On the extensional rheology of human blood R J Poole a, A Swift a, T V How b a Department of Engineering, University of Liverpool, Brownlow Hill, Liverpool, L69 3GH, UK b Division 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). Capillary Break-up Extensional Rheometer 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 (  ) 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 =- 20 ms t > 0 D = 4 mm h 0 = 2 mm h f  8 mm  = h f / h 0 D MID (t) Figure 1: Schematic of the CaBER geometry containing a fluid sample (a) at rest and (b) undergoing filament thinning for t>0. 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% < H < 52%) Rheological characterisation TA 1000 N double-concentric cylinder: steady shear, oscillatory shear Thermo Haake CaBER: ‘uniaxial’ extension t= -20 ms Figure 3: The filament midpoint diameter for five different runs for donor 3 (H=50%). Filled symbols indicate samples which formed solid ‘ligaments’ at late times. Figure 5: The filament midpoint diameter for four different runs for donor 2 (H=52%). Filled symbols again indicate when solid ligament formed. Note large variation in results for nominally identical conditions. Figure 2: Sequence of images showing the initial configuration and extensional deformation of a filament of blood (H=50%) followed by the onset of viscocapillary thinning and ultimate break-up (t c  75 ms). The diameter of the endplates is 4 mm. 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. Figure 4: The filament midpoint diameter for five different runs for donor 1 (H=46%). Filled symbols indicate samples which formed solid ‘ligaments’ at late times. 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: Newtonian liquid (McKinley and Tripathi, JoR 2000) Ideal elastic liquid (Entov and Hinch, JNNFM 1997) Alternatively you may calculate a Hencky strain at the midpoint and estimate an apparent ‘extensional viscosity’: 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. t  100 ms t> 1000 ms t= -4 mst= 26 ms t= 63 ms inertia dominated solid ‘ligament’ viscoelastic response λ EX =0.145 s λ EX =0.125 s