Two‐Dimensional Mass‐Transfer Model of a Flat‐Plate Dialyzer with Ultrafiltration Operation

Tu, Jr-Wei; Ho, Chii‐Dong

doi:10.1002/ceat.200900566

Cited by 7 publications

(9 citation statements)

References 36 publications

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“…The experimental work is cost prohibitive at the present time and there is only the available experimental data from the flat-plate dialyzer for confirmation. The present study could be analogized from those in our previous work on the flat-plate module [ 35 ]; this is a forthcoming work for our laboratory and will be conducted in the near future. In order to validate the theoretical predictions of the two-dimensional mathematical formulations in the concentric circular membrane dialyzer, a comparison was made with the experimental results conducted by the flat-plate dialyzer under ultrafiltration operation in our previous work [ 35 ] which neglected the tube curvature effect in the concentric tube [ 36 ].…”

Section: Resultsmentioning

confidence: 79%

“…A two-dimensional mathematical model of the concentric tubular dialysis-and-ultrafiltration module is developed theoretically. Though the mass-transfer characteristics in the present study could be analogized from those in our previous work on the flat-plate module [ 35 ], the manners of velocity and transport across the membrane are somehow different and the mass-transfer mathematical formulation is relatively complicated. This study actually extends the one-dimensional modeling of the flat-plate module to a two-dimensional analysis of the concentric tubular dialysis-and-ultrafiltration system in the present study to obtain improvements in dialysis efficiency and rate; however, no theoretical study in its simplified expression has been reported in the literature for a concentric tubular dialyzer with an ultrafiltration operation.…”

Section: Introductionmentioning

confidence: 96%

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Device Performance of a Tubular Membrane Dialyzer Incorporating Ultrafiltration Effects on the Dialysis Efficiency

Lim

et al. 2023

Membranes

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Membrane dialysis is one of the membrane contactors applied to wastewater treatment. The dialysis rate of a traditional dialyzer module is restricted because the solutes transport through the membrane only by diffusion, in which the mass-transfer driving force across the membrane is the concentration gradient between the retentate and dialysate phases. A two-dimensional mathematical model of the concentric tubular dialysis-and-ultrafiltration module was developed theoretically in this study. The simulated results show that the dialysis rate improvement was significantly improved through implementing the ultrafiltration effect by introducing a trans-membrane pressure during the membrane dialysis process. The velocity profiles of the retentate and dialysate phases in the dialysis-and-ultrafiltration system were derived and expressed in terms of the stream function, which was solved numerically by the Crank–Nicolson method. A maximum dialysis rate improvement of up to twice that of the pure dialysis system (was obtained by employing a dialysis system with an ultrafiltration rate of and a constant membrane sieving coefficient of . The influences of the concentric tubular radius, ultrafiltration fluxes and membrane sieve factor on the outlet retentate concentration and mass transfer rate are also illustrated.

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Section: Resultsmentioning

confidence: 79%

Section: Introductionmentioning

confidence: 96%

Device Performance of a Tubular Membrane Dialyzer Incorporating Ultrafiltration Effects on the Dialysis Efficiency

Lim

et al. 2023

Membranes

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“…However, for the hollow fiber system with ultrafiltration, the velocity distribution is more complex and is developed by a two-dimensional mathematical model to simulate the mass transport in a hollow-fiber artificial kidney, assuming the shell side as a porous medium [ 10 ]. The influence of ultrafiltration operations on mass transfer in a hollow-fiber hemodialyzer was discussed by Jagannathan and Shettigar [ 11 , 12 ] and applied in the context of a circular conduit dialyzer [ 13 ] and parallel-plate dialyzer with ultrafiltration operations [ 14 ]. The treatment time tolerated by patients can be reduced by applying a hemodialysis membrane with ultrafiltration operations in hollow-fiber hemodialyzers [ 15 , 16 ], which is the active cure to elongate the lives of people suffering from end-stage renal diseases (ESRD) [ 17 ].…”

Section: Introductionmentioning

confidence: 99%

“…The aims in this work are to develop the two-dimensional mathematical statements of a hollow-fiber membrane dialyzer with operating ultrafiltration and to obtain the theoretical predictions compared with experimental data. The general applicability of such a mathematical formulation was developed similar to the parallel-plate dialysis-and-ultrafiltration system in our previous work [ 14 ]. The previous work was confined to a parallel-plate channel while the present paper deals with the conjugated problems in a circular tube with an imaginary shell.…”

