Red blood cells are the subject of diverse studies. One branch is the observation and theoretical modelling of their behaviour in a shear flow. This work deals with the flow of single red cells suspended in solutions much more viscous than blood plasma. Below a critical shear rate (γ t ) the red cells rotate with little change of their resting shape. Above that value they become elongated and aligned in the shear field. We measuredγ t at viscosities (η 0 ) ranging from 10.7 to 104 mPa s via observation along the vorticity of a Poiseuille flow in a glass capillary; η 0γt decreased steeply with increasing η 0 up to a value of 25 mPa s and remained constant for higher values. Present theoretical models are not in keeping with the measured data. Modifications of basic model assumptions are suggested.

Elongation measurements of red cells subjected to simple shear flow are usually performed using a single suspending medium (viscosity g 0 ) and varying the mean shear rate ð _ cÞ. Such data are often plotted versus the shear stress ðs ¼ g 0 _ cÞ suggesting that the elongation scales with s. In this work, normal blood samples were tested in a rheoscope varying both g 0 and _ c. The ranges of _ c were chosen to restrict the elongation of the red cells to low values where the behavior is dominated by their intrinsic properties. It was found that the elongation scales with g s 0 _ c with s decreasing from two at g 0 5 20 mPas to unity at g 0 5 70 mPas. Above g 0 5 70 mPas, the elongation is therefore essentially determined by the membrane elasticity alone. A side observation was a large variation of the elongation both intraindividually and interindividually. ' International Society for Advancement of CytometryKey terms rheoscope; image processing; computer modeling; scaling behavior; shape distributions; share of cell viscosities A standard method to measure the mechanical properties of red cells is to suspend the cells in solutions much more viscous than blood plasma and to measure their elongation when the suspension is subjected to simple shear flow (1,2). In addition to being elongated, the membrane moves around the elongated shape thus inducing an eddy flow within the cytoplasm. The membrane motion has been termed tanktread motion (1). The elongation is usually quantified by an elongation index EI ¼ LÀB LþB , where L and B denote the length and the width of the elongated cell. Measurements of EI of different blood samples are usually performed using a constant viscosity of the suspending medium (g 0 ) under variation of the mean shear rate ð _ cÞ. Such data are often plotted versus the shear stress of the undisturbed shear flow ðs ¼ g 0 _ cÞ suggesting that EI scales with s. If, on the other hand, the same blood sample was tested varying both g 0 and _ c, it was shown that EI does not scale with s. Using four viscosities between 12 and 51 mPas, EI was found to scale with g 1:5 0 _ c (3). An exponent greater unity can also be inferred from other experimental results (4,5).To explain this finding, the following hypothesis is put forward. (i) Besides elastic stresses, viscous stresses resist an elongation of tank-treading red cells. (ii) A variable contribution of the viscous stresses being three dimensional in the cytoplasm and two dimensional in the membrane is responsible for an exponent greater unity.To rationalize the hypothesis, we consider the following experiment. We first measure EI with a certain set of _ c and g 0 . Then we decrease _ c by a certain amount and increase g 0 to such an extent that EI remains constant. The elastic stresses and bending moments in the membrane remain essentially constant as EI did not change.

Red cells suspended in solutions much more viscous than blood plasma assume an almost steady-state orientation when sheared above a threshold value of shear rate. This orientation is a consequence of the motion of the membrane around the red cell called tank-treading. Observed along the undisturbed vorticity of the shear flow, tank-treading red cells appear as slender bodies. Their orientation can be quantified as an angle of inclination (θ) of the major axis with respect to the undisturbed flow direction. We measured θ using solution viscosities (η0) and shear rates (γ˙) covering one and three orders of magnitude, respectively. At the lower values of η0, θ was almost independent of γ˙. At the higher values of η0, θ displayed a maximum at intermediate shear rates. The respective maximal values of θ increased by ∼10° from 10.7 to 104 mPas. After accounting for the absent membrane viscosity in models by using an increased cytoplasmic viscosity, their predictions of θ agree qualitatively with our data. Comparison of the observed variation of θ at constant γ˙ with model results suggests a change in the reference configuration of the shear stiffness of the membrane.