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Inelastic constitutive equations for complex flows (1995)

Souza Mendes, Paulo R. ; Padmanabhan, Mahesh ; Scriven, L. E. ; [et al.]

Springer

Rheologica acta 34 (1995), S. 209-214

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ISSN: 1435-1528

Keywords: Constitutive model ; flow-sensitive viscosity ; complex flow modelling

Source: Springer Online Journal Archives 1860-2000

Topics: Chemistry and Pharmacology , Physics

Notes: Abstract A new class of inelastic constitutive equations is presented and discussed. In addition to the rate-of-strain tensor, the stress is assumed to depend also on the relative-rate-of-rotation tensor, a frame-indifferent quantity that brings information about the nature of the flow. The material functions predicted by these constitutive equations are given for simple shear and uniaxial extension. A special case of these equations takes the Newtonian form, except that the viscosity is a function of the invariants of both kinematic tensors on which the stress depends. This simple constitutive equation has potential applications in liquid flow process simulations, since it combines simplicity with the capability of responding independently to shear and extension, as real liquids seem to do. Finally, possible forms for the new viscosity function are discussed.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF00398440

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Coating flow theory by finite element and asymptotic analysis of the navier-stokes systemThis invited paper is an extended and refereed version of one presented at the Fourth International Symposium on Finite Elements in Flow Problems held in Tokyo, Japan, 26-29 July 1982. (1984)

Kistler, S. F. ; Scriven, L. E.

Chichester : Wiley-Blackwell

International Journal for Numerical Methods in Fluids 4 (1984), S. 207-229

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ISSN: 0271-2091

Keywords: Coating Flows ; Viscous Flows ; Free Surfaces ; Free Boundaries ; Boundary ; Parameterization Moving Spine Method ; Engineering ; Engineering General

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics

Notes: Coating flows are laminar free surface flows, preferably steady and two-dimensional, by which a liquid film is deposited on a substrate. Their theory rests on mass and momentum accounting for which Galerkin's weighted residual method, finite element basis functions, isoparametric mappings, and a new free surface parametrization prove particularly well-suited, especially in coping with the highly deformed free boundaries, irregular flow domains, and the singular nature of static and dynamic contact lines where fluid interfaces intersect solid surfaces. Typically, short forming zones of rapidly rearranging two-dimensional flow merge with simpler asymptotic regimes of developing or developed flow upstream and downstream. The two-dimensional computational domain can be shrunk in size by imposing boundary conditions from asymptotic analysis of those regimes or by matching to one-dimensional finite element solutions of asymptotic equations.The theory is laid out with special attention to conditions at free surfaces, contact lines, and open inflow and outflow boundaries. Efficient computation of predictions is described with emphasis on a grand Newton iteration that converges rapidly and brings other benefits. Sample results for curtain coating and roll coating flows of Newtonian liquids illustrate the power and effectiveness of the theory.

Additional Material: 20 Ill.