Interfacial Shape and Evolution Equations for Liquid Films and Other Viscocapillary Flows

Higgins, Brian; Scriven, L. E.

doi:10.1021/i160071a002

Cited by 30 publications

(8 citation statements)

References 20 publications

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“…(1), they determined the deformation gradient tensor F. One of the two solutions was taken as Finally, a useful application of Frenet-Serret's formula to the flow and deformation along streamlines is presented in comparison with another ordinary tensor approach. The use of orthogonal streamline coordinates is also powerful in other fields of fluid mechanics and the works of Higgins and Scriven [6] and Finnigan [7] may be referred to.…”

Section: F= _ C~#mmentioning

confidence: 99%

A note on the calculation of strain histories in orthogonal streamline coordinate systems

Adachi

1986

Rheol Acta

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An extension of a previous work concerning the calculation of strain histories along streamlines is made to get more complete and useful expressions of Finger's strain tensor in a cylindrical (or Cartesian) coordinate system as well as in an orthogonal streamline coordinate system. One of the results shows that Winter's tracking model is correct.Relations among the recent three results of Winter, Adachi and Crochet et al. are presented clearly. Moreover useful applications of Frenet-Serret's formula to the study of the deformation and flow kinematics along streamlines are shown in comparison with the ordinary tensor approach.

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Section: F= _ C~#mmentioning

confidence: 99%

A note on the calculation of strain histories in orthogonal streamline coordinate systems

Adachi

1986

Rheol Acta

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“…the isoparametric mapping and the transformations of derivatives and integrals appear elsewhere.' 1,13,15 The computations were started from an initial rest state {u = v = p = 0, h&,H(')}. The initial configuration of the interface, h(r), need not have been parallel to the disks, but in what follows the interface was a plane h(O) parallel to the disks unless otherwise stated.…”

Section: Exitmentioning

confidence: 99%

Analysis of lubricated squeezing flow

Papanastasiou

Macosko

Scriven

1986

Numerical Methods in Fluids

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SUMMARYA thin film of low-viscosity lubricating liquid between a solid wall and a viscous material reduces shear stress on the latter and tends to make it flow as though it were slipping along the wall. The result when the lubricated material is being squeezed out of the gap between approaching parallel plates is flow more nearly irrotational, or extensional, the more effective the lubricating film on the plates. Two Newtonian analyses of this flow situation are reported. One is an approximate, asymptotic analytical solution for Newtonian lubricating flow in the films and combined mixed flow, shear and extension, in the viscous layer. The second is a full twodimensional axisymmetric solution of the momentum and continuity equations along with the kinematic condition which governs the motion of the interface. Both analyses indicate that there are two limiting flow regimes, depending on the ratio of the thickness ofeach of the two phases to radius and on the viscosity ratio of the two liquids. In one limit the flow is parallel squeezing and the lubricant layer slowly thins and persists a long time. In the other the lubricant is expelled preferentially. Implications of the results are discussed for rheological characterization of viscoelastic liquids and for prediction of lubricated or autolubricated flows in processing situations.

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“…An overview on viscocapillary¯ows can be found in [3,4]. Christodoulou et al treated the¯uid mechanics of slide coating, [5].…”

Section: Introductionmentioning

confidence: 99%

Influence of the capillarity on a creeping film flow down an inclined plane with an edge

Aksel

2000

Archive of Applied Mechanics (Ingenieur Archiv)

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Interfacial Shape and Evolution Equations for Liquid Films and Other Viscocapillary Flows

Cited by 30 publications

References 20 publications

A note on the calculation of strain histories in orthogonal streamline coordinate systems

A note on the calculation of strain histories in orthogonal streamline coordinate systems

Analysis of lubricated squeezing flow

Influence of the capillarity on a creeping film flow down an inclined plane with an edge

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