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The coating dynamics of a drying paint film with a yield stress is studied. The liquid is modeled as a binary mixture with one volatile component, solvent, and one nonvolatile component, resin. When the solvent has a different surface tension than the resin, solvent evaporation can lead to the creation of surface tension gradients which can potentially overcome the yield stress and dramatically affect the flow history. Using the lubrication approximations to derive the flux of the liquid film parallel to the substrate, we find that the presence of the yield stress causes several distinct flow regimes. The total flux of each of these regimes is summed, and using the continuity equation we derive an evolution equation giving the height of the free surface as a function of the distance along the substrate and time. The resulting equations are discretized and solved numerically using finite differences. High order derivative is treated implicitly, allowing for large time steps and reducing the computational requirements. We find that the presence of a yield stress greatly affects the leveling behavior of the coating. Critical yield stresses exist that can cause maximal leveling of the coating film.

Spin coating is frequently used by the coating industry to achieve a very uniform final coating layer on a given substrate. Most of the research into this area has focused on flat substrates, but in this work we use scaling arguments and perturbation methods to derive the lubrication form of the equations governing the fluid motion of a thin liquid film on a curved, rotating, axisymmetric substrate. Though the substrate must be axisymmetric, the coating need not be. Though the slope of the substrate must be continuous, the curvature of the substrate need not be. One application for this work is the spin coating of food and beverage cans, most of which have a curved bottom due to structural reasons. Using an implicit finite difference scheme, we use our derivation to develop a numerical model to simulate the spin coating of the interior of a model soup can. We assume that the coating is initially uniform and model how centrifugal forces drive the coating outward past a series of axisymmetric undulations on the can bottom.

We consider the effect of a magnetic field generated by a current flowing in the axial direction, in a cylindrical conducting medium on the evolution of a thin magnetic liquid film coating the outside of the cylinder. We first derive the new governing equations when a body force, due to the interaction of the magnetic dipoles in the liquid with the magnetic field due to the current in the cylinder, is included with surface tension and gravitational forces. The equations are discretized and solved numerically using an alternating direction implicit algorithm. Simulations demonstrate that the transition from a uniform coating to the formation of undulations to a final configuration of distinct drops follows a similar evolution for a wide range of cylinder radii and magnetic field strengths. Magnetic forces generally oppose the effects of gravity, and consequently the drainage toward the bottom of the cylinder is slowed, the characteristic time for drop formation is delayed, and the final coating is not conf...