Understanding transport phenomena and degradation of bioresorbable medical polymers - Durability and Reliability of Medical Polymers - page 86

c

[4.36] Rrc

s

Rr RRr

s s
R s s Rr s Rr Rr

s
Rr t

p

initially, the membrane is completely dry, so the water, containing amide,
penetrates by capillary fl ow. Assuming the pore walls are wettable (contact
angle = 0°), the fl ow velocity in the longitudinal direction (perpendicular to
the membrane surface) into the matrix is:

sd

dz
t

[4.37]

V = = 4

d

2

ma z

where s is the superfi cial tension, z the penetration depth and a the tortuosity
coeffi cient. This last coeffi cient assumes that in this model, pores are open to
small pipes with radius d which cross the membrane with an average length
of l and thus: a = l/L . Therefore, the penetration depth and the average
velocity may be expressed as:

sd t sd

am t

sd t t

[4.38]

V z fi = =

2

fi V

s

=

2

2 8 am

2

am
2 am 2

am t t 8

This stage continues until the penetration depth is equal to half of the
membrane depth. Thus for time (Fig. 4.2):

2
2 am

2
2 am 2 L 2 am am

*

[4.39]

t t

<

=

2 sd

The process is dominated by convection ( Pe >> 1) and so the amount of
amide that reacts during the time unit J tot , is equal to the amount that enters
the membrane and is represented by the sum of the entering mass fl ow of

￿ ￿ ￿ ￿ ￿ ￿

Convection Diffusion

t *

0 2 4 6 8 10 12 14

t (h)

4.2 Kinetics of the hydrolytic reaction showing the respective
dominant phenomena: convection for t < t * and diffusion for t < t * .