Biomedical Engineering Reference
In-Depth Information
fluids and, therefore, on power absorption, mixing characteristics and mass transfer rate.
Shear stress in the systems depends on the shear rate and the specific input power:
1
P
τ
=
(1)
γ
V
where
τ
is the shear stress (Pa); γ is the shear rate (1/s); P is the power input (W) and V is
the volume of fluid (m
3
).
For Newtonian fluids, the viscosity is the ratio of shear stress and shear rate, i.e.:
τ
μ=
(2)
γ
being μ is the viscosity (Pa·s).
Therefore, equation (1) can be written as follows:
1
μ
⎛
⎞
2
τ
=
⎝
⎠
(3)
V
For non-Newtonian fluids obeying the power law (equation 4):
n
τ
=
K
γ
·
(4)
being K the consistency index (Pa·s
n
) and n the flow index of the fluid. In this case equation
(1) can be written as:
n
(
1
⎛
P
⎞
n
+
⎛
⎞
n
τ
=
⎜
⎝
K
·
⎟
⎠
⎝
⎠
(5)
V
For agitation under turbulent flow, the power number is almost constant and the specific
input power for Newtonian fluids can be expressed as:
3
5
P
ρ
·
N
·
d
⎛
⎞
=
i
·
N
⎝
⎠
(6)
p
V
V
where ρ is the density of fluid (kg/m
3
); N is the agitation rate (s
-1
); d
i
is the diameter of the
impeller (m) and N
p
is the power number. The power number is defined as a dimensionless
number which expresses the ratio between pressure energy and kinetic energy and depends on
the various geometrical parameters of the impeller (diameter and height) and reactor
(diameter and height), the agitation rate and the fluid properties (density and viscosity). If the
