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Brinkmanship is the activity of threatening to do something dangerous to get what you want. Learn more about this term, its usage in politics and business, and its synonyms and antonyms.
BRINKMANSHIP definition: 1. the activity, especially in politics, of trying to get what you want by saying that if you do…. Learn more.
Brinkman Equations Theory. The dependent variables in the Brinkman equations are the Darcy velocity and the pressure. The flow in porous media is governed by a combination of the continuity equation and the momentum equation, which together form the Brinkman equations:
- Theory of Porous Media in Brief
- Biphasic Materials
- The Darcy and Darcy–Brinkman Equations
- Remark
- Remark 1
- Remark 2
- Triphasic Materials
- GeneratedCaptionsTabForHeroSec
As the classical equations described above, the equations governing porous media mechanics are based on a macroscopic, continuum mechanical description, where the porous solid material and the pore content are smeared out over the control volume. This leads to a continuum-mechanical setting, where the balance equations of the overall aggregate as w...
The biphasic medium \(\varphi \) under discussion is understood as a deformable porous solid material \(\varphi S\) saturated by a single pore fluid \(\varphi F\). Both constituents, solid and fluid, are taken as materially incompressible components, meaning that their intrinsic densities \(\rho {\alpha R}\) remain constant under isothermal conditi...
Concerning the reduction in the setting (37) towards the findings by Darcy and the modification by Brinkman, one has to be aware that the classical equations proceed from a non-deforming solid skeleton, such that \(\mathbf{u}_S\equiv \mathbf{0}\). Thus, \((\mathbf{u}_S)\prime _S\) is dropped from (37)\(_1\), while (37)\(_2\)does not play any role a...
As Darcy’s law (51) has been obtained without the need to use the assumption of a non-deforming skeleton, Darcy’s law also holds without further restrictions when \(\mathbf{v}_{FV}\) is identified as \(nF\mathbf{w}_F\)including the skeleton motion: The Darcy–Brinkman equation In contrast to the Darcy law valid at the macroscopic range with \(L\gg {...
In contrast to the Darcy equation, the Brinkman equation cannot be adopted to fluid flow in deformable porous solids without discussion. This is due to the fact that the term \(\text{ div }\,\mathbf{T}F_\mathrm{fric}=\mu {FR}\varDelta \,\mathbf{v}_F\) was found on the basis of (43)\(_1\). However, for deformable solid skeletons, (43)\(_1\) has to b...
As has been stated after (19), Brinkman wanted to show that his equation containing a corrector term compared to the original Darcy equation was appropriate to describe situations with low and high permeabilities. This usually describes a situation, where a transition from a porous domain towards a free flow domain is considered. On the other hand,...
For the investigation of the continuum-mechanical validity of the Richards equation, the consideration of a triphasic medium of solid skeleton, pore water and pore gas is necessary. According to Sect. 3.2, the triphasic medium \(\varphi \) under discussion is understood as a deformable porous solid material \(\varphi S\) that is saturated by two im...
The article reviews the classical hydromechanical equations of Darcy, Forchheimer, Brinkman and Richards, and their significance in the light of the Theory of Porous Media. It derives the Brinkman equation as a generalization of Darcy's law for inertial and tortuosity effects, and discusses its validity and applications.
- Wolfgang Ehlers
- Wolfgang.Ehlers@mechbau.uni-stuttgart.de
- 2020
Brinkmanship is the art or practice of pushing a dangerous situation or confrontation to the limit of safety especially to force a desired outcome. Learn more about the word history, examples, and related entries of brinkmanship from Merriam-Webster dictionary.
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Brinkman definition: a person who is skilled in or practices brinkmanship.. See examples of BRINKMAN used in a sentence.
