A new Navier-Stokes and Darcy's law combined model for fluid flow in crossflow filtration tubular membranes

Damak, Kamel; Ayadi, Abdelmoneim; Zeghmati, Belkacem; Schmitz, Philippe

doi:10.1016/s0011-9164(04)90041-0

Cited by 85 publications

(52 citation statements)

References 28 publications

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“…A comprehensive review about the CFD methods applied to membrane processes has been made by Ghidossi et al (2006) [13]. Most studies were made under laminar conditions since most of the membrane processes work under these conditions [14][15][16][17]. The slit-type configuration represents the basic model to characterize the flow in industrial membrane modules, thus restricting the flow to laminar conditions and causing severe problems of CP.…”

Section: Introductionmentioning

confidence: 99%

Visualization and modeling of the polarization layer in crossflow reverse osmosis in a slit-type channel

Salcedo‐Díaz

García-Algado

Garcia‐Rodriguez

et al. 2014

Journal of Membrane Science

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The evolution of the concentration polarization layer during crossflow reverse osmosis in a slit channel has been studied. Digital Holographic Interferometry allows visualizing the polarization layer as an interference fringe pattern. An especial module with four windows has been designed to see the development of the polarization layer along the membrane channel. Several experiments with a constant transmembrane pressure of 6 bar, three different feed concentrations (3, 6 and 9 kg/m 3 ) and three different Re (13, 38 and 111) had been carried out. The process has been modelled simulating the experimental conditions. The computed results were found to be consistent with the experimental ones. All the experiments show a continuous increase of the polarization layer along the channel, regardless of the crossflow velocity, except near the outlet of the cell due to an edge effect. This increase in the polarization layer is greater at lower Re, although it does not influence very much the permeate flux. In contrast, what substantially affects the permeate flux, much more than Re number, is the feed concentration due to its osmotic pressure.

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Section: Introductionmentioning

confidence: 99%

Visualization and modeling of the polarization layer in crossflow reverse osmosis in a slit-type channel

Salcedo‐Díaz

García-Algado

Garcia‐Rodriguez

et al. 2014

Journal of Membrane Science

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“…According to Damak et al [5][6][7] and Pak et al [8], as the fluid is forced to pass under the membrane in crossflow, the solvent is forced to flow through the membrane due to the action of a pressure difference across the permeable membrane. The decrease in permeate flow rate is closely related to the decrease in driving force and increased resistance to permeation.…”

Section: Advances In Mechanical Engineeringmentioning

confidence: 99%

Separation Process by Porous Membranes: A Numerical Investigation

Cunha

Souza

Neto

et al. 2014

Advances in Mechanical Engineering

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A major problem associated with the membrane separation processes is the permeate flux drop, limiting the widespread of industrial application of this process. This occurs due to the accumulation of solute concentration near the membrane surface. An exact quantification of the concentration polarization as a function of process conditions is essential to estimate the system performance satisfactorily. In this sense, this work aims to predict the behavior of the concentration polarization boundary layer along the length of a permeable tubular membrane, over various operation conditions. The numerical solution of the Navier-Stokes equation, coupled to Darcy's and mass transfer equations, is obtained by the commercial software ANSYS CFX 12, considering a twodimensional computational domain. The study evaluates the effects of axial Reynolds and Schmidt numbers on the concentration polarization boundary layer thickness during the cross-flow filtration process. Numerical results have shown that the mathematical model is able to predict the formation and growth of the concentration polarization boundary layer along the length of the tubular membrane.

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“…The feed stream in the tube or outside of the membrane, is modeled by the Navier-Stokes equations. The simplified mass and momentum equations, i.e., Navier-Stokes equations expressed in cylindrical coordinates with axisymmetry assumption, are as (Damak et al, 2004):…”

Section: Full-scale Description Of the Process In Hollow Fiber Membranementioning

confidence: 99%

“…When someone knows the mass transfer rate through the membrane, these rate equations now can be put into the full-scale mass balance equation as boundary value to describe the concentration distribution on the lumen side, feed side or on the shell side, permeate side. The full-scale description of flow in crossflow filtration tubular membrane or in flat sheet membrane is also very often the object of investigations (Damak et al, 2004). A fluid dynamic description of free flows is usually easy to perform, and in a great majority of examples, the well known Navier-Stokes equations can be used to coupling Darcy's law and the Navier-Stokes equations (Mondor & Moresoli, 1999;Damak et al, 2004).…”

Section: Introductionmentioning

confidence: 99%

“…The full-scale description of flow in crossflow filtration tubular membrane or in flat sheet membrane is also very often the object of investigations (Damak et al, 2004). A fluid dynamic description of free flows is usually easy to perform, and in a great majority of examples, the well known Navier-Stokes equations can be used to coupling Darcy's law and the Navier-Stokes equations (Mondor & Moresoli, 1999;Damak et al, 2004). A steady-state, laminar, incompressible, viscous and isothermal flow in a cylindrical tube with a permeable wall is considered.…”

Section: Introductionmentioning

confidence: 99%

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