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Porous Media

A Porous Media Approach for Analyzing a Countercurrent Dialyzer System

[+] Author and Article Information
Yoshihiko Sano

Department of Mechanical Engineering,  Shizuoka University, 3-5-1 Johoku, Hamamatsu 432-8561, Japan

Akira Nakayama1

Department of Mechanical Engineering, Shizuoka University, 3-5-1 Johoku, Hamamatsu 432-8561, Japan; School of Civil Engineering and Architecture,  Wuhan Polytechnic University, Wuhan, Hubei 430023, Chinatmanaka@ipc.shizuoka.ac.jp

1

Corresponding author.

J. Heat Transfer 134(7), 072602 (May 25, 2012) (11 pages) doi:10.1115/1.4006104 History: Received August 19, 2011; Revised November 21, 2011; Published May 24, 2012; Online May 25, 2012

A porous media approach based on the volume-averaging theory has been proposed to investigate solute diffusion and ultrafiltration processes associated with hemodialysis using a hollow fiber membrane dialyzer. A general set of macroscopic governing equations has been derived for the three individual phases, namely, the blood phase, the dialysate phase, and the membrane phase. Thus, conservations of mass, momentum, and species are considered for blood compartments, dialysate compartments, and membranes within a dialyzer to establish a three concentration equation model. These macroscopic equations can be simultaneously solved for the various cases of inlet velocities of blood and dialysate. An analytic expression for the solute clearance was obtained for the one-dimensional case, in which important dimensionless parameters controlling the dialyzer system are identified for the first time.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Control volume in a porous medium

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Figure 3

Ultrafiltration through a membrane

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Figure 4

Comparison of the present model and Kedem–Katchalsky model

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Figure 5

Velocity and solute variations along the axial coordinate for the case of pure diffusion

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Figure 6

Velocity and solute variations along the axial coordinate for the case of symmetric flow rates

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Figure 7

Effect of blood flow velocity on the pure diffusive clearance of solutes (●:Experiment by Jaffrin [25] ——, : Present model; L=20cm,N=8500,db=220μm,tm=45μm,A=11.94cm2, Lp=5.63×10-11m/sPa,Pm(creatinine)=4.172×10-6m/s,Pm(vitaminB12)=1.675×10-6m/s)

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Figure 8

Effect of ultrafiltration flow rate on the clearance enhancement (●:Experiment by Jaffrin [26] ——, : Present model; ——— : Linear approximation; L=20cm,N=8500,db=220μm,tm=45μm,A=11.94cm2, Lp=5.63×10-11m/sPa,Pm(creatinine)=4.172×10-6m/s,Pm(vitaminB12)=1.675×10-6m/s, Aub(0)=200ml/min, Aud(1)=-500ml/min)

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Figure 9

Temporal variation of the solute concentration (creatinine: A(ub(0)-ub(1)) = 60 ml/min, Vb=42,000ml, CL=164.8 ml/min, γ=0.364)

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