A theoretical treatment of die swell in a Newtonian liquid

Horsfall, F.

doi:10.1016/0032-3861(73)90086-4

Cited by 16 publications

(5 citation statements)

References 8 publications

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“…In the case of finite element calculations, where the continuity equation is solved directly, Chang et al (1979) and Omodei (1979Omodei ( , 1980 have reported that both normal and tangential stresses on the surface differed significantly from their expected values. Similar observations can also be noticed from the finite difference result of Horsfall (1973). This discrepancy, however, decays almost exponentially as one moves downstream from the exit.…”

Section: T = -P = -As/[r(l2)]supporting

confidence: 84%

Dynamics of a creeping Newtonian jet with gravity and surface tension: A finite difference technique for solving steady free‐surface flows using orthogonal curvilinear coordinates

Dutta

Ryan

1982

AIChE Journal

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A finite difference technique capable of simulating steady, incompressible, viscous, free‐surface flows has been successfully applied to the motion of a creeping Newtonian jet, including both surface tension and gravitational forces. In accordance with experimental results, the numerical solutions predict either a 12 or 16% increase in the jet dimensions depending on whether the jet emerges from a circular or a slit die. Both gravity and surface tension inhibit the swelling behavior.

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Section: T = -P = -As/[r(l2)]supporting

confidence: 84%

Dynamics of a creeping Newtonian jet with gravity and surface tension: A finite difference technique for solving steady free‐surface flows using orthogonal curvilinear coordinates

Dutta

Ryan

1982

AIChE Journal

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“…His results suggested that the velocity profile will oscillate prior to stabilizing. Horsfall (1973) used a finite-difference method of solving the equations of motion for an incompressible Newtonian fluid at zero Reynolds number subject to a zero normal stress at the extrudate surface. His predictions of the die swell ratio were approximately one half of those obtained experimentally.…”

Section: Hydrodynamic Approachmentioning

confidence: 99%

Velocity distributions in die swell

Whipple¹,

Hill²

1978

AIChE Journal

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\ SLIT n ADJUSTABLE 3 MM GHT INTERRUPTER u -CAMERA Fig. 2. Die cross section and light path. A, B, C = velocity curve fit parameters A~A = cross-sectional area at section lA, Figure 8 Aw = interfacial area between sections 1A and 2, Figure 8 B = die swell, ratio of die and extrudate area or widths K = ratio of average square to the square of the average of the velocity pa = atmospheric pressure Re = Reynolds number, u D p /~ 8 , = transverse velocity component vy = axial velocity component 1A = average of the square of the velocity in the 1 direction at section 1A

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“…Reynolds and S numbers was performed by Batchelor & Horsfall (1971), who also used extrusion into a bath of matching density to avoid problems with gravitational forces. For a Newtonian fluid with a viscosity of lo5 poise, they reported a mean swelling of 13.5%.…”

Section: Introductionmentioning

confidence: 99%

The solution of viscous incompressible jet and free-surface flows using finite-element methods

1974

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We discuss the creation of a finite-element program suitable for solving incompressible, viscous free-surface problems in steady axisymmetric or plane flows. For convenience in extending program capability to non-Newtonian flow, non-zero Reynolds numbers, and transient flow, a Galerkin formulation of the governing equations is chosen, rather than an extremum principle. The resulting program is used to solve the Newtonian die-swell problem for creeping jets free of surface tension constraints. We conclude that a Newtonian jet expands about 13%, in substantial agreement with experiments made with both small finite Reynolds numbers and small ratios of surface tension to viscous forces. The solutions to the related ‘stick-slip’ problem and the tube inlet problem, both of which also contain stress singularities, are also given.

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A theoretical treatment of die swell in a Newtonian liquid

Cited by 16 publications

References 8 publications

Dynamics of a creeping Newtonian jet with gravity and surface tension: A finite difference technique for solving steady free‐surface flows using orthogonal curvilinear coordinates

Dynamics of a creeping Newtonian jet with gravity and surface tension: A finite difference technique for solving steady free‐surface flows using orthogonal curvilinear coordinates

Velocity distributions in die swell

The solution of viscous incompressible jet and free-surface flows using finite-element methods

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