Section: Introductionmentioning

confidence: 99%

Two-Dimensional Theoretical Analysis and Experimental Study of Mass Transfer in a Hollow-Fiber Dialysis Module Coupled with Ultrafiltration Operations

Chen

et al. 2023

Membranes

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This research theoretically and experimentally develops a hollow-fiber dialysis module coupled with ultrafiltration operations by introducing a trans-membrane pressure during the membrane dialysis process, which can be applied to the waste metabolic end products in the human body for improving the dialysis efficiency. The solutes were transported by both diffusion and convection from the concentration driving-force gradient between retentate and dialysate phases across the membrane, compared to the traditional dialysis processes by diffusion only. A two-dimensional modeling of such a dialysis-and-ultrafiltration system in the hollow-fiber dialysis module was formulated and solved using the stream function coupled with the perturbation method to obtain the velocity distributions of retentate and dialysate phases, respectively. The purpose of the present work is to investigate the effect of ultrafiltration on the dialysis rate in the hollow-fiber dialyzer with ultrafiltration operations. A highest level of dialysis rate improvement up to about seven times (say 674.65% under Va=20 mL/min) was found in the module with ultrafiltration rate Vw=10 mL/min and membrane sieving coefficient θ=1, compared to that in the system without operating ultrafiltration. Considerable dialysis rate improvements on mass transfer were obtained by implementing a hollow-fiber dialysis-and-ultrafiltration system, instead of using the hollow-fiber dialyzer without ultrafiltration operation. The experimental runs were carried out under the same operating conditions for the hollow-fiber dialyzers of the two experimental runs with and without ultrafiltration operations for comparisons. A very reasonable prediction by the proposed mathematical model was observed.

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“…Tu et al [13] developed a theoretical model for a twodimensional flow of filtrate in a flat-plate dialyzer with the operation of ultra filtration In their study, they used the Crank-Nicolson technique to numerically solve the governing theoretical model. They also derived the fluid velocity profile and the concentration distribution in the dialysis system's membrane with the ultra filtration operation.…”

Section: Introductionmentioning

confidence: 99%

A mathematical model of blood flow in a permeable channel: application to flat plate dialyzer

Kahshan

Rahimi‐Gorji

et al. 2020

Phys. Scr.

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This article presents the theoretical study of the physiological phenomenon brought up by filtration of a non-Newtonian Casson fluid between two parallel permeable membranes. This situation corresponds to blood filtration process in a flat plate hemodialyzer (FPH). Seepage of fluid across the membrane is considered in accordance with the Darcy’s law and the equations of motion governing the flow are modeled. Using the low Reynolds number and long membrane length assumption, equations of motion are solved exactly. Equations describing velocity and pressure filed and various flow variables are derived and effects of wall slip parameter, wall filtration coefficient and the yield stress are presented graphically. A strong influence of these parameters is observed on the flow in an FPH. Theoretical values of the membrane filtration coefficient and mean pressure drop in an FPH are calculated and they are found to be in close agreement with the corresponding available empirical and experimental values in the literature. For certain limiting range of physical parameters, derived solutions reveal that the axial flow rate of Casson fluid in an FPH decays at an exponential rate. This is a physically valid and widely admitted result, used by several researchers in studying the blood filtration process in renal tubules of mammalian kidneys. Since the presented solutions in this article are reduced to their corresponding Newtonian fluid flow solutions between permeable membrane, therefore, it is concluded that a wide range of applications in physiology and engineering can be covered up by the present investigation.

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Two‐Dimensional Mass‐Transfer Model of a Flat‐Plate Dialyzer with Ultrafiltration Operation

Cited by 7 publications

References 36 publications

Device Performance of a Tubular Membrane Dialyzer Incorporating Ultrafiltration Effects on the Dialysis Efficiency

Device Performance of a Tubular Membrane Dialyzer Incorporating Ultrafiltration Effects on the Dialysis Efficiency

Two-Dimensional Theoretical Analysis and Experimental Study of Mass Transfer in a Hollow-Fiber Dialysis Module Coupled with Ultrafiltration Operations

A mathematical model of blood flow in a permeable channel: application to flat plate dialyzer

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