Discussion of Predictions from Polar Fluid Theory Which Are Independent of Spin Boundary Conditions

1982 ◽  
Vol 26 (3) ◽  
pp. 317-319 ◽  
Author(s):  
Kenneth A. Kline
Keyword(s):  
Boundary Conditions ◽  
Polar Fluid ◽  
Fluid Theory

scholarly journals Rotational Particle Separation in Solutions: Micropolar Fluid Theory Approach

Polymers ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1072
Author(s):  
Vladimir Shelukhin
Keyword(s):  
Mathematical Model ◽  
Rotational Diffusion ◽  
Particle Separation ◽  
Theory Approach ◽  
Steady Flows ◽  
Concentric Cylinder ◽  
Polar Fluid ◽  
Fluid Theory ◽  
Couette Cell ◽  
Granular Fluid

We develop a new mathematical model for rotational sedimentation of particles for steady flows of a viscoplastic granular fluid in a concentric-cylinder Couette geometry when rotation of the Couette cell inner cylinder is prescribed. We treat the suspension as a micro-polar fluid. The model is validated by comparison with known data of measurement. Within the proposed theory, we prove that sedimentation occurs due to particles’ rotation and rotational diffusion.

Effects of Suspending Abrasives on the Lubrication Properties of Slurry in Chemical Mechanical Polishing of Silicon Wafer

2006 ◽  
Vol 304-305 ◽  
pp. 359-363 ◽  
Author(s):  
J.Y. Liu ◽  
Zhu Ji Jin ◽  
Dong Ming Guo ◽  
Ren Ke Kang
Keyword(s):  
Silicon Wafer ◽  
Chemical Mechanical Polishing ◽  
Fluid Pressure ◽  
Three Dimensional ◽  
Mechanical Polishing ◽  
Polar Fluid ◽  
Light Load ◽  
Fluid Theory ◽  
Lubrication Properties ◽  
Load Conditions

The lubrication properties of the slurry between the silicon wafer and the pad in chemical mechanical polishing (CMP) are critical to the planarity of the silicon wafer. Moreover, the suspending abrasives, which are contained in the slurry, have an extremely important influence on the lubrication properties of the slurry. In the CMP process of the large-sized silicon wafers, the influence of suspending abrasives on the slurry becomes more prominent. In order to explore the effects of suspending abrasives on the lubrication properties of the slurry under the light load conditions, a three-dimensional lubrication model based on the micro-polar fluid theory is developed. The effects of suspending abrasives on the fluid pressure acting on the wafer and the distribution of the slurry film between the silicon wafer and the pad are discussed.

Viscous fluid damping in a laterally oscillating finger of a comb-drive micro-resonator based on micro-polar fluid theory

2016 ◽  
Vol 32 (3) ◽  
pp. 397-405 ◽  
Author(s):  
Sahra Azma ◽  
Ghader Rezazadeh ◽  
Rasoul Shabani ◽  
Elnaz Alizadeh-Haghighi
Keyword(s):  
Viscous Fluid ◽  
Comb Drive ◽  
Polar Fluid ◽  
Fluid Damping ◽  
Fluid Theory ◽  
Micro Resonator

Use of the Magnetostatic Analogue In Electromagnetic Lens Engineering

1970 ◽  
Vol 28 ◽  
pp. 360-361
Author(s):  
John W. Coleman
Keyword(s):  
Boundary Conditions ◽  
High Performance ◽  
Force Fields ◽  
Optical Design ◽  
Direct Conversion ◽  
Design Engineering ◽  
Design Data ◽  
Scalar Potentials ◽  
Geometric Elements ◽  
At Will

In the design engineering of high performance electromagnetic lenses, the direct conversion of electron optical design data into drawings for reliable hardware is oftentimes difficult, especially in terms of how to mount parts to each other, how to tolerance dimensions, and how to specify finishes. An answer to this is in the use of magnetostatic analytics, corresponding to boundary conditions for the optical design. With such models, the magnetostatic force on a test pole along the axis may be examined, and in this way one may obtain priority listings for holding dimensions, relieving stresses, etc..The development of magnetostatic models most easily proceeds from the derivation of scalar potentials of separate geometric elements. These potentials can then be conbined at will because of the superposition characteristic of conservative force fields.

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