Fluid mechanics and cross-flow filtration: some thoughts

Belfort, Georges; Nagata, Naohiko

doi:10.1016/0011-9164(85)85052-9

Cited by 108 publications

(27 citation statements)

References 34 publications

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“…A significant contribution to modelling of cross-flow microfiltration is by Belfort and Nagata [1] who emphasized the need for detailed understanding of the fluid dynamics to analyse the effects of concentration polarisation and membrane fouling. In a later article, Belfort [2] attempted modelling of multiphase flows of macromolecules and colloidal suspensions through cross-flow filtration membranes.…”

Section: Introductionmentioning

confidence: 99%

Development of a predictive mathematical model for coupled stokes/Darcy flows in cross-flow membrane filtration

Hanspal

Waghode

Nassehi

et al. 2009

Chemical Engineering Journal

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a b s t r a c tFree flow regimes accompanied by porous walls feature commonly in a variety of natural processes and industrial applications such as groundwater flows, packed beds, arterial blood flows and cross-flow and dead-end filtrations. Cross-flow microfiltration or ultrafiltration processes are generally employed in a range of industrial situations ranging from oil to medical applications. The coupled free/porous fluid transport phenomenon plays an equally important role along with the particle transport mechanisms concerning the separation efficiency of cross-flow membrane filtration. To provide a theoretical background for the experimental outcomes of cross-flow filtration, a mathematically sound model is desired which can reliably represent the interfacial boundary whilst maintaining the continuity of flow field variables across the interface between the free and porous flow regimes. Notwithstanding the numerous attempts reported in the literature, the development of a generic mathematical model for coupled flows has been prohibited by the complexities of interactions between the free and the porous flow systems. Henceforth, the aim of present work is to gain a better mathematical understanding of the interfacial phenomena encountered in coupled free and porous flow regimes applicable to cross-flow filtration systems. The free flow dynamics can be justifiably represented by the Stokes equation whereas the non-isothermal, non-inertial and incompressible flow in a low permeability porous medium can be handled by the Darcy equation. Solutions to the system of partial differential equations (PDEs) are obtained using the finite element method employing mixed interpolations for the primary field variables which are velocity and pressure. A nodal replacement scheme previously developed by the same authors has been effectively enforced as the boundary constraint at the free/porous interface for coupling the two physically different flow regimes in a single mathematical model. A series of computational experiments for permeability values of the porous medium ranging between 10 −6 and 10 −12 m 2 have been performed to examine the susceptibility of the developed model towards complex and irregular shaped geometries. Our results indicate that at high permeability values, the discrepancy in mass balance calculations is observed to be significant for a curved porous surface, which may be attributed to the inability of the Darcy equation to represent the flow dynamics in a highly permeable medium. At a low permeability, a very small amount of fluid permeated through the free/porous interface as most of the fluid leaves the domain through the free flow exit. The geometry and permeability of the free/porous interface are found to affect the amount of fluid passing through the porous medium significantly. All the numerical solutions that are presented have been theoretically validated for their accuracy by computing the overall mass continuity across the computational domains.

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Section: Introductionmentioning

confidence: 99%

Development of a predictive mathematical model for coupled stokes/Darcy flows in cross-flow membrane filtration

Hanspal

Waghode

Nassehi

et al. 2009

Chemical Engineering Journal

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“…Due to a pressure difference across the membrane a permeating stream flows laterally through the duct or channel walls. As discussed by Belfort (1988Belfort ( , 1989 and Belfort and Nagata (1985), the performance of such a pressure-driven membrane process is related to the tangential fluid mechanics across the membrane surface. When applied to liquids containing species like macromolecules, colloids and so on, it is well known that a concentrated layer appears near the membrane so reducing the permeate flux.…”

Section: Introductionmentioning

confidence: 99%

“…When applied to liquids containing species like macromolecules, colloids and so on, it is well known that a concentrated layer appears near the membrane so reducing the permeate flux. This build-up of dissolved solutes, also called concentration polarization, can be predicted and controlled at the membane-solution interface through an understanding of the fluid mechanics and mass transfer (Belfort and Nagata, 1985;Clifton et al, 1984;Van den Berg and Smolders, 1989;Gekas and Olund, 1988;Ren6 and Lalande, 1991). Most of the models used to characterize mass transfer during crossflow filtration make use of a mass transfer coefficient correlation.…”

Section: Introductionmentioning

confidence: 99%

Friction factors and roughness measurements of tubular mineral membranes

Rene¹,

Leuliet²,

Delplace³

1993

Experiments in Fluids

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No direct measurement of the relative roughness is available for mineral porous media because of the low mechanical resistance of such materials. In this study a method for the experimental determination of the internal diameter and the equivalent roughness is proposed for different commercial membranes tised in ultrafiltration and microfiltration processes. The use of classical friction factor correlations is also discussed. The main results are the estimation of the hydraulic diameter of tubular membranes and the use of a quadratic form in order to predict friction factors and the equivalent roughness with an accuracy better than 15%.

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“…Hence, the value of K at a particular temperature is constant and can be evaluated by rearranging Eq. (15). As an example, Table 3 presents the experimental FO data that is used to determine the value of K for a thin film composite FO membrane.…”

Section: Flux Predictionmentioning

confidence: 99%

“…The mass transfer coefficient is commonly calculated using Sherwood (Sh) number relations which are empirical correlations as a function of Reynolds Schmidt numbers [13]. The Sh number relationships available in the literature were either adapted from the analogy between heat and mass transfer or were derived for flow in non-porous smooth [13][14][15]. These relations were later modified for the ultrafiltration (UF) experiments [13,14].…”

Section: Introductionmentioning

confidence: 99%

Effect of Internal and External Concentration Polarizations on the Performance of Forward Osmosis Process

Bhinder¹,

Shabani²,

Sadrzadeh³

2018

Osmotically Driven Membrane Processes - Approach, Development and Current Status

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Forward osmosis (FO) as an osmotically driven membrane process is severely affected by the concentration polarization phenomenon on both sides of the membrane as well as inside the support layer. Though the effect of internal concentration polarization (ICP) in the porous support on the draw solution side is far more pronounced than that of the external concentration polarization (ECP), still the importance of ECP cannot be neglected. The ECP becomes particularly important when the feed flow rate is enhanced to increase the permeation flux by increasing the agitation and turbulence on the membrane surface. To capture the effect of ECP a suitable value of mass transfer coefficient must be determined. In this chapter, an FO mass transport model that accounts for the presence of both ICP and ECP phenomena is first presented on the basis of solution-diffusion model coupled with diffusion-convection. Then, three methods for the estimation of mass transfer coefficient based on empirical Sherwood (Sh) number correlations, pressure-driven reverse osmosis (RO), and osmosis-driven pressure retarded osmosis (PRO) are proposed. Finally, a methodology for the prediction of water flux through FO membranes using the theoretical model and calculated/measured parameters (hydraulic permeability, salt resistivity of the support layer, and mass transfer coefficient) is presented.

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Fluid mechanics and cross-flow filtration: some thoughts

Cited by 108 publications

References 34 publications

Development of a predictive mathematical model for coupled stokes/Darcy flows in cross-flow membrane filtration

Development of a predictive mathematical model for coupled stokes/Darcy flows in cross-flow membrane filtration

Friction factors and roughness measurements of tubular mineral membranes

Effect of Internal and External Concentration Polarizations on the Performance of Forward Osmosis Process

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