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Please use this identifier to cite or link to this item: http://hdl.handle.net/1783.1/6134
Title: A scaling approach to the derivation of hydrodynamic boundary conditions
Authors: Qian, Tie-Zheng
Qiu, Chunyin
Sheng, Ping
Keywords: Hydrodynamic boundary condition
Onsager principle
Surface-layer scaling process
Issue Date: Sep-2008
Citation: Journal of fluid mechanics, v. 611, September 2008, p. 333-364
Abstract: We show hydrodynamic boundary conditions to be the inherent consequence of the Onsager principle of minimum energy dissipation, provided the relevant effects of the wall potential appear within a thin fluid layer next to the solid wall, denoted the surface layer. The condition that the effect of the surface layer on the bulk hydrodynamics must be independent of its thickness h is shown to imply a set of consistent ‘scaling relationships’ between h and the surface-layer variables/parameters. The use of the scaling relations, in conjunction with the surface-layer equations of motion derived from the Onsager principle, directly leads to the hydrodynamic boundary conditions.We demonstrate the surface-layer scaling process both physically and mathematically, and relate the parameters of the boundary conditions to those in the surface-layer equations of motion. In spatial regions outside the surface layer, equivalence between the use of surface-layer dynamics and boundary conditions is numerically demonstrated for Couette flows. As an application of the present approach, we derive the liquid-crystal hydrodynamic boundary conditions in which the rotational and translational dynamics are coupled.
Rights: © Cambridge University Press 2008. This paper was published in Journal of Fluid Mechanics, v. 611, September 2008, p. 333-364 and is reprinted with permission
URI: http://hdl.handle.net/1783.1/6134
Appears in Collections:MATH Journal/Magazine Articles
PHYS Journal/Magazine Articles

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