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Design analysis of parallel plate and hollow fibres haemofilters

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Abstract

A theoretical model of mass transfer by ultrafiltration (u.f.) at large transmembranes pressures in parallel plate and hollow fibres haemofilters is presented. The analysis assumes that the maximum u.f. flow QFM is limited by protein concentration polarisation and that the concentration boundary layer is thin. It takes into account the decrease of local blood flow along the membrane and therefore remains valid when the u.f. flow rate is a large fraction of the incoming blood flow Qbi. It is found that the ratio QFM/Qbi increases nonlinearly with S/(Qbidh) where S is the membrane area and dh the hydraulic diameter of the blood film. A parallel-plate haemofilter will have 20% more ultrafiltration than one of hollow fibre of the same membrane area and blood volume. However, if the two units have the same u.f. flow rate, the hollow fibre one will have the smaller blood volume. For a fibre type haemofilter at a given blood flow, QFM is a function of the total fibre length and is independent of fibre diameter. By using a blood film thickness in the vicinity of 150 μ, adequate clearances (0·4Qbi) can be obtained with membranes areas of 0·6 to 0·7 m2, significantly less than with present haemodialysers.

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Abbreviations

A′ :

constants of Graetz correlation

b :

membrane width

C g :

gel concentration

C p :

local protein concentration

d :

fibre diameter

D :

diffusion coefficient

d h :

hydraulic perimeter

G :

Graetz number

h :

blood-channel thickness

H :

haematocrit

J :

local h.f. flux

k :

local mass transfer coefficient

K :

averaged mass transfer coefficient

L :

membrane length

N :

number of fibres

n :

exponent of Graetz correlation

p :

blood pressure

Q b :

blood-flow rate

Q FM :

maximum u.f. rate

S :

membrane area

V b :

blood velocity:Q b/hb

x :

distance along membrane

y :

normal co-ordinate

β:

dilution ratio

γ:

shear rate at membrane

μ:

blood viscosity

μp :

plasma viscosity

i :

inlet conditions

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  1. Department of Biological Engineering, Technological University of Compiègne, 60206, Compiègne, France

    M. Y. Jaffrin

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  1. M. Y. Jaffrin
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Jaffrin, M.Y. Design analysis of parallel plate and hollow fibres haemofilters. Med. Biol. Eng. Comput. 19, 321–327 (1981). https://doi.org/10.1007/BF02442552

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  • DOI: https://doi.org/10.1007/BF02442552

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