| This dissertation is concerned with the mathematical analysis of improved real-time, at-line polymer characterization using capillaries in industrial polymer processing. The motivation for this work derives directly from the desire for increased quality control of polymers used in commercial products without additional protractive testing.; Flow-referenced differential capillary viscometers are studied in a mathematically rigorous fashion. Modeling and formal asymptotic analysis yield a problem which is studied analytically and solved numerically. The results obtained provide a theoretical formulation for the experimental correlation of molecular weight to the elastic and diffusive characteristics of dilute polymeric solutions. This work provides a significant step toward the unambiguous characterization of polymers applicable in industrial environments.; The governing equations are analyzed for dilute solutions, that is, asymptotically as the dilution goes to zero. Those equations are then considered in the second limit of small Peclet number. In this special case, analytic solutions are obtained which help illuminate the process dependence on salient parameters and guide the numerics for the general case. This formal asymptotic development sheds new light on the classic Taylor dispersion problem for dilute polymeric solutions but more than that extends those ideas to fluids with high viscosity differential as well as to fluids with elasticity.; Free-radical polymerization in capillaries is also investigated. The analysis provided is, more specifically, applicable to photoinitiated polymerization: a procedure of considerable industrial interest. In the context of dilute polymerizing solutions, a coupled system of nonlinear advection-reaction-diffusion equations is derived and its numerical solution studied. The main interests are the interplay between the mechanisms of reaction and dispersion as well as the spatial variation in average polymer chain length due to the dispersion process in capillaries.; The work concludes with a summary of the main results and a discussion of directions for future related research. |
