Kinetic theory is used to investigate cross-stream migration of a rigid polymer undergoing rectilinear flow in the vicinity of a wall. Hydrodynamic interactions between the polymers and the boundary result in a cross-stream migration. In simple shear flow, polymers migrate away from the wall, creating a depletion layer in the vicinity of the wall which thickens as the flow strength increases relative to the Brownian force. In pressure-driven flow, an off-center maximum in the center-of-mass distribution occurs due to a competition between hydrodynamic interactions with the wall and the anisotropic diffusivity induced by the inhomogeneous flow field.
We use slender-body theory to simulate a rigid fibre within simple shear flow and parabolic flow at zero Reynolds number and high Péclet numbers (weak Brownian motion). Hydrodynamic interactions of bulk fibres with the bounding walls are included using previously developed methods (Harlen, Sundararajakumar & Koch, J. Fluid Mech., vol. 388, 1999, pp. 355–388; Butler & Shaqfeh, J. Fluid Mech., vol. 468, 2002, pp. 205–237). We also extend a previous analytic theory (Park, Bricker & Butler, Phys. Rev. E, vol. 76, 2007, 04081) predicting the centre-of-mass distribution of rigid fibre suspensions undergoing rectilinear flow near a wall to compare the steady and transient distributions. The distributions obtained by the simulation and theory are in good agreement at sufficiently high shear rates, validating approximations made in the theory which predicts a net migration of the rigid fibres away from the walls due to a hydrodynamic lift force. The effect of the inhomogeneous distribution on the effective stress is also investigated.
Experiments and numerical simulations have been performed to investigate the deformation and break-up of a cloud of rigid fibres falling under gravity through a viscous fluid in the absence of inertia and interfacial tension. The cloud of fibres is observed to evolve into a torus that subsequently becomes unstable and breaks up into secondary droplets which themselves deform into tori in a repeating cascade. This behaviour is similar to that of clouds of spherical particles, though the evolution of the cloud of fibres occurs more rapidly. The simulations, which use two different levels of approximation of the far-field hydrodynamic interactions, capture the evolution of the cloud and demonstrate that the coupling between the self-motion and hydrodynamically induced fluctuations are responsible for the faster break-up time of the cloud. The dynamics of the cloud are controlled by a single parameter which is related to the self-motion of the anisotropic particles. The experiments confirm these findings.
Following recent work [e.g., J. Park et al., J. Rheol. 56, 1057–1082 (2012); T. Yaoita et al., Macromolecules 45, 2773–2782 (2012); and G. Ianniruberto et al., Macromolecules 45, 8058–8066 (2012)], we introduce the idea of a configuration dependent friction coefficient (CDFC) based on the relative orientation of Kuhn bonds of the test and surrounding matrix chains. We incorporate CDFC into the “toy” model of Mead et al. [Macromolecules 31, 7895–7914 (1998)] in a manner akin to Yaoita et al. [Nihon Reoroji Gakkaishi 42, 207–213 (2014)]. Additionally, we incorporate entanglement dynamics (ED) of discrete entanglement pairs into the new Mead–Banerjee–Park (MBP) model in a way similar to Ianniruberto and Marrucci [J. Rheol. 58, 89–102 (2014)]. The MBP model predicts a deformation dependent entanglement microstructure which is physically reflected in a reduced modulus that heals slowly following cessation of deformation. Incorporating ED into the model allows “shear modification” to be qualitatively captured. The MBP model is tested against experimental data in steady and transient extensional and shear flows. The MBP model captures the monotonic thinning of the extensional flow curve of entangled monodisperse polystyrene (PS) melts [A. Bach et al., Macromolecules 36, 5174–5179 (2003)] while simultaneously predicting the extension hardening found in PS semidilute solutions where CDFC is diluted out [P. K. Bhattacharjee et al., Macromolecules 35, 10131–10148 (2002)]. The simulation results also show that the rheological properties in nonlinear extensional flows of PS melts are sensitive to CDFC but not to convective constraint release (CCR) while those for shear flows are influenced more by CCR. The monodisperse MBP toy model is generalized to arbitrary polydispersity.
A numerical model that incorporates temperature-dependent non-Newtonian viscosity was developed to simulate the extrusion process in extrusion-based additive manufacturing. Agreement with the experimental data was achieved by simulating a polylactic acid melt flow as a non-isothermal power law fluid using experimentally fitted parameters for polylactic acid. The model was used to investigate the temperature effect on the flow behavior, the cross-sectional area, and the uniformity of the extruded strand. OpenFOAM, an open source simulation tool based on the finite volume method, was used to perform the simulations. A computational module for solving the equations of non-isothermal multiphase flows was also developed to simulate the extrusion process under a small gap condition where the gap between the nozzle and the substrate surface is smaller than the nozzle diameter. Comparison of the strand shapes obtained from our model with isothermal Newtonian simulation, and experimental data confirms that our model improves the agreement with the experimental data. The result shows that the cross-sectional area of the extruded strand is sensitive to the temperature-dependent viscosity, especially in the small gap condition which has recently increased in popularity. Our numerical investigation was able to show nozzle temperature effects on the strand shape and surface topography which previously had been investigated and observed empirically only.
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