On the extensional rheology of human blood

1
On the extensional rheology of human blood R J
Poolea, A Swifta, T V Howb aDepartment of
Engineering, University of Liverpool, Brownlow
Hill, Liverpool, L69 3GH, UK bDivision of
Clinical Engineering, Faculty of Medicine,
University of Liverpool, Duncan Building, Daulby
Street, Liverpool, L69 3GA
Non-Newtonian properties of blood Blood is a
suspension of cellular elements in a salt and
protein solution called plasma. Although the
plasma behaves as a Newtonian liquid, these
cellular elements, 99 of which are deformable
red blood cells, give rise to its non-Newtonian
properties. Blood is frequently modelled in
haemodynamics research as a Newtonian liquid,
even though it is known that it exhibits numerous
non-Newtonian characteristics. In shear, in
addition to displaying thixotropy, it is
shear-thinning and possesses a yield stress, and
in oscillation it has been shown to be
viscoelastic. The shear-thinning property of
blood is perhaps its most well known
non-Newtonian characteristic but even this is
frequently ignored and blood is modelled as a
constant viscosity inelastic liquid. Here we
report on the response of whole human blood in a
uniaxial extensional flow. As far as we are
aware, no previous measurements have been made of
the extensional properties of blood. To
investigate the extensional properties we used
the Capillary Break-up technique (CaBER, Thermo
Haake).

• Blood
• Eight samples obtained from healthy volunteers
• Anti-coagulant added (heparin)
• Special procedure used to draw blood to minimise
  cell damage
• Natural haematocrit level (44 lt H lt 52)

Rheological characterisation TA 1000 N
double-concentric cylinder steady shear,
oscillatory shear Thermo Haake CaBER uniaxial
extension
t -20 ms
t -4 ms
t 26 ms
t 63 ms
Capillary Break-up Extensional Rheometer
Figure 2 Sequence of images showing the initial
configuration and extensional deformation of a
filament of blood (H50) followed by the onset
of viscocapillary thinning and ultimate break-up
(tc? 75 ms). The diameter of the endplates is 4
mm.
viscoelastic response
?EX0.125 s
? hf / h0
?EX0.145 s
inertia dominated
solid ligament
hf ? 8 mm
DMID (t)
D 4 mm
h0 2 mm
Figure 4 The filament midpoint diameter for five
different runs for donor 1 (H46). Filled
symbols indicate samples which formed solid
ligaments at late times.
Figure 3 The filament midpoint diameter for
five different runs for donor 3 (H50). Filled
symbols indicate samples which formed solid
ligaments at late times.
t - 20 ms
t gt 0
Figure 1 Schematic of the CaBER geometry
containing a fluid sample (a) at rest and (b)
undergoing filament thinning for tgt0.
In this simple technique a cylindrical liquid
bridge of the test liquid is formed between two
circular plates 4 mm in diameter. An axial step
strain is then applied (i.e. the end plates are
rapidly pulled apart to a fixed separation) which
results in the formation of an elongated liquid
thread. The thread diameter reduces due to
surface tension (s) and information about the
extensional properties of the liquid can be
deduced from the evolution of the filament
midpoint diameter which is monitored using a
laser micrometer.
t? 100 ms
tgt 1000 ms
Figure 5 The filament midpoint diameter for
four different runs for donor 2 (H52). Filled
symbols again indicate when solid ligament
formed. Note large variation in results for
nominally identical conditions.
Figure 6 Two images showing late times for a
CaBER test in which a solid ligament is formed.
Ligament was found to occur on more than half the
tests and was clear, solid and between 10 and 200
µm in diameter.
A simple one-dimensional analysis, neglecting
axial curvature and assuming that the filament is
axially uniform, shows that the filament can be
characterised simply by its midpoint diameter
Ideal elastic liquid (Entov and Hinch, JNNFM 1997)
Newtonian liquid (McKinley and Tripathi, JoR 2000)

• Conclusions
• Preliminary measurements show that the
  extensional properties of
• blood can be measured using the capillary
  break-up technique.
• Blood exhibits a viscoelastic response before
  intense thinning prior to
• break-up.
• Despite the presence of an anti-coagulant, a
  large number of samples
• produced a clear, solid, ligament after this
  intense thinning. The
• diameter of this ligament varied considerably
  between both tests and
• samples but was generally between 10 and 200 µm
  in diameter.

Alternatively you may calculate a Hencky strain
at the midpoint and estimate an apparent
extensional viscosity