Flow and Film Thickness of Bingham Plastic Liquids on a Rotating Disk

Jenekhe, Samson A.; Schuldt, S. B.

doi:10.1080/00986448508911165

Cited by 26 publications

(9 citation statements)

References 22 publications

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“…Analyses of the flow of non-Newtonian liquids were also presented by lenekhe and Schuldt 6 for the Carreau model, and also for liquids characterized by the power law 6 and Bingham liquids. 7 In these analyses it was shown that the liquid characterized by the Carreau model, which has been found to be suitable for polymer solutions, 8 forms a uniformly thick film during centrifugation due to its Newtonian-like behavior at low shear rates while the Bingham and power-law liquids do not form uniformly thick films.…”

Section: Introductionmentioning

confidence: 99%

The film formation dynamics in spin coating

Ohara

Matsumoto

Ohashi

1989

Physics of Fluids A: Fluid Dynamics

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Thin film formation using the process of spin coating is investigated. The liquid film and surrounding gas phase two-dimensional (2-D) full governing equations with applicable boundary conditions are formulated. The heat and mass transfer that occurs in the gas and liquid phase and across the free surface, including the evaporation of solvent, are taken into account. The governing equations and boundary conditions are then reduced to a I-D case based on the variables radial dependency. The detailed film formation process that commences at the start of the spinning and ends with the dry-up of the coated film is numerically simulated by utilizing the I-D governing equations. The complex effects of various process parameters, e.g., spinning speed, initial solute concentration, and disk heating, are clarified by the present numerical analysis. It was found that the final film thickness is mainly determined at the time when the film thinning rate resulting from radial convection has the same order as the film thinning rate resulting from solvent evaporation.

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Section: Introductionmentioning

confidence: 99%

The film formation dynamics in spin coating

Ohara

Matsumoto

Ohashi

1989

Physics of Fluids A: Fluid Dynamics

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“…The velocities in the respective regions are found to be u 1 *ϭ⑀s ͩ HϪ 2 2 ͪ , u 2 *ϭs ͩ HϪ 2 2 ͪ Ϫ͑1Ϫ⑀ ͒,…”

Section: Discussionmentioning

confidence: 99%

“…Our coneshaped surfaces agree qualitatively with those obtained experimentally by Jenekhe and Schuldt. 2 The paradox of their model was overcome by using the biviscosity model, and letting the two parameters ⑀ and ␦ tend to zero, while kϭ␦/⑀ was kept fixed. In addition to the shear stress, the normal stress components were also included in the yield criterion.…”

Section: Discussionmentioning

confidence: 99%

Spin-coating of a viscoplastic material

Burgess

Wilson

1996

Physics of Fluids

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The flow of a thin film of a yield-stress material on a rotating disc is considered. For the constitutive relation we use the biviscosity model, of which the usual Bingham model is a limiting case. We show that this limiting process conflicts with the usual thin film approximation, so that care is needed to avoid contradictions. It is found that the flow consists of three regions: (1) an inner region centered on the axis of rotation which is unyielded, (2) a shear flow region adjacent to the disc which is bounded above by the yield surface and (3) a region near to the free surface which is unyielded and has the yield surface as lower boundary. It is in the third region that difficulties occur in the straightforward ‘‘Bingham limit.’’ For on the one hand the material is rigid, and on the other it is supposed to move outwards radially. This conflict can be removed by using the biviscosity model and a suitable limiting process.

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“…The spin coating of yield stress fluids was mainly the subject of theoretical studies. The authors (Jenekhe and Schuldt 1985;Burgess and Wilson 1996;Tsamopoulos et al 1996) essentially addressed the difference from Newtonian films, particularly demonstrating that the fluid thickness cannot be uniform. Jenekhe and Schuldt (1985) first analyzed the spin-coating flow of yield stress fluids within the frame of the lubrication approximation.…”

Section: Introductionmentioning

confidence: 99%

“…The authors (Jenekhe and Schuldt 1985;Burgess and Wilson 1996;Tsamopoulos et al 1996) essentially addressed the difference from Newtonian films, particularly demonstrating that the fluid thickness cannot be uniform. Jenekhe and Schuldt (1985) first analyzed the spin-coating flow of yield stress fluids within the frame of the lubrication approximation. They showed that there is a fluid region close to the solid surface and an unsheared region close to the free surface, the thickness of which decreases with the distance from the central axis.…”

Section: Introductionmentioning

confidence: 99%

Flow of a yield stress fluid over a rotating surface

Tabuteau¹,

Baudez²,

Château

et al. 2006

Rheol Acta

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We study the flow of yield stress fluids over a rotating surface when both the viscoelastic solid behavior below a critical deformation (γ c) and liquid properties beyond γ c can play a significant role. We review the detailed characteristics of the flow in the solid regime in the specific case of a pure elongational strain (large height to radius ratio). We, in particular, show that there exists a critical rotation velocity (ω c) associated with the transition from the solid to the liquid regime. We then consider the specific case of lubricational regime (small height to radius ratio) in the liquid regime. In that case we describe the different possible evolutions of the equilibrium shape of the material as a function of the rotation velocity (ω), from which we extrapolate the transient shape evolutions as ω increases. We show that for a sufficiently large rotation velocity the sample separates into two parts, one remaining at rest around the rotation axis, the other going on moving radially. These predictions are then compared with systematic spin-coating tests under increasing rotation velocity ramps followed by a plateau at ω f with typical yield stress fluids. It appears that there exists a critical velocity below which the material undergoes a limited elongation and beyond which it starts to spread significantly over the solid surface. For a larger ω f value the sample forms a thick peripheral roll, leaving behind it a thin layer of fluid at rest relatively to the disc. These characteristics are in qualitative agreement with the theoretical predictions. Beyond a sufficiently large ω f value this roll eventually spreads radially in the form of thin fingers. Moreover, in agreement with the theory in the lubricational regime, the different curves of deformation vs ω fall along a master curve when the rotation velocity is scaled by ω c for different accelerations, different sample radii, or different material yield stress. The final thickness of the deposit seems to be mainly governed by the displacement of the roll, the characteristics of which take their origin in the initial stage of the spreading, including the solid-liquid transition.

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Flow and Film Thickness of Bingham Plastic Liquids on a Rotating Disk

Cited by 26 publications

References 22 publications

The film formation dynamics in spin coating

The film formation dynamics in spin coating

Spin-coating of a viscoplastic material

Flow of a yield stress fluid over a rotating surface

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