Biomedical Engineering Reference
In-Depth Information
FIGURE 2.22
The apparent viscosity within
the microcirculation would represent the viscos-
ity of the individual fluid and cell pockets, which
may have different nominal values for viscosity.
The apparent viscosity could be considered a
weighted average of these different viscosities but
is realistically just an estimated value. Under most
conditions, the apparent viscosity is not the same
as the bulk viscosity.
8
μ
m
μ
1
μ
2
μ
3
in volume of the system). Within the microcirculation, this assumption is not valid because
we must include mass transfer across the blood vessel wall within the solution. Also, in
Chapter 3, we will develop the Navier-Stokes formula, which can be used to determine
the characteristics of any flow field. In the microcirculation, this formula simplifies to the
Stokes equations because the viscous effects dominate the flow, compared with the inertial
effects (the relationship between inertial and viscous effects comprise the Reynolds num-
ber). The Stokes equations will be described in detail in Part 3 and Part 4. It is also impor-
tant to note that small changes in blood vessel diameter have large effects on the pressure
and velocity distribution within the blood vessel (see Sections 6.4 and 6.5). The take-home
message from this discussion is that all of the fundamental relationships described for
the macrocirculation will still be accurate within the microcirculation. However, some of
the critical parameters that govern flow will change, which can either simplify (Stokes
flow) or complicate (fluid exchange) the problem at hand. It is also critical to determine
the appropriate value for viscosity within the microcirculation because we can no longer
assume that the fluid is homogeneous described by one viscosity.
2.11 FLUID STRUCTURE INTERACTION
The interaction of a flowing fluid and a deformable boundary is defined as a fluid struc-
ture interaction (FSI). As you can image, this should be a major consideration when solving
biofluids mechanics problems because all blood vessels are deformable. A secondary defi-
nition for FSI is the interaction of components within the fluid and the surrounding con-
taining medium. Again this is critical in biofluids problems, in which cells, especially
platelets and white blood cells, can interact with and adhere to endothelial cells. FSI pro-
blems are typically too complex to solve analytically because of the changes in the blood
vessel wall location along with the redistribution of cells to the vessel wall. A large compo-
nent of biofluids computational fluid dynamic research is currently concerned with FSI
(see section 13.2). In this textbook, we will not develop the equations needed to solve these
types of problems, but we will describe some of the applications associated with FSI and
when it would be critical to use this analysis to accurately solve biofluids problems.
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