Striation thickness reduction from kinematical arguments

2 Striation Thickness Reduction from Kinematical Arguments 

A more systematic approach for the calculation of the striation thickness and mixing efficiency was presented by Ottino and co-workers (1979, 1981). They developed the mathematical formulation for the calculation of the lineal and areal stretch of a material line and area, respectively, subjected to any deformation gradient field. In this text we use the formulation for the lineal stretch because it is easier to apply and correlates to the areal stretch by a simple relation. We should emphasize at this point that the formulation is valid in the absence of interfacial forces between minor and major components. This is true for systems with negligible interfacial tension forces, such as, for systems with either negligible interfacial tension or large length scale or both. 

Suppose that a polymer melt is processed in a mixer which deforms the particles of the melt. At time r = 0 we identify a differential material line at position xo of length dxo and orientation mo. After a deformation (e.g., shear, elongation) is applied to the melt by the mixer, we identify the same line 

The deformation applied is characterized by the deformation-gradient tensor, F, with components (for a rectangular coordinate system) equal to 

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See also in sourсe #XX -- [ , ]

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