Numerical Simulation for Blood Flow - Microsurgery: Advances, Simulations, and Applications - page 167

deformation (extension ⋅ shear deformation), inner stress arises
during luid's deformation process.
The simplest deformation occurs when a viscous luid is placed
between parallel plates, and one of the plates moves at constant rate
(Fig. 5.5).

du
dy

U N

(5.24)

yx

y

x

Figure 5.5 Wall shear stress on a lat plate.

Here, because shear stress acts in a direction of x axis in a plane
vertical to y axis. This resistance law can be generalized as “shear
stress U proportional to shear deformation γ acts in viscous luid.”

u

¥
§ ¦ u u

µ
· ¶

v
x

u
y

U U H N (5.25)

xy yx xy

u

u

¥
§ ¦ u u

µ
· ¶

w
y

v
z

U U H N

(5.26)

yz zy yz

u

u

¥
§ ¦

u u

µ
· ¶

u
z

w
x

U U H N
zx

(5.27)

xz zx

u

In the case of ideal luid, only pressure “ p ” is considered normal
stress. As for linkage between normal stress and deformation in
viscous luid, distortion effect γ xx = ∂u/∂x + ∂u/∂x is on the pattern