Effects of Cyclic Loading and Binding to Extracellular Matrix on Macromolecular Transport in Soft Biological Tissue - Progress in Organic and Physical Chemistry: Structures and Mechanisms - page 91

where i B .

The way of presentation the results will become clear after short insight into me-
chanics of poroelastic materials, because the existence of convective transport in the
gel during deformation and its effectiveness is closely tied with the ability of the gel
to squeeze the À uid through its pores. The convective À ow distribution inside the gel
depends strictly on the frequency of loading. This can be shown by solving the ¿ rst
equation in the system (22) for three sample frequencies:

= F , B , F +

′

1,10,100 , R g

= 100 , and

f =

0.05 . As a result, the À uid velocity amplitudes versus the normalized distance
from the surface are presented on the Figure 1 for those frequencies. By analyzing the
curves it may be concluded that there is a characteristic depth where the convective
À ow is signi¿ cant. This distance depends on frequency. For higher frequencies the
surface layer, which is able to increase mass transfer is narrower. At low frequencies
the slope of velocity pro¿ le is more À at, but the amplitude is lower.
This relation has been pointed out b y other authors [9, 15, 18]. The expression

ε 0 =

h

H A ⋅ k

for the characteristic depth is . The maximum convection velocity drops =

f

considerably by this depth and consequently, there is negligible mass transport accel-
eration deeper in the gel. The zero velocity depth can be estimated as 2

h . When the ⋅

2

concentration front reaches x

h , the gain in mass uptake starts to decrease. That is =

2

h as the length of the gel ( h

why we choose 2

= h ) to solve the transport-reaction

⋅

equations.

FIGURE 2 The maximum velocity of fluid flow during cyclic loading of the gel as a function
of depth for the three frequencies.