922 cases of shear damage were described, shear stress was only quantiﬁed indirectly by using the liquid ﬂow rate or the number and frequency of pump passages. A ﬁrst step towards quantiﬁcation of the shear rate or shear stress was done by Contreras et al. [17] and Garc´ıa Camacho et al. [18]. They used the energy dissipation to calculate an average shear rate or shear stress. For Phaeodactylum tri- cornutum, a shear rate value of 7,000 s-1 led to the highest growth rate caused by a balance between mass transfer limitations and shear damage [17]. Sensitivity to shear stress is dependent on the microalgae species used. This has been shown in a study with the dinoﬂagellate Proto- ceratium reticulatum, where a damage threshold was observed already at an average shear stress of 0.16 mPa, which was equivalent to a shear rate of 0.12 s-1 [18]. In order to apply a well-deﬁned shear stress, Couette devices have been used in several studies. Couette devices consist of coaxial cylinders, where either the inner cylinder rotates and the outer remains stationary or vice versa. The effect of shear stress on photosynthesis of Spirulina plat- ensis has been studied using a Couette device [19]. It was found that the oxygen production rate and the chain length of Spirulina platensis started to decrease when the shear stress exceeded 0.3 Pa. Experiments on cyanobacteria [20] indi- cated that a shear rate of as little as 2.2 s-1 reduced nitro- genase activity and CO2 ﬁxation. However, the applied shear stress levels were not given, because the shear viscosity was not measured. Couette shearing devices have also been used to study the effect of shear stress on bioluminescence of different dinoﬂagellate species [21–24]. Bioluminescence threshold values were to the order of 0.1–1 Pa, where the shear stress was calculated as a function of the shear rate and the viscosity of the medium. Shear stress thus appears to trigger bioluminescence in these cases, but the relationship to cell damage or viability is unclear. The aim of this study is to determine the shear sensi- tivity of Chaetoceros muelleri. In addition, the time scale in which the effects of shear stress take place will be examined. The purpose was to understand whether the adverse effects were caused by a prolonged exposure to excessive shear stress or if the algal cells were damaged instantaneously. The combination of shear cylinders as Couette devices and rheological measurements was used in order to study the effect of a uniform and well-deﬁned shear stress on the viability of Chaetoceros muelleri. Materials and methods Culture preparation The diatom Chaetoceros muelleri (CCMP 1316) was obtained from NIOO (Netherlands Institute of Ecology, 123 1 ð Þ 2 ð Þ Bioprocess Biosyst Eng (2010) 33:921–927 Yerseke, The Netherlands). Chaetoceros muelleri was cul- tivated in natural seawater from the Easterscheldt (location Yerseke) enriched with Walne medium modiﬁed from Laing [25]. The salinity of the seawater used was 32 g L-1. Cultures of Chaetoceros muelleri were maintained in 10 mL test tubes, 250 mL Erlenmeyer ﬂasks containing 100 mL medium and 3 L Erlenmeyer ﬂasks containing 2 L medium at 20 C. Light was supplied continuously by white ﬂuorescent light. Every week 10% of the culture was transferred to new medium. All shear stress experiments were carried out with batch cultures from the 3 L Erlenmeyer ﬂasks after 1 week of growth, at which point the algae were in the early sta- tionary phase. Locust bean gum (LBG) was applied as a thickener to increase the medium viscosity. In the rest of this article, the term medium refers to the enriched sea- water including the thickener. The thickener was used in the following concentrations: 0, 0.3 and 0.5%. Cell con- centrations in the experiments varied between 5 and 10 million per mL. The cell concentrations in the LBG solutions were 50% of the original culture, because 50 mL of the original culture was mixed with 50 mL of 0.6 or 1.0% LBG solution. Shearing the algae The effect of shear stress on the viability of Chaetoceros muelleri was studied, using four shear cylinders developed at the Laboratory of Food Process Engineering. The shear cylinders have the following dimensions: an inner cylinder with a length of 145.5 mm and a radius of 20 mm and an outer cylinder with a radius of 21 mm. Between the inner and the outer cylinder is a gap of 1 mm. The total volume between the cylinders is 20 mL. The inner cylinder rotates and the outer cylinder is stationary. The shear rate applied in the shear cylinders is proportional to the rotational speed; the conversion factor of rotational speed (rpm) to shear rate (s-1) is 2.157. The maximum shear rate of the shear cylinders is 1,079 s-1 obtained at a rotational speed of 500 rpm. The shear rate is given as: 2RoRix c_ ¼ R2o Ri2 2pn x ¼ 60 where c_ is the shear rate (s-1), x is the angular velocity of the outer cylinder (s-1), Ro is the outer cylinder inner radius (m) and Ri is the inner cylinder outside radius (m) with: where n is the rotational speed (rpm) of the shear cylinder. In the ﬁrst experiment Chaetoceros muelleri without LBG was exposed to different levels of rotational speed,