An analysis of local flow effects in flow‐induced orientation and crystallization

Abstract

SynopsisAn analysis is presented of the effects of external flow kinematics on the so-called local flow in seeded, flow-induced crystallization and orientation. The flow field around a growing crystal or nucleation seed is modelled by the Stokes flow equations past a prolate ellipsoid of high aspect ratio. Exact solutions for various flow kinematics, worked out elsewhere by the singularity method, are applied here to the analysis of local gradients. The results show that along the symmetry axis of the spheroid, the extensional gradients which result for various free-stream velocity fields are primarily the result of the constant-velocity free-stream component. However, free-stream, extensional flow can significantly enhance the region of such high gradients. Along the symmetry plane of the spheroid, primarily shearing gradients result, with small extensional gradients occurring when the free-stream flow has extensional components. Results of chain extension and birefringence calculations are also presented and discussed.A key feature in the dynamics of the crystallization process is the difference in influence of the macroscopic flow kinematics on the primary nucleation and continuous growth steps. In the former case, it has been borne out by a number of studies that nucleation of fibrous crystals is related to the presence of regions of extensional flow, while continued growth of an already nucleated or seeded fiber can occur in predominantly shearing flows.2 Mackley3 gave an explanation for this observation by introducing the idea of "local flow." He pointed out that though extensional flow is necessary to nucleate a fiber, subsequent growth will be more influenced by the local flow around the tip of the fiber than by the macroscopic velocity field existing in the main flow. To show the effectiveness

Formation of fibrous crystals in flowing blends of polyethylene melts

“…The three terms on the right hand side represent respective contributions to the macroscopic flow due to a uniform free stream flow, a planar extensional flow, and a stagnation-like quadratic extensional flow. Chwang and Wu [11] and Chwang [12] have obtained complete closed form solutions to the Stokes flow equations for the local flow past a prolate spheroid immersed in such unbounded free stream flows (see also [8]). Their integral expressions can be evaluated analytically in the region near the spheroid symmetry axis, leading to the following results for the dimensiona ~b / x less local stretch rate, 9-= V1 ~x ' along the spheroid symmetry axis (y = 0) for each of the indicated free stream flow fields.…”

“…We have found that running at a die temperature of 140 °C allows crystallization to occur at the seed tip and direct visualization of the phase transformation has been possible by observing the process through optical windows under normal and polarized light. Following the method discussed by Dairanieh and McHugh [8], a mathematical analysis of the local flow in the vicinity of the needle has also been carried out for the geometry used in this experiment and is presented.…”

“…The presence of an elongated object, such as a needle, creates a region of 162 high elongational flow along its symmetry axis, localized within a few microns of the body tip. Calculations treating the seed as a prolate spheroid have shown that extensional gradients as high as 10 4 S -1 can be generated from uniform free stream flows as low as 1 cm/s [2,8], thus enabling the generation of high stretch rates under slow flow conditions. For more complex free stream kinematics one finds that local extensional gradients are still largely controlled by the constant velocity component in the main flow; however, the region of influence of such gradients can be enhanced by extensional free stream components such as would occur in converging flow [8].…”

“…Calculations treating the seed as a prolate spheroid have shown that extensional gradients as high as 10 4 S -1 can be generated from uniform free stream flows as low as 1 cm/s [2,8], thus enabling the generation of high stretch rates under slow flow conditions. For more complex free stream kinematics one finds that local extensional gradients are still largely controlled by the constant velocity component in the main flow; however, the region of influence of such gradients can be enhanced by extensional free stream components such as would occur in converging flow [8]. Measurements [9] have further demonstrated that the kinematics in such strong, local flows are relatively insensitive to the nonNewtonian nature of the fluid, enabling the use of Stokes flow solutions to predict the kinematics for viscoelastic flows as well.…”

Polarized Light Scattering from Polymer Textures

“…Evolution of microdiffraction patterns of shear crystallized polyethylene specimens with shear rate from spherulitic through complex patterns toward scattering from oriented fibrils; vertical shear direction [47] strain-induced crystallization [50,51], while the structure formation is more temperature sensitive.…”