-dimensional model in describing the three-dimensional tube-drawing process.

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Section: ) Radiusmentioning

confidence: 99%

The surface-tension-driven evolution of a two-dimensional annular viscous tube

Griffiths¹,

Howell²

2007

J. Fluid Mech.

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“…Savva & Bush 2009). The theoretical framework for modelling thin viscous sheets can been found, for instance, in Buckmaster, Nachman & Ting (1975), Howell (1996) or Ribe (2002).…”

Section: Introductionmentioning

confidence: 99%

Newtonian pizza: spinning a viscous sheet

2010

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We study the axisymmetric stretching of a thin sheet of viscous fluid driven by a centrifugal body force. Time-dependent simulations show that the sheet radius R(t) tends to infinity in finite time. As time t approaches the critical time t * , the sheet becomes partitioned into a very thin central region and a relatively thick rim. A net momentum and mass balance in the rim leads to a prediction for the sheet radius near the singularity that agrees with the numerical simulations. By asymptotically matching the dynamics of the sheet with the rim, we find that the thickness h in the central region is described by a similarity solution of the second kind, with h ∝ (t * − t) α where the exponent α satisfies a nonlinear eigenvalue problem. Finally, for non-zero surface tension, we find that the exponent increases rapidly to infinity at a critical value of the rotational Bond number B = 1/4. For B > 1/4, surface tension defeats the centrifugal force, causing the sheet to retract rather than to stretch, with the limiting behaviour described by a similarity solution of the first kind.

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“…Purely viscous two-dimensional sheets have been considered by Buckmaster, Nachman & Ting (1975) (referred to hereafter as BNT) and Wilmott (1989), and the onset of buckling in a two-dimensional sheet impinging on a plate is considered by Yarin & Tchavdarov (1994). The linear stability of a viscous sheet subjected to shear was treated by Benjamin & Mullin (1988).…”

Section: Introductionmentioning

confidence: 99%

Models for thin viscous sheets

Howell¹

1996

Eur. J. Appl. Math

128

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Leading-order equations governing the dynamics of a two-dimensional thin viscous sheet are derived. The inclusion of inertia effects is found to result in an illposed model when the sheet is compressed, and the resulting paradox is resolved by rescaling the equations over new length-and timescales which depend on the Reynolds number of the flow and the aspect ratio of the sheet. Physically this implies a dominant lengthscale for transverse displacements during viscous buckling. The theory is generalised to give new models for fully three-dimensional sheets.

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The buckling and stretching of a viscida

Cited by 77 publications

References 3 publications

The surface-tension-driven evolution of a two-dimensional annular viscous tube

The surface-tension-driven evolution of a two-dimensional annular viscous tube

Newtonian pizza: spinning a viscous sheet

Models for thin viscous sheets

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