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Theory of laminar mixing
Author(s) -
Erwin Lewis
Publication year - 1978
Publication title -
polymer engineering and science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.503
H-Index - 111
eISSN - 1548-2634
pISSN - 0032-3888
DOI - 10.1002/pen.760181312
Subject(s) - simple shear , mixing (physics) , laminar flow , materials science , mechanics , shear (geology) , shear flow , shear rate , tensor (intrinsic definition) , pure shear , flow (mathematics) , shear stress , strain rate tensor , strain rate , deformation (meteorology) , infinitesimal strain theory , orientation (vector space) , thermodynamics , geometry , physics , mathematics , composite material , rheology , finite element method , quantum mechanics
An expression is derived for the increase in mixedness due to an arbitrary deformation of a material. For mixtures having initial orientation this expression is a function of the principal values of the strain tensor and the orientation of the fluid. For mixtures without initial orientation, this expression is simply a function of the principal values of the strain tensor. Mixing in pure shear, simple shear, and pure elongation is determined. The rate of mixing for each of these deformations in steady flow is derived. A comparison of these rates of mixing with the energy consumed in the deformation shows that simple shear flow is a very inefficient way to accomplish mixing. For the example cited, five orders of magnitude greater energy is required to accomplish mixing in shear flow as opposed to extensional flows.