Bioprocess Biosyst Eng (2010) 33:921–927 which were 0, 4, 20, 100 and 500 rpm, respectively. The levels of rotational speed applied to the algae in 0.3% LBG were 0, 4, 10, 15, 20, 100 and 500 rpm, respectively. The algae in 0.5% LBG were exposed to the following levels of rotational speed: 0, 2, 4, 10, 20 and 100 rpm. The exposure time to the different levels of shear stress was 1 h and the temperature 4 C. All exposures in the shear cylinders were done in triplicate. A second experiment was carried out to investigate the time dependence of shear stress effect. Algae in 0.3% LBG were exposed to a rotational speed of 100 rpm for different times of exposure ranging from 1 to 120 min. The tem- perature was 4 C as in the ﬁrst experiment. All tests were done in triplicate. For all treatments the Taylor number was calculated to ﬁnd out whether ﬂow instabilities occurred. Taylor vortices will be formed when the Taylor number is higher than the limiting value of 41.3 [26, 27]. The Taylor number is deﬁned as: j 1 3=2k=g xqRi2ðdcc 3 Þ ð Þ Ta ¼ where x is the angular velocity, q is 1,024 kg m-3 for seawater with algae at 4 C, g is the apparent viscosity (Pa s) and dcc is the ratio of the outer to the inner cylinder radius, which is 1.05. Rheological characterization The shear stress was measured with a sample of 3.6 mL of the algae (without LBG, in 0.3 and 0.5% LBG solution) after exposure in the shear cylinders. A rheometer (type Physica MCR 301, Anton Paar) was used to measure the exact shear stress applied in the shear cylinders. The measurements were done at 4 C. From the shear stress, the apparent viscosity can be calculated using the following equation: g ¼ sc_ ð4Þ where s is the shear stress (Pa), g is the apparent viscosity (Pa s) and c_ is the shear rate (s-1). For Newtonian ﬂuids, g is independent of c_ and for non- Newtonian ﬂuids, g depends on c_ [26]. The power-law model was used to describe this dependence [28, 29]. g ¼ mjc_jn 1 s ¼ cgn The parameters m and n were measured from a log–log plot with apparent viscosity against shear rate. The same power-law model is used to measure the dependence between shear rate and shear stress [26]. 5 ð Þ 6 ð Þ The parameters c and n were also measured from a log–log plot of shear stress versus shear rate. 923 Assessment of the viability The viability of the algae was measured by using the ﬂuorescein diacetate (FDA) staining method. Esterases in viable cells cleave FDA with the formation of ﬂuorescein as a result. Fluorescein is a compound that ﬂuoresces green in viable cells and does not give ﬂuorescence in non-viable cells [30, 31]. A FDA stock solution was prepared by dissolving 46 mg FDA (Sigma) in 10 mL acetone (11 mM) and stored in the dark at -4 C. One milliliter of the sample containing the algae was incubated with 10 lL FDA stock solution for 20 min [32]. Then the total amount of algal cells and the viable cells were counted in a cell chamber (hemocytometer DHC-B02-5 Bu¨ ker Tu¨rk) using a ﬂuorescence microscope (Olympus IX71). Viability of the algae was taken as the percentage of ﬂuorescing algae. In LBG, the algal cells did not settle at the bottom of the cell chamber, but were suspended over the 0.1 mm depth of the cell chamber. To count the cells, it was therefore necessary to scan over the depth of the cell chamber by adjusting the focus of the microscope. Results and discussion Flow regime characterization Figure 1 shows the relation between the shear rate and shear stress applied to the algae suspension without LBG, in 0.3% LBG and in 0.5% LBG. As expected, higher shear stress levels could be obtained through an increase in either the shear rate or the viscosity, with the help of a thickener. LBG led to a shear-thinning behavior. The slopes of the ﬂow curves with shear stress as a function of shear rate on a logarithmic scale are less steep for the LBG concentrations. This can also be seen in the power-law model functions where n \ 1 for the algae in LBG, while n & 1 for the algae without LBG (Eq. 6). The shear stress levels that were applied in the further experiments were calculated with the power-law model functions in Fig. 1 and are presented in Table 1. Viscosity as a function of shear rate is shown in Fig. 2 for the algae without LBG, the algae in 0.3% LBG and 0.5% LBG, respectively. The viscosity of the algae without LBG, which is the original culture of Chaetoceros muelleri in the medium, is almost independent of the shear rate. Therefore, the algae without LBG behave nearly Newto- nian. This Newtonian behavior suggests that there is little interaction between the algal cells in the suspension and that they behave as separate cells, rather than as clustered cells. Non-Newtonian behavior is apparent for the algae in LBG, where shear-thinning is evident. Therefore, the 123