Modelling and Simulation of Spin Coating on a Spherical Substrate

Shepherd, Ross; Sellier, Mathieu; Boujo, Édouard

doi:10.14264/7e6b295

Cited by 4 publications

(8 citation statements)

References 10 publications

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“…These governing equations ensures the conservation of mass and linear momentum respectively, and can be highly non-linear. In general, there exists no analytical solution for the Navier-Stokes equations, however models have been developed to predict the thickness of evolving thin film flows over rotating flat (Lee et al, 2019) and curved surfaces (Shepherd et al, 2022).…”

Section: Fluid Mechanics Of Spin Coatingmentioning

confidence: 99%

Applications of Rotational Manipulators in the Manufacture and Characterization of Highly Curved Thin Films

McIntyre,

Sellier,

Gooch

et al. 2023

Proc. Des. Soc.

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What do common devices such as smartphones, CD’s and solar panels all have in common? They are all examples of innovative technology that is still limited to flat, rigid geometries. This is primarily due to the limitations of the manufacturing processes used to create components within these devices, key among them the thin polymer films produced through spin coating.Spin coating is a technique used due to its ability to effectively create uniform films on the scale of micro or nanometres. However, it relies on a planar substrate to produce uniform layers, thus restricting the design of components manufactured using this process to simple, flat objects. As the requirement for curved device geometries expands, complex alternative fabrication methods are being implemented in industry.For spin coating to remain relevant, a viable process for controlling the fluid flow over curved surfaces must be developed. This research investigates the hypothesis that coating distributions can be controlled through optimized rotation of a curved substrate. Where a multi-axis rotational manipulator and novel characterization system have been developed to investigate the fabrication of curved devices using the improved spin coating technique.

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Section: Fluid Mechanics Of Spin Coatingmentioning

confidence: 99%

Applications of Rotational Manipulators in the Manufacture and Characterization of Highly Curved Thin Films

McIntyre,

Sellier,

Gooch

et al. 2023

Proc. Des. Soc.

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“…Setting a = c = r s , we recover the evolution equation governing the dynamics of a thin film on a rotating sphere derived in [14,15] using a different approach.…”

Section: Lubrication Model For the Spheroidmentioning

confidence: 99%

“…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. Building on what is already known concerning the evolution of a thin liquid film on a rotating cylinder [6][7][8], a stationary [9][10][11][12][13] and a rotating sphere [14,15], in this study we consider the fluid dynamics of a liquid layer on a rotating spheroid as a natural extension of the spherical and cylindrical cases with two distinct principal radii of curvature.…”

Section: Introductionmentioning

confidence: 99%

Thin Liquid Film Dynamics on a Spinning Spheroid

Duruk

Boujo

Sellier

2021

Fluids

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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.

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“…The total volumetric body force acting on the fluid is the combination of these respective forces, as shown in Eqs. (1-4) [4], where T r denotes the time-dependent rotational transformation matrix between the two reference frames [5]. Aligning the axis of rotation ω with gravity g conserves the orientation of these vectors in both reference frames.…”

Section: Introductionmentioning

confidence: 99%

“…Table 1 shows the definition of the dimensionless numbers which can be used along with the aspect ratio, δ = h c /L c , to identify the dominant forces within the system [15]. In these expressions, L c denotes the characteristic length of the surface or substrate radius for the case of a sphere, and h c describes the average film thickness over the substrate surface [4]. ω c is the characteristic angular velocity which is commonly expressed as the magnitude of rotational speed achieved by the substrate during the coating process.…”

Section: Introductionmentioning

confidence: 99%

Film thickness characterization in dual-axis spin coating of a sphere

McIntyre,

Sellier,

Gooch

et al. 2024

Eur. Phys. J. Spec. Top.

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The versatility of spin coating technology makes it a preferred method for producing the thin film layers used to manufacture products from solar panels and smartphones to sunglasses and CDs. However, the process requires a flat, rigid substrate to produce uniform films, which limits its use to planar devices. A novel multi-axis manipulator has been developed to extend the application of spin coating, enabling controlled thin film deposition onto curved surfaces. Various rotational schemes were studied to link the flow of a liquid film over a curved surface to forces induced by complex rotational dynamics. When the angular velocity exceeds a threshold, centrifugal force dominates the flow, pushing the fluid away from the instantaneous axis of rotation. This produces axisymmetric coating profiles when using consistent single or dual-axis rotation. Areas of near uniformity present around the spin axis poles for single-axis rotation and around the substrate’s equator for dual-axis schemes. Sensitivities between the spherical substrate dynamics and the evolving fluid flow were investigated, exploring the parameters that promoted the production of uniform curved film layers for microfabrication processes. This enabled the evolution of the spin coating technique to effectively form curved polymer coatings with improved thickness control. The presented research outlines the capabilities of a multi-axis spin coating machine when used to coat spherical substrates. Therefore, enabling the use of fluid mechanics models to identify the optimal motion kinematics required to create uniform curved films.

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Modelling and Simulation of Spin Coating on a Spherical Substrate

Cited by 4 publications

References 10 publications

Applications of Rotational Manipulators in the Manufacture and Characterization of Highly Curved Thin Films

Applications of Rotational Manipulators in the Manufacture and Characterization of Highly Curved Thin Films

Thin Liquid Film Dynamics on a Spinning Spheroid

Film thickness characterization in dual-axis spin coating of a sphere

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