## Abstract

In this study, we focus on the response of biological, rheological, and physical properties of dilute suspensions of cyanobacterium Synechocystis sp. CPCC 534 to shear induced by stirring. Experiments were carried out at three different stirring rates in well-controlled conditions, and the results are compared with stationary conditions where only molecular diffusion and cell motility govern the transport phenomena and cell growth. Our results show that the growth, biomass, total chlorophyll, and carotenoid production of Synechocystis sp. under various shear conditions were improved significantly, and the yield was nearly doubled. The viscosity of Synechocystis suspensions, subjected to different shear rates, was also measured. The data showed Newtonian behavior for suspensions at different cell concentrations. Cell concentration showed a noticeable increase in the viscosity of suspensions. However, we observed that this increase was smaller than the one predicted for a suspension of hard spheres. Addition of shear to the cyanobacterium Synechocystis sp. culture demonstrated a positive impact on the production of value-added products from the micro-organism. The obtained results can be used to improve the bioreactor design for better productivity.

## 1 Introduction

Photosynthetic micro-algae and cyanobacteria (called micro-organisms for brevity) can be used as a feedstock to produce “third generation” biofuels, which means they do not require the use of any food crops or arable land for their production. Photosynthetic micro-organisms can convert inorganic carbon (e.g., CO2) to biomass using solar energy to support their metabolism [1]. Biofuels derived from these sources are considered a sustainable alternative to fossil-sourced fuels. In addition, they contain a higher amount of lipids, can grow, and survive in various climates, and have a relatively constant production rate [2]. Biodiesel produced from third generation sources is 15-300 times more efficient than traditional crops on an area basis [3]. However, parameters such as light, temperature, and especially nutrient availability impact the lipid content and composition in micro-organisms [46]. The average lipid content may vary between 1% and 75% of dry weight [79]. Pigments (chlorophyll (Chla), carotenoids, and phycobilins such as phycocyanin (PC) and allophycocyanin) produced by different cyanobacteria, also play a substantial role in food, cosmetics, and pharmaceutical industries. Many of them have strong coloring, fluorescent, and anti-oxidant properties. They are widely used as food colorants in chewing gum, beverages, confectionery, jelly, soft drinks, dairy products, and cosmetics such as lipstick, eyