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Modeling and simulation on dynamics and instability of non-Newtonian fluids in thin film processes

  • Ilyoung Kwon (권일영, 대학원 화공생명공학과 화공생명공학전공)

초록/요약

This thesis deals with instability and uniformity of two typical systems involved in the thin film process, i.e., polymer thin film manufacturing and concentrated suspension system under sheared flows. With numerical approaches, unique dynamic features of each system have been studied in two parts. In the first part, draw resonance, as the common instability in the extensional deformation processes for thin threads or films, has been studied in isothermal 1-D fiber spinning and 2-D film casting processes and its onset conditions have been determined by frequency response method (Kase and Araki, 1982). The original method has been extended to viscoelastic fluids and secondary force-included system in the fiber spinning process, and then applied to the film casting process with viscoelastic fluids. Thanks to the method used in here, stability windows (or operability windows) for stable operations of the 2-D film casting system have been constructed, which have not been presented before using linear stability analysis. The windows include the results of Newtonian and viscoelastic fluids, the upperconvected Maxwell and Phan-Thien and Tanner models, as the constitutive equation of molten polymers. The method has the merit of being able to perform sensitivity analysis of the system as well as stability analysis at a time through numerical Laplace transform converting transient responses to a step disturbance into amplifications and phase angles in frequency domain, unlike other existing methods. Also, it has been confirmed that a difference of flow velocities along streamlines, via analysis of steady-state velocity profiles in 2-D film casting, are strongly related with the tendency of onset conditions of the instability according to operation conditions. The relation between instability onsets and flow patterns allows the state of the film being drawn to be classified into planar, transition and neck-in types according to airgap distances of the process. In the second part, numerical analysis with continuum-based diffusive flux model (Phillips et al., 1992) has been conducted to observe the migration phenomenon where concentrated suspensions (in this study, Newtonian suspending fluids and unimodal spherical solid particles without buoyant force and Brownian motion) flow in parallel slit channel flows with non-symmetric velocity profile. The non-symmetric profiles in the slit channel are represented with a linear combination of drag-driven and pressure-driven flows as a planar Couette-Poiseuille flow. Factors governing the migration dynamics in the diffusive flux model (particle size, concentration, and flow length from an inlet of the channel) are unified into a non-dimensional length element,Z, and the effect of the non-symmetricity on the dynamics is presented by evolution of concentration distribution along increasing Z. From the results, symmetric flow conditions show the shortest (or smallest) Z to arrive at the fully-developed state, and increasing non-symmetricity of velocity profile (zero shear-rate position moves from the center of channel gap to a wall side) shows more longer (or larger) Z than that of the symmetric conditions. This change of Z for the development has been analytically interpreted by introducing a concept of effective diffusion gap, which is varied according to the non-symmetricity. Moreover, the non-symmetric migration from the diffusive flux model has been compared quantitatively with that from the lattice Boltzmann methods, one of the effective theoretical approaches which can solve Stokesian dynamics of suspension flows, and it has been confirmed that the continuum-based suspension system properly reflects the migration phenomenon by collisions between individual particles explained as the shear-induced migration process, even in the non-symmetric flow conditions.

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목차

Abstract
Abstract (in Korean)
Contents
List of figures
List of tables
I. Introduction
1. Extensional deformation processes
2. Concentrated suspension system
II. Part 1: Dynamic analysis of extensional deformation processes via frequency response method
1. Transfer functions in extensional deformation processes
2. Fiber spinning process
2.1. Literature review on fiber spinning process
2.2. Governing equations and boundary conditions
2.3. Transient profiles under tension-controlled system
2.4. Stability analysis using frequency response method
2.5. Sensitivity analysis using frequency response method
2.6. Conclusions
3. Film casting process
3.1. Literature review on film casting process
3.2. Governing equations and boundary conditions
3.3. Transient profiles under tension-controlled system
3.4. Stability analysis using frequency response method
3.4.1. Stability window for Newtonian film casting
3.4.2. Deformation types and stability
3.4.3. Stability window for viscoelastic film casting
3.5. Sensitivity analysis using frequency response method
3.5.1. Comparison of two methods
3.5.2. Effect of aspect ratio on sensitivity
3.5.3. Effect of viscoelasticity
3.6. Conclusions
III. Part 2: Dynamics of concentrated suspensions under non-symmetric shear flows
1. Literature review on concentrated suspension system
2. Mathematical modeling
2.1. Viscosity model and equation of motion (EOM)
2.2. Diffusive flux model
2.3. Numerical method and imposed flow conditions
3. Model validation
4. Particle migrations by 1-D DFM
4.1. Steady-state profiles under various flow conditions
4.2. Transient evolution of particle migration
5. Particle migrations by 2-D DFM
5.1. Regularization of the 2-D particle migration development
5.2. Migration development under non-symmetric flow conditions
5.2.1. Mild non-symmetric flow condition
5.2.2. Severe non-symmetric flow condition
5.2.3. Effective diffusion gap for non-symmetric migration
6. Comparison between 1-D and 2-D DFMs
7. Role of the advection on the particle transport in 2-D DFM
8. Conclusions
Appendix A: Particle migration of concentrated suspensions via LBM
Appendix B: Governing equations of suspension system in FVM
B.1. Diffusive flux model
B.2. Equation of motion
B.3. Simulation procedures
IV. Concluding remarks
V. References

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