Existence of R‐bounded solution operator families for a compressible fluid model of Korteweg type on the half‐space

2020 ◽  
Vol 44 (2) ◽  
pp. 1744-1787
Author(s):  
Hirokazu Saito
Keyword(s):  
Half Space ◽  
Compressible Fluid ◽  
Bounded Solution ◽  
Fluid Model ◽  
Solution Operator

A novel approach for measuring the intrinsic nanoscale thickness of polymer brushes by means of atomic force microscopy: application of a compressible fluid model

Nanoscale ◽  
2013 ◽  
Vol 5 (23) ◽  
pp. 11679 ◽  
Author(s):  
José Luis Cuellar ◽  
Irantzu Llarena ◽  
Jagoba J. Iturri ◽  
Edwin Donath ◽  
Sergio Enrique Moya
Keyword(s):  
Atomic Force Microscopy ◽  
Compressible Fluid ◽  
Polymer Brushes ◽  
Fluid Model ◽  
Force Microscopy ◽  
Atomic Force ◽  
Novel Approach

Transient Fluid Forces on a Rigid Circular Cylinder Subjected to Small Amplitude Motions

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Cédric Leblond ◽  
Vincent Melot ◽  
Jean-François Sigrist ◽  
Christian Lainé ◽  
Bruno Auvity ◽  
...  
Keyword(s):  
Circular Cylinder ◽  
Compressible Fluid ◽  
Small Amplitude ◽  
Fluid Model ◽  
The Body ◽  
Analytical Models ◽  
Fluid Forces ◽  
History Effects ◽  
Perturbation Problem ◽  
Dimensional Boundary

The present paper treats the transient fluid forces experienced by a rigid circular cylinder moving along a radial line in a fluid initially at rest. The body is subjected to a rapid displacement of relatively small amplitude in relation to its radius. Both infinite and cylindrically confined fluid domains are considered. Furthermore, non-negligible amplitude motions of the inner cylinder, and viscous and compressible fluid effects are addressed, successively. Different analytical methods and models are used to tackle each of these issues. For motions of non-negligible amplitude of the inner cylinder, a potential flow is assumed and the model, formulated as a two-dimensional boundary perturbation problem, is solved using a regular expansion up to second order. Subsequently, viscous and compressible effects are handled by assuming infinitesimal amplitude motions. The viscous fluid forces are formulated by solving a singular perturbation problem of the first order. Compressible fluid forces are then determined from the wave equation. A nonlinear formulation is obtained for the non-negligible amplitude motion. The viscous and compressible fluid forces, formulated in terms of convolution products, are linked to fluid history effects induced by wave propagation phenomena in the fluid domain. These models are expressed with dimensionless parameters and illustrated for a specific motion imposed on the inner cylinder. The different analytical models permit coverage of a broad range of motions. Hence, for a given geometry and imposed displacement, the appropriate fluid model can be identified and the resulting fluid forces rapidly estimated. The limits of these formulations are also discussed.

A Study of Vocal Fold Vibration Using a Slightly Compressible Fluid Domain

2009 ◽  
Author(s):  
D. J. Daily ◽  
S. L. Thomson
Keyword(s):  
Boundary Conditions ◽  
Incompressible Fluid ◽  
Compressible Fluid ◽  
Vocal Fold ◽  
Computational Models ◽  
Fluid Model ◽  
Vocal Folds ◽  
Moving Wall ◽  
Slightly Compressible ◽  
Vocal Fold Vibration

During human voice production, air forced from the lungs through the larynx induces vibration of the vocal folds. Computational models of this coupled fluid-solid system have traditionally utilized an incompressible fluid domain. However, studies have shown that coupling of tracheal acoustics with vocal fold dynamics is significant. Further, in the absence of compressibility, some models fail to achieve self-sustained vibration. This presentation discusses a slightly compressible airflow model, fully coupled with a vocal fold tissue model, as a possible substitute for the traditional incompressible approach. The derivation and justification of the slightly compressible fluid model are discussed. Results are reported of a study of the nature of the coupling between the fluid and vocal fold regions for both slightly compressible and incompressible fluid domains using a commercial fluid-solid finite element package. Three different types of inlet boundary conditions, including constant pressure, constant velocity, and moving wall, are explored. The incompressible and slightly compressible models with the three boundary conditions are compared with each other and with experimental data obtained using synthetic self-oscillating vocal fold models. The results are used to validate the slightly compressible flow model as well as to explore candidate boundary conditions for vocal fold vibration simulations.

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