Mathematical model of strain of droplets of a dispersed-phase polymer in flow of molten polymer blends

Abstract

A mathematical model of strain of a dispersed-phase-polymer droplet in flow of a molten polymer blend from a wide reservoir to a narrow one has been created with the use of the structural-continuum approach. The system of differential equations obtained has numerically been solved by the Runge-Kutta method. The model satisfactorily describes the actual processes of flow of molten polymer blends in the entrance zone of a molding orifice: the values of the droplet strains are a function of the relation of the viscosities of the starting components and their absolute values, the volume concentration of the dispersed phase, the interphase tension, and the elasticity of the droplet. The adequacy of the model created has been confirmed by comparison of the droplet strains calculated using the equations obtained and the theoretical conclusions and experimental results.The use of polymer blends is one efficient method of creating materials with a prescribed set of properties. Polymer blends may be considered as specific colloidal systems whose properties are determined by the type of structure formation and the surface phenomena at the phase boundary [1]. Processing of molten blends offers a new method of molding of ultrafine synthetic fibers (microfibers) of diameter from several fractions to tenths of a fraction of a micrometer. This phenomenon has been called specific fiberization [2]. The empirical approach is dominant in investigating the processes of formation of a structure in polymer dispersions. Romankevich et al. have made an attempt to describe the process of formation of microfibers in the matrix of the other polymer in the case of flow of a molten binary mixture; the emphasis was on the strain of a polymer droplet in the channel of the molding orifice and after the exit from it or in subsequent thermoorientational stretching [3, 4]. The mechanism of the phenomenon of specific fiberization, whose essence is that the fiberization of one polymer in the mass of the other (matrix) polymer is carried out in the field of tensile forces arising in transition from a wide reservoir to a narrow one, has been formulated and experimentally confirmed in [2].The present work seeks to create a mathematical model of strain of a droplet of the dispersed-phase component in flow of a molten polymer blend in the entrance zone of a molding orifice.To describe the processes occurring in dispersion flow one must know of numerous characteristics of the dispersion: the viscoelastic properties of the components, the volume concentration of the dispersed phase, the shape, size, and interaction of particles, etc. It is possible to allow for these indices in detail within the framework of the structural (microscopic) approach which has widely been used in investigating comparatively simple media, such as diluted suspensions with simply shaped particles. The possibility of using the structural method in the rheology of dispersions is limited by their diversity and complex morphology. The structural-continuum method proposed in [5,6] combi...

Surface Structured Polymer Blend Fibers and Their Application in Fiber Reinforced Composite

“…The in-situ fibration of the second phase can also happen in polymer-blends with compatibilizer [53] and polymer-blends after the stretching process [54]. The in-situ fibration of the second phase resulting from tailoring the rheological properties and interfacial properties of polymers have been also studied by many researchers [16,23,24,[27][28][29]48,52,55] based on experimental and mathematic studies. These studies suggest that it is possible to build surface structures and improve the mechanical properties of polymer-blend fibers simultaneously.…”

“…Theoretically, the morphology of polymer blends is controlled by the microrheological behaviors of the second phase, including deformation, break-up, coalescence, and migration under the action of hydrodynamic and interfacial tension during processing flow [ 18 , 19 , 20 ]. The microrheological behaviors of the second phase during capillary flow and fiber spinning have been investigated by many researchers based on theoretical and experimental studies [ 16 , 21 , 22 , 23 ]. The viscosity ratio and blend ratio have been approved to be effective parameters for tuning the morphologies and properties of polymer blends [ 24 , 25 , 26 ].…”

“…The melt processing can generate morphologies ranging from dispersed drops to fibers to lamella to co-continues structures in the bend ratio of 0-50% [20]. Tsebrenko and co-authors' studies also showed that specific fiber formation could be controlled by tailoring the rheological and interfacial properties [23,[27][28][29]. Our previous studies found that unique gradient morphologies with long thin fibrils near the surface region and short large droplets near the center region of the filament, as well as the inverse pattern, can be produced by tunning the viscosity ratio of polymer blends and shear flow in capillary [14,15].…”