924 Bioprocess Biosyst Eng (2010) 33:921–927 Fig. 1 Shear stress as a function of shear rate: algae without LBG (diamonds), algae in 0.3% LBG (squares) and algae in 0.5% LBG (triangles) Fig. 2 Viscosity as a function of shear rate: algae without LBG (diamonds), algae in 0.3% LBG (squares) and algae in 0.5% LBG (triangles) apparent viscosity needs to be determined at the different shear rates for the calculation of the accurate shear stress levels applied. A study of shearing insect cells has also indicated that assuming Newtonian behavior of cell cul- tures could cause substantial error in shear stress estimates [29]. The Taylor number for every apparent viscosity value was calculated with Eq. 3 (Table 1). In all experiments laminar ﬂow was maintained, except at the highest shear rate of 1,079 s-1 in the algae dispersion without LBG. Taylor vortices may have been formed during that exper- iment and this could have led to secondary ﬂow to a certain extent. The highest shear rate that can be applied for algae without LBG, while keeping the algae in laminar ﬂow, is about 150 s-1. The use of LBG increased the viscosity, leading to a lower Taylor number. For that reason, LBG or other thickeners can be used to reach higher shear stress under stable laminar ﬂow to the extent that they do not affect the viability directly. Maldonado and Latz [24] also used thickeners to increase the viscosity for applying two different shear stress levels at the same shear rate to study the short-term effect of shear stress on a dinoﬂagellate. The dimensions of the shear cylinders are also important in creating a stable laminar ﬂow, because the diameter of the inner cylinder and the gap between the inner and outer cylinder are relatively small. A Couette device with a bigger inner cylinder diameter and a relatively bigger gap leads to a smaller critical angular velocity with the formation of Taylor vortices or turbulent ﬂow as a result [33, 34]. It is difﬁcult to determine the applied shear stress if ﬂow instabilities are present. The effect of shearing treatment on viability In all processing conditions tested, the shape of the cells was unaltered. This holds for the viable cells as well as for the non-viable cells. The total cell concentration of the algae that were exposed to the high shear stresses did not decrease either. The viable and non-viable cells could only be discriminated by the FDA staining method, where the viable cells showed ﬂuorescence (Fig. 3). Obviously, the affected cells must be damaged internally without any visible external impact observed in quiescent conditions after the shearing treatment. Table 1 Shear stresses applied and Taylor numbers in relation with shear rates Rotational speed (rpm) Shear rate Shear stress without Taylor number Shear stress 0.3% (s-1) LBG (Pa) 0% LBG LBG (Pa) Taylor number 0.3% LBG Shear stress 0.5% LBG (Pa) Taylor number 0.5% LBG 0 2 4 10 15 20 100 500 123 0 4.31 8.63 21.57 32.36 43.14 215.7 1,079 0 – 0.016 – – 0.077 0.376 1.83 0 – 1.04 – – 5.39 27.6 141 0 – 0.541 1.07 1.44 1.78 5.89 19.4 0 – 0.031 0.097 0.162 0.232 1.76 13.3 0 0.795 1.31 2.53 – 4.15 13.2 – 0 0.0052 0.013 0.041 – 0.100 0.783 –