Free surface and thin film flows in planar and cylindrical geometries appear in a wide variety of industrial applications, such as ink-jet printing, fiber-spinning, agricultural and industrial spraying, film coating and curtain coating. It is common for these flows to undergo some form of instability, a feature that may or may not be desired. In either case, controlling instabilities is paramount to maintaining quality control in applications. The results of this project will contribute to the fundamental understanding of the role that: fluid properties (specifically, surface tension, viscosity and elasticity); flow conditions (Stokes versus inertial flows); and flow geometry (planar versus cylindrical), play on hydrodynamic stability. Three problems will be studied in detail: (1) the motion and stability of time-dependent free surface extensional flows of viscous and viscoelastic fluids; (2) the dynamics of free surface perturbations that form along a coated wire; and (3) the dynamics and stability of thin film coating flows. The project is interdisciplinary in scope with theoretical, numerical and experimental components involved. The equations which model these flows: the Navier-Stokes equations, the Cauchy equations coupled to a viscoelastic constitutive model, 1D slender asymptotic equations and thin film equation will be analyzed using techniques in partial differential equations, linear stability analysis, asymptotic analysis and numerical methods. Experiments serve two purposes: observations in the lab will be used to gain intuition into the mathematical modeling, and theoretical and numerical predictions will be compared directly to experimental data to check the validity of these results. This project includes the training of undergraduate students in mathematical methods, numerical simulation and experiments providing an interdisciplinary research experience.
Free surface and thin film flows appear in a wide variety of industrial applications, such as ink-jet printing, fiber-spinning, agricultural and industrial spraying, film coating and curtain coating. It is common for these flows to undergo some form of instability, a feature that may or may not be desired. In either case, controlling instabilities is paramount to maintaining quality control in applications, whether it involves producing a spray of equal drop size, reducing secondary drop formation in ink-jet printing to prevent splatter on the printed page or applying an even coat of paint with no drip marks or dry patches. The results of this project will contribute to the fundamental understanding of the role that fluid properties, flow conditions and flow geometry play on the stability of a flow. Three problems will be studied in detail: (1) the motion and stability of time-dependent free surface extensional flows of viscous and viscoelastic fluids; (2) the dynamics of free surface perturbations that form along a coated wire; and (3) the dynamics and stability of thin film coating flows. The project is interdisciplinary in scope with theoretical, numerical and experimental components involved. Experiments serve two purposes: observations in the lab will be used to gain intuition into the mathematical modeling, and theoretical and numerical predictions will be compared directly to experimental data to check the validity of these results. This project includes the training of undergraduate students in mathematical methods, numerical simulation and experiments providing a truly interdisciplinary research experience.
