Parrish, Chance2023-09-192023-09-192021-05https://hdl.handle.net/11299/257081University of Minnesota Ph.D. dissertation. May 2021. Major: Chemical Engineering. Advisor: Satish Kumar. 1 computer file (PDF); xi, 192 pages.The coating and drying of non-flat discrete objects is a key manufacturing step for a wide variety of products such as medical devices, endoprostheses, and rotationally molded hollow plastic objects. While uniform coatings are often desired for these purposes, controlling coating uniformity may be difficult due to the complicated shapes of some objects and to the large number of phenomena acting on the coating. The objective of this thesis is to enhance our fundamental understanding on the roles of substrate curvature and drying on rotating discrete objects. Herein, we examine three model problems of flow on rotating cylinders, a useful model geometry to examine coating behavior on discrete objects. For the flow of a volatile, particle-laden liquid film on rotating cylinder, lubrication theory has been used to derive a set of evolution equations describing variations in coating thickness and composition as a function of time and the angular coordinate. In the absence of gravity, a linear stability analysis and nonlinear simulations demonstrate that thickness variations arising from liquid flow may give rise to non-uniform drying which diminishes the uniformity of the coating thickness and composition. When gravitational effects are significant, a parametric study reveals that both thickness and composition variations are minimized at large rotation rate, low drying rate, and moderate initial particle concentration. From here, we examine the behavior of non-volatile coatings on cylinders with varying axial and angular curvature to characterize the coating disturbances which may arise due to varying substrate curvature. We first investigate the three-dimensional evolution of thin coatings on topographically patterned cylinders whose curvature variations are small. A lubrication-theory-based model is derived to describe the coating behavior as a function of time, the angular coordinate, and axial coordinate. At large rotation rates, simulations incorporating gravitational effects indicate that the balance between centrifugal and surface-tension forces control the spacing and rate at which thickness disturbances form. A long-wave analysis and linear stability analyses in the absence of gravity provide useful predictions of the coating behavior which agree well with these simulation results. At lower rotation rates, gravitational forces dominate, and simulation results indicate that cylinder topography tends to alter the rate at which droplets form, but does not systematically affect the spacing between droplets. Complementary flow visualization experiments yield results that agree quantitatively with these model predictions at large and low rotation rates. From the experiments, the most uniform coatings are limited to moderate rotation rates, where thickness disturbances develop slowly. While the model developed for cylinders with small curvature variations is useful for characterizing the effect of substrate curvature on coating behavior, the accuracy of this lubrication-based model is expected to deteriorate when curvature variations are large. To efficiently examine the flow of liquid coatings on such objects, the lubrication-theory-based model is extended to examine flow on 2D noncircular cylinders whose curvature variations are large. Good quantitative agreement is found between model predictions and Galerkin finite element method simulations when the coating thickness is small, while qualitative agreement is found for thicker coatings. Encouraged by this agreement, a parametric study is conducted to examine coating behavior on rotating elliptical cylinders. Four regimes of coating behavior are found spanning gravity-dominated regimes and surface-tension-dominated regimes. Overall, from these investigations of coating behavior on rotating cylinders with nonuniform angular and axial curvature, the parameter space yielding smooth coatings is small, and additional steps, such as the addition of surfactants, should be considered to widen this coating window.encapillarycoatingdiscrete objectdryinglubricationsurface tensionThesis or Dissertation