Two-Dimensional Analysis of an Elastic Layer Coupled to a Viscous Fluid

2004 ◽  
Vol 71 (2) ◽  
pp. 162-167 ◽  
Author(s):  
Jongwon Seok ◽  
Andrew T. Kim ◽  
Timothy S. Cale ◽  
John A. Tichy
Keyword(s):  
Viscous Fluid ◽  
Critical Thickness ◽  
Chemical Mechanical Planarization ◽  
Finite Thickness ◽  
Applied Pressure ◽  
Direct Application ◽  
Two Dimensional ◽  
Soft Layer ◽  
Additive Property ◽  
Linear Elasticity Theory

A two-dimensional elastohydrodynamic analysis is performed on a system consisting of a viscous fluid flowing between a sliding soft layer of finite thickness and a tilted flat plate. The behavior of a soft layer subject to a distributed contact pressure is described in detail. Green’s functions are obtained for each Fourier coefficient of the distributed applied pressure, utilizing the additive property of linear elasticity theory. The resulting equations are numerically evaluated for some typical cases. As a function of the contact dimension, calculations are performed for the critical thickness of the layer beyond which the deformed shape essentially resembles that of the layer having an infinite thickness, in the case of a uniformly applied pressure. We also investigate the effect of layer thickness on the hydrodynamics, which illustrates that conditions in which the infinite half-space assumptions can be justified are highly limited. The findings of this paper have direct application to the modeling of chemical mechanical planarization (CMP).

Effect of Applied Pressure on the Ceria Chemical Mechanical Planarization

2021 ◽  
Vol MA2021-01 (20) ◽  
pp. 825-825
Author(s):  
Donggeon Kwak ◽  
Seungjujn Oh ◽  
Junho Yun ◽  
Juhwan Kim ◽  
Taesung Kim
Keyword(s):  
Chemical Mechanical Planarization ◽  
Applied Pressure

A SEMI-ANALYTICAL METHOD FOR A FLOW OF NON-VISCOUS FLUID AROUND AN AIRFOIL WITH A SHARP TRAILING EDGE

2021 ◽  
pp. 4-10
Author(s):  
Alexey A. Bondarchuk ◽  
Mezhlum A. Sumbatyan
Keyword(s):  
Viscous Fluid ◽  
Analytical Method ◽  
Velocity Vector ◽  
Point Vortex ◽  
Two Dimensional ◽  
Double Layer Potential ◽  
Boundary Contour ◽  
Trailing Edge ◽  
Layer Potential ◽  
Two Dimensional Flow

In the present work we propose a method to study a two-dimensional flow of non-viscous fluid around an airfoil with a sharp trailing edge, by the double-layer potential theory. The circulation of velocity vector is modeled by the potential of a point vortex whose center is located inside the boundary contour. The magnitude of the circulation is defined on the basis of the Joukowski-Chaplygin postulate. There are presented some results for a Joukowski rudde, as well as for the airfoil in the form of a pair of interacting circles. It is performed a comparison of the circulation with its theoretical value.

Stress Driven Patterning of Epitaxial Films

1993 ◽  
Vol 318 ◽  
Author(s):  
Michael A. Grinfeld
Keyword(s):  
Surface Energy ◽  
Surface Morphology ◽  
Film Thickness ◽  
Critical Thickness ◽  
Epitaxial Films ◽  
Layer By Layer ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Periodic Spacing

ABSTRACTWe study possible morphologies of epitaxial films atop attractive substrates appearing as a result of competition of misfit stresses, van der Waals forces and surface energy. Corresponding formula for the critical thickness of the dislocation-free Stranski-Krastanov pattern is established for the isotropic deformable films and substrates. If the film thickness exceeds the critical magnitude the layer-by-layer pattern switches to islanding. At the first stage the islands have a shape of striae (i.e. long parallel trenches with periodic spacing). We discuss also i)the circumstances in which surface morphology of the film corresponds to a two-dimensional superlattice of islands rather than a one dimensional lattice of striae and ii)the influence of a buffer inter-layer.

Numerical Investigation of EHD Conduction Pumping of Liquid Film With Phase-Change

2007 ◽  
Author(s):  
Miad Yazdani ◽  
Jamal Seyed-Yagoobi
Keyword(s):  
Heat Transfer ◽  
Liquid Film ◽  
Phase Change ◽  
Flow System ◽  
Thin Liquid Film ◽  
Finite Thickness ◽  
Constant Heat Flux ◽  
Two Dimensional ◽  
Enhanced Heat Transfer ◽  
Constant Heat

Electrohydrodynamic (EHD) conduction pumping is associated with the heterocharge layers of finite thickness in the vicinity of the electrodes, generated by the process of dissociation of the neutral electrolytic species and recombination of the generated ions. This paper numerically investigates the EHD conduction pumping of a thin liquid film in the presence of phase change. The flow system comprises a liquid film flowing over a two-dimensional flat plate while the vapor phase extended far beyond the interface to result in almost motionless vapor. The channel is separated into four different sections: the entrance, electrode, evaporation, and downstream sections. The entrance, electrode and downstream regions are adiabatic while a constant heat flux is applied in the evaporation side. The concept of EHD conduction pumping of liquid film in the presence of phase change is demonstrated in this paper. The enhanced heat transfer due to conduction pumping is evaluated.

Natural Convection in a Micro Size Horizontal Cylindrical Annulus With Periodic Volumetric Heat Flux

2009 ◽  
Author(s):  
Kamyar Mansour
Keyword(s):  
Heat Flux ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Viscous Fluid ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Similarity Parameter ◽  
Symbolic Calculation ◽  
Cylindrical Annulus ◽  
Gap Ratio

We consider the two-dimensional problem of steady natural convection in a narrow (Micro size) Horizontal Cylindrical annulus filled with viscous fluid and periodic volumetric heat flux. The solution is expanded in powers of a single combined similarity parameter, which is the product of the Gap ratio to the power of four, and Rayleigh number and the series extended by means of symbolic calculation up to 16 terms. Analysis of these expansions allows the exact computation for arbitrarily accuracy up to 50000 figures. Although the range of the radius of convergence is almost zero but Pade approximation lead our result to be good even for much higher value of the similarity parameter.

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