A method is proposed for simulating the dynamic behavior of rigid and flexible fibers in a flow field. The fiber is regarded as made up of spheres that are lined up and bonded to each neighbor. Each pair of bonded spheres can stretch, bend, and twist, by changing bond distance, bond angle, and torsion angle between spheres, respectively. The strength of bonding, or flexibility of the fiber model, is defined by three parameters of stretching, bending, and twisting constants. By altering these parameters, the property of the fiber model can be changed to be rigid to flexible. The motion of the fiber model in a flow field is determined by solving the translational and rotational equations for individual spheres under the hydrodynamic force and torque exerting on. This method was applied to simulate rotational motions with and without bending deformation of the fiber in a simple shear flow under the conditions of infinitely dilute system, no hydrodynamic interaction and low Reynolds number of a particle. For the rigid fiber, the computed period of rotation and the computed distribution of orientation angle agree with those calculated by Jeffery’s equation with an equivalent ellipsoidal aspect ratio. For the flexible fiber, the period of rotation decreases rapidly with the growth of bending deformation of the fiber and rotation orbits deviate from a circular one of the rigid fiber. These tendencies are similar to experimental ones described by Forgacs and Mason. These results show that the proposed method using bonded spheres’ model can reproduce the dynamic behavior of rigid and flexible fibers in a flow field successfully.
A new method is presented to simulate the motion of concentrated fiber suspensions in shear flow at low Reynolds numbers without Brownian motion. The hydrodynamic interaction among fibers is considered in a particle simulation method (PSM), in which a fiber is modeled by arrays of spheres. The motion of each constituent sphere of a fiber, which are dispersed into a unit cell with periodic boundaries, is followed to predict the microstructure and the rheological properties. The hydrodynamic interaction is decomposed into two parts, intra- and interfiber ones. In the former, the many-body problem is solved by calculating the mobility matrix for each fiber to obtain the hydrodynamic force and torque exerted on each sphere. In the latter, only the near-field lubrication force is considered between spheres of one fiber and another. The validity of this approximate treatment was first examined for the sphere dispersed system. The simulated microstructure and the rheological properties were in very good agreement with results of both experiments and the Stokesian dynamics. The methodology was then applied to concentrated rigid and flexible fiber suspensions. The overshoot of suspension viscosity was observed at the early stage for rigid fiber suspensions, but not for flexible ones. This was because of the transient change of the microstructure from the flow-directional orientation to the planar orientation of rigid fibers. The normal stress was calculated for the flexible fiber suspension and clearly showed that the elasticity of fiber suspensions was due to the deformation of fibers. The proposed simulation method can predict the effect of such parameters as the aspect ratio, flexibility, and volume fraction of fibers on the microstructure and the rheological properties of fiber suspensions.
The recently developed simulation method, named as the particle simulation method (PSM), is extended to predict the viscosity of dilute suspensions of rodlike particles. In this method a rodlike particle is modeled by bonded spheres. Each bond has three types of springs for stretching, bending, and twisting deformation. The rod model can therefore deform by changing the bond distance, bond angle, and torsion angle between paired spheres. The rod model can represent a variety of rigidity by modifying the bond parameters related to Young’s modulus and the shear modulus of the real particle. The time evolution of each constituent sphere of the rod model is followed by molecular-dynamics-type approach. The intrinsic viscosity of a suspension of rodlike particles is derived from calculating an increased energy dissipation for each sphere of the rod model in a viscous fluid. With and without deformation of the particle, the motion of the rodlike particle was numerically simulated in a three-dimensional simple shear flow at a low particle Reynolds number and without Brownian motion of particles. The intrinsic viscosity of the suspension of rodlike particles was investigated on orientation angle, rotation orbit, deformation, and aspect ratio of the particle. For the rigid rodlike particle, the simulated rotation orbit compared extremely well with theoretical one which was obtained for a rigid ellipsoidal particle by use of Jeffery’s equation. The simulated dependence of the intrinsic viscosity on various factors was also identical with that of theories for suspensions of rigid rodlike particles. For the flexible rodlike particle, the rotation orbit could be obtained by the particle simulation method and it was also cleared that the intrinsic viscosity decreased as occurring of recoverable deformation of the rodlike particle induced by flow.
SYNOPSISNylon 6-clay hybrid ( N C H ) is a molecular composite of nylon 6 and uniformly dispersed silicate layers of montmorillonite. We found that the phase with the high melting temperature (HMT phase) in the NCH annealed under elevated pressure. The melting temperature of the H M T phase was 240°C. Nylon 6 annealed under elevated pressure did not have the H M T phase. Thus, the presence of the H M T phase was characteristic of the NCH. The relative heat of fusion of the H M T phase (heat of fusion of H M T phase/heat of fusion in the pressure annealed NCH ) increased with increase in pressure. High-pressure differential thermal analysis (DTA) measurement revealed that the temperature, a t which the relative heat of fusion showed a maximum value, was below about 20°C of the melting temperature of the original NCH under elevated pressure. It was considered that the nylon 6 crystallite near the melting temperature and the molecular mobility under elevated pressure were necessary to the appearance to the H M T phase. 0 1994 John Wiley & Sons, Inc. I NTRO D UCTlO NNylon 6-clay hybrid ( N C H ) is a molecular composite of nylon 6 in which silicate monolayers of montmorillonite, 1 nm in thickness and 100 nm in width, are uniformly dispersed.'-4 NCH is readily processed in the molten state by injection molding or extrusion molding. It is well known that high pressure above 0.3 GPa strongly enhances the rate at which polyethylene crystallizes in extended forms. Extended-chain crystal (ECC) of polyethylene is grown either by pressure-induced crystallization or by annealing of folded chain crystal near the melting temperature, as was reported by Rees and Bassett.' The melting temperature and the crystallinity of the polyethylene with ECC are higher than those of folded-chain crystals of p~lyethylene.~ In the NCH annealed under elevated pressure, it is expected that the melting temperature and the crystallinity are increased due to the growing of the ECC.In this study, the NCH was crystallized by annealing under elevated pressure above 0.15 GPa. The
We estimated the energy barriers of proton transfers in the systems of (CF3SO3/H/SO3CF3)− and (CF3SO3/H/H2O/SO3CF3)− as models of a water‐swollen Nafion membrane by an ab initio density functional quantum calculation method with consideration of the hydration effect. As a result, the proton transfer between the SO 3− sites, which is accompanied by one water molecule, was found to be one of the proton‐transfer mechanisms in the water‐swollen Nafion membrane; that is, the surface diffusion mechanism was found to be important for the proton transfer in that membrane. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1905–1914, 2004
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