a property of fluid
: ability of a fluid to flow freely, relates applied stress to the
resulting strain rate
U
h
y
x
no-slip condition
( )
y
u y
U
h
=
linear profile
(
)
yx
yx
f
τ
=
∈
general relations will be considered later!
For simple fluids such as water, oil, or gases relationship is linear
Or Newtonian
2
yx
yx
U
du
h
dy
τ
µ
µ
µ
=
=
∈ =
μ: (coef. of) viscosity [N s /m
2
= Pa.s] , μ= μ(T,p)
different for liquids & gases
(
)
yx
yx
f
τ
=
∈
is not linear, the fluid is non-newtonian

time rate of deformation,
Є
inviscid flow (ideal
fluid)
du/dy
0
τ
shear
stress
ideal bingham plastic
Pseudoplastic – shear thinning μ
↓
as
τ↑
Polimer solutions , toothpaste
dilatant – shear tickening,
suspensions, starch,
sand
Newtonian ,
μ=constant
yield
stress
Rigid body
2
n
yx
yx
K
τ
≅
∈
Power-law approx.
n=1 Newtonian K=μ
n<1 pseudoplastic
n>1 dilatant (kaboran)
K, n : material parameters
Power-Law:
0
1
T
n
n
T
yx
yx
yx
ke
τ
−
⎛
⎞
=
∈
∈
⎜
⎟
⎝
⎠
(rheological models of blood)