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A theoretical model for ice growth due to droplets of supercooled fluid impacting on a subzero substrate is presented. In cold conditions rime (dry) ice forms and the problem reduces to solving a simple mass balance. In milder conditions glaze (wet) ice forms. The problem is then governed by coupled mass and energy balances, which determine the ice height and water layer thickness. The model is valid for “thin” water layers, such that lubrication theory may be applied and the Peclet number is small; it is applicable to ice accretion on stationary and moving structures. A number of analytical solutions are presented. Two- and three-dimensional numerical schemes are also presented, to solve the water flow equation, these employ a flux-limiting scheme to accurately model the capillary ridge at the leading edge of the flow. The method is then extended to incorporate ice accretion. Numerical results are presented for ice growth and water flow driven by gravity, surface tension, and a constant air shear.

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Microphase separation of a polystyrene-block-polyisoprene-block-polystyrene triblock copolymer thin film under confined conditions (i.e., graphoepitaxy) results in ordered periodic arrays of polystyrene cylinders aligned parallel to the channel side-wall and base in a polyisoprene matrix. Polymer orientation and translational ordering with respect to the topographic substrate were elucidated by atomic force microscopy (AFM) while film thickness and polymer profile within the channel were monitored by cross-sectional transmission electron microscopy (TEM) as a function of time over a 6 h annealing period at 120 degrees C. Upon thermal annealing, the polymer film simultaneously undergoes three processes: microphase separation, evaporation of trapped solvent, and mass transport of polymer from the mesas into the channels. A significant volume of solvent is trapped within the polymer film upon spin coating arising from the increased polymer/substrate interfacial area due to the topographic pattern. Mass transport of polymer during this process results in nonuniform films, where subtle changes in the film thickness within the channel have profound effects on the microphase separation process. The initially disordered structure within the film underwent an orientation transition via an intermediate formation of perpendicular cylinders (nonequilibrium) to a parallel (equilibrium) orientation with respect to the channel base. Herein, we present a time-resolved study of the cylinder reorientation process detailing how changing film thickness during the annealing process dramatically affects both the local and lateral orientation of the observed structure. Finally, a brief mathematical model is provided to evaluate spin coating over a complex topography following a classical asymptotic approximation of the Navier-Stokes equations for the as-deposited films.

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