Maximum Principle for Pressure in Ideal Incompressible Fluid Flows

Golubkin, V. N.; Kovalev, Vitalii Petrovich; Sizykh, G. B.

doi:10.1615/tsagiscij.2017019567

Cited by 2 publications

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“…1). The implicit assumption is that one can apply the maximum principle for pressure [16]. When this principle is valid, the maximum and minimum pressure values are located at the domain's boundary.…”

Section: Resultsmentioning

confidence: 99%

On the application of the Spiegler-Kedem model to forward osmosis

2019

BMC Chem Eng

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In Forward Osmosis the diffusion of the solute is counter to that of the solvent i.e. there is so-called "reverse salt diffusion". Furthermore, the ratio of the two fluxes is generally taken to be a constant because of the assumption of ideal semi-permeability. However with the Spiegler-Kedem (S-K) model there is an allowance for a minor deviation from ideal semi-permeability and the ratio of the solute flux and solvent flux is no longer constant. The theoretical variation of the solute flux with increasing draw solution concentration is illustrated for various degrees of deviation from ideal semi-permeability. A novel variant of the S-K model is also introduced and predictions compared with those obtained using the standard form. With the acceptance that the form of "breakthrough" involving co-current flow is impossible, a limitation is imposed upon the S-K model but even with this limitation the theoretically predicted variation of solvent flux with increasing draw concentration is for certain sets of parameters of an unexpected form for minor deviation from ideal semi-permeability. That intriguing counter-intuitive outcomes can result from application of the S-K model indicates a need to rethink its formulation of the equations and the expressions for the coefficients. This will have implications for forward osmosis and possibly reverse osmosis modelling.

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Section: Resultsmentioning

confidence: 99%

On the application of the Spiegler-Kedem model to forward osmosis

2019

BMC Chem Eng

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“…В работе исследован вопрос о месте точек минимума давления. Исследованию этого вопроса уделяли внимание основатели современной гидродинамики [9][10][11][12][13] и посвящают свои работы современные авторы [14][15][16][17][18][19][20]. Дело в том, что место точек минимума давления важно для исследования процесса возникновения кавитации [17].…”

Section: Introductionunclassified

Gravitational principle of minimum pressure for incompressible flows

Prosviryakov¹

2021

DREAM

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We consider the flows of ideal (Euler equations) and Newtonian viscous (Navier–Stokes equations) incompressible fluids in the gravitational field of mass forces. In this case, the gravitational field created by the liquid itself (self-gravity) is also taken into account. It is shown that some well-known principles of maximum pressure, according to which either the pressure is constant in the flow region, or the minimum pressure is reached at the boundary of this region if the forces of self-gravity are taken into account, exclude the case of constant pressure. It is also demonstrated that self-gravity makes it impossible for waves and solitons to pass with pressure minima to the surface of a body flown around by a viscous fluid.

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Maximum Principle for Pressure in Ideal Incompressible Fluid Flows

Cited by 2 publications

References 0 publications

On the application of the Spiegler-Kedem model to forward osmosis

On the application of the Spiegler-Kedem model to forward osmosis

Gravitational principle of minimum pressure for incompressible flows

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