Flow management in nanofiltration spiral wound modules with ladder-type spacers

Geraldes, Vı́tor

doi:10.1016/s0376-7388(01)00753-0

Cited by 119 publications

(60 citation statements)

References 23 publications

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“…This geometry of a spiral-wound membrane module should be compared with Fig. 3 in the paper by Geraldes et al [3]. The flow field would represent an input to an advection-diffusion model of the distribution of solute within the module.…”

Section: Practical Implications For Membrane Modulesmentioning

confidence: 99%

“…The streamlines are calculated assuming Stokes flow: the limit of vanishing Reynolds number, wherein viscous effects dominate over inertial effects. Although Reynolds numbers in the range 50-1000 may be encountered in actual membrane modules [3], the dominance of viscous over inertial forces sufficiently near the singular points means that we can rely on the Stokes equations to elucidate the singularity [15]. Regarding observable ramifications of the Beavers-Joseph slip condition (9), Fig.…”

Section: Practical Implications For Membrane Modulesmentioning

confidence: 99%

“…1). Within spiral-wound membrane modules, such a geometry can be found at the junction between the membrane and (1) the sealed entry or exit section of the wall [1,2], or (2) a transverse filament of a ladder-type spacer [3][4][5][6][7]. These two cases are distinguished by the respective wedge angles Θ = π versus Θ = π/2.…”

Section: Introductionmentioning

confidence: 99%

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Stokes flow singularity at a corner joining solid and porous walls at arbitrary angle

Nitsche

2017

J Eng Math

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Motivated by the internal flow geometry of spiral-wound membrane modules with ladder-type spacers, we consider the Stokes flow singularity at a corner that joins porous and solid walls at arbitrary wedge angle Θ. Seepage flux through the porous wall is coupled to the pressure field by Darcy's law; slip is described by a variant of the Beavers-Joseph boundary condition. On a macroscopic, outer length scale, the singularity appears like a jump discontinuity in the normal velocity, characterized by a non-integrable 1/r divergence of the pressure. For arbitrary Θ, we develop an algebraic criterion to determine the admissible radial exponent(s) in a leading, inner similarity solution-which represents a weaker, integrable singularity in the pressure. A complete map of exponent versus Θ is provided for 0 < Θ < 2π : this has an intricate structure with infinitely many solution branches clustering around Θ = π and Θ = 2π . By generalizing the similarity form with a (ln r ) term and iterating on the slip and seepage conditions, we can carry the outer and inner power series to arbitrarily high order. Nevertheless, a numerical splice is required in between. For this purpose, we apply an iterative, numerical-asymptotic patching scheme described by Nitsche and Parthasarathi (J Fluid Mech 713:183-215, 2012). Detailed velocity and pressure profiles are calculated for three wedge angles (Θ = 3π/4, π/2, π/4) and two dimensionless slip lengths (σ = 20, 40). The general trends for decreasing wedge angle are (i) weakening of the pressure singularity, (ii) increasing magnitude of the radial component of velocity, and (iii) movement of the inner-outer transition farther from the corner. Wedges with Θ < π are seen to differ fundamentally from the flat wedge (Θ = π ) previously considered by Nitsche and Parthasarathi (2012).Keywords Low-Reynolds-number flow · Porous walls · Generalized similarity solutions · Boundary integral method Electronic Supplementary material The online version of this article

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Section: Practical Implications For Membrane Modulesmentioning

confidence: 99%

Section: Practical Implications For Membrane Modulesmentioning

confidence: 99%

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Stokes flow singularity at a corner joining solid and porous walls at arbitrary angle

Nitsche

2017

J Eng Math

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“…Moreover, spiral wound modules are often preferred in industry because they offer a good balance between ease of operation, fouling control, permeation rate and packing density (Geraldes et al, 2002;Schwinge et al, 2004). Some membrane processes have been used in winemaking for a long time.…”

Section: Introductionmentioning

confidence: 99%

“…Due to the low feed flow rates, the role of feed spacers in mass transfer enhancement is of utmost importance (Geraldes et al, 2002).Several experimental works in plane-channels 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 6 containing different periodic arrays of small-diameter cylinders (mimicking spacers) showed that the presence of them caused a flow destabilization (Karniadakis et al, 1988;Koutsou et al, 2004;Zovatto and Pedrizzetti, 2001). In fact, it has been concluded (Karniadakis et al, 1988) that this cylinders act as eddy promoters and their presence leads to the destabilization of the flow by essentially the same mechanism as in rectangular channels but at much lower Reynolds numbers (on the order of hundreds rather than thousands).…”

Section: Introductionmentioning

confidence: 99%

Comparative study of red grape must nanofiltration: Laboratory and pilot plant scales

Salgado

Palacio

Prádanos

et al. 2015

Food and Bioproducts Processing

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Steric and electrostatic interactions govern nanofiltration of amino acids

Shim

Chellam

2007

Biotech & Bioengineering

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Crossflow nanofiltration experiments were performed to investigate the factors influencing the removal of amino acids by a commercially available polymeric thin-film composite membrane. The removals of five monoprotic (Ala, Val, Leu, Gly, and Thr), one diprotic (Asp), and one dibasic (Arg) amino acids in a range of permeate fluxes, feed pH values, and ionic strengths were analyzed using a phenomenological model of membrane transport. At any given pH and ionic strength, reflection coefficients (rejection at asymptotically infinite flux) of monoprotic amino acids increased with molar radius demonstrating the role of steric interactions on their removal. Additionally, consistent with Donnan exclusion, higher reflection coefficients were obtained when the membrane and the amino acids both carried the same nature of charge (positive or negative). In other words, both co-ion repulsion and molecular size determined amino acids removal. Importantly, the removal of effectively neutral amino acids were significantly higher than neutral sugars and alcohols of similar size demonstrating that even near their isoelectric point, zwitterionic characteristics preclude them from being considered as strictly neutral.

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Flow management in nanofiltration spiral wound modules with ladder-type spacers

Cited by 119 publications

References 23 publications

Stokes flow singularity at a corner joining solid and porous walls at arbitrary angle

Stokes flow singularity at a corner joining solid and porous walls at arbitrary angle

Comparative study of red grape must nanofiltration: Laboratory and pilot plant scales

Steric and electrostatic interactions govern nanofiltration of amino acids

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