12.3 Blood as Fluid and its Circulation in Marine Organisms
383
12.3 Blood as Fluid and its Circulation in Marine Organisms
In this section we will briefly summarize a description of the mechanical properties of blood and basic information on blood circulation. More details can
be found in Pedley (1980), and Fung (1993, 1997). Blood is a suspension of
formed elements, namely the red cells, white cells and platelets. Usually, these
elements occupy about 45% (by volume) of the blood. The remainder is made
up of plasma. Plasma is a solution of large molecules, but on the scale of motion
normally encountered in blood vessels, it can be regarded as a homogeneous
Newtonian fluid of molecular dynamic viscosity, fJ" of 0.0012-0.0016 kg/m/s.
However, in very small blood vessels, whole blood cannot be regarded as
a homogeneous fluid, as the diameter and spacing of red cells is comparable
with capillary diameters. In this case, blood is a non-Newtonian incompressible
viscoplastic fluid. It means that for blood flow in small capillaries the Newton's
relationship (1.2) does not apply and the coefficient, v, of the dynamic viscosity
is not a constant value. The anomalous behaviour of blood viscosity is mainly
attributed to the shear-dependent deformation and agregation of red blood
cells. Chien (1970) experimentally found that with an increase in shear rate
(du/dz), the viscosity decreases suspension of red blood cells. The variation of
blood viscosity with plasma protein concentration, hematocrit and shear rate
can be explained as a function of the change in effective cell volume.
However, in most arteries blood behaves in a Newtonian fashion, and the
viscosity can be assumed to be a constant (Ku, 1997). When the diameter
of blood vessels exceeds 100 fJ,m, and the scale of the microstructure is much
smaller than that of the flow, blood is usually treated as a homogeneous fluid
of density p = 1.05 X 10 3 kg/m\ dynamic viscosity fJ, = 0.004 kg/mis, and
kinematic viscosity v = 4 X 10- 6 m 2 /s.
The blood pressure at any location is made up of two components: the hydrostatic component due to both atmospheric pressure and water hydrostatic
pressure at a given depth (see Sect. 2.2), and the dynamic component due to
the pressure generated by the heart and the frictional loss in the blood vessels.
This last component is alone responsible for the motion of the blood and is
commonly known as 'blood pressure'. The work required to circulate the blood
is provided by the heart. In mammals (also aquatic), the heart makes up about
0.58% of the body mass. For fish hearts, experimental data (34 species of fish
ranging from 0.005 to 32 kg) suggest the following relationship between heart
and body size (Schmidt-Nielsen, 1989):
(12.23)
Thus, there is an almost linear dependence of heart mass on fish body mass.
A typical fish of 1 kg mass will have a heart of 2.2 g. The relative size of a fish's
heart is about two and half times smaller than the relative size of a mammal's
heart.
383
12.3 Blood as Fluid and its Circulation in Marine Organisms
In this section we will briefly summarize a description of the mechanical properties of blood and basic information on blood circulation. More details can
be found in Pedley (1980), and Fung (1993, 1997). Blood is a suspension of
formed elements, namely the red cells, white cells and platelets. Usually, these
elements occupy about 45% (by volume) of the blood. The remainder is made
up of plasma. Plasma is a solution of large molecules, but on the scale of motion
normally encountered in blood vessels, it can be regarded as a homogeneous
Newtonian fluid of molecular dynamic viscosity, fJ" of 0.0012-0.0016 kg/m/s.
However, in very small blood vessels, whole blood cannot be regarded as
a homogeneous fluid, as the diameter and spacing of red cells is comparable
with capillary diameters. In this case, blood is a non-Newtonian incompressible
viscoplastic fluid. It means that for blood flow in small capillaries the Newton's
relationship (1.2) does not apply and the coefficient, v, of the dynamic viscosity
is not a constant value. The anomalous behaviour of blood viscosity is mainly
attributed to the shear-dependent deformation and agregation of red blood
cells. Chien (1970) experimentally found that with an increase in shear rate
(du/dz), the viscosity decreases suspension of red blood cells. The variation of
blood viscosity with plasma protein concentration, hematocrit and shear rate
can be explained as a function of the change in effective cell volume.
However, in most arteries blood behaves in a Newtonian fashion, and the
viscosity can be assumed to be a constant (Ku, 1997). When the diameter
of blood vessels exceeds 100 fJ,m, and the scale of the microstructure is much
smaller than that of the flow, blood is usually treated as a homogeneous fluid
of density p = 1.05 X 10 3 kg/m\ dynamic viscosity fJ, = 0.004 kg/mis, and
kinematic viscosity v = 4 X 10- 6 m 2 /s.
The blood pressure at any location is made up of two components: the hydrostatic component due to both atmospheric pressure and water hydrostatic
pressure at a given depth (see Sect. 2.2), and the dynamic component due to
the pressure generated by the heart and the frictional loss in the blood vessels.
This last component is alone responsible for the motion of the blood and is
commonly known as 'blood pressure'. The work required to circulate the blood
is provided by the heart. In mammals (also aquatic), the heart makes up about
0.58% of the body mass. For fish hearts, experimental data (34 species of fish
ranging from 0.005 to 32 kg) suggest the following relationship between heart
and body size (Schmidt-Nielsen, 1989):
(12.23)
Thus, there is an almost linear dependence of heart mass on fish body mass.
A typical fish of 1 kg mass will have a heart of 2.2 g. The relative size of a fish's
heart is about two and half times smaller than the relative size of a mammal's
heart.