Abstract
The present work explores the impact of rotation on the dynamics of a thin liquid layer deposited on a spheroid (bi-axial ellipsoid) rotating around its vertical axis. An evolution equation based on the lubrication approximation was derived, which takes into account the combined effects of the non-uniform curvature, capillarity, gravity, and rotation. This approximate model was solved numerically, and the results were compared favorably with solutions of the full Navier–Stokes equations. A key advantage of the lubrication approximation is the solution time, which was shown to be at least one order of magnitude shorter than for the full Navier–Stokes equations, revealing the prospect of controlling film dynamics for coating applications. The thin film dynamics were investigated for a wide range of geometric, kinematic, and material parameters. The model showed that, in contrast to the purely gravity-driven case, in which the fluid drains downwards and accumulates at the south pole, rotation leads to a migration of the maximum film thickness towards the equator, where the centrifugal force is the strongest.
Highlights
Spin coating is a process which is routinely used in the microfabrication of multiple devices, including printed circuit boards, displays, solar cells, or microfluidic devices
The process of spin coating has been optimized for flat, rigid surfaces, and much is currently understood about spin coating such surfaces
The present study aims to broaden the current understanding of the dynamics of a thin liquid film subjected to rotation on a non-flat surface through mathematical modeling and numerical simulations
Summary
Spin coating is a process which is routinely used in the microfabrication of multiple devices, including printed circuit boards, displays, solar cells, or microfluidic devices. The pioneering work of Schwartz and Weidner in [16] to formulate the lubrication approximation governing the leading order dynamics of a thin liquid film on a curved substrate was later extended, generalized, and formalized in [17,18,19,20]. This general framework was elegantly applied in [21] to shed light on the dynamics of droplets on virtual leaf surfaces.
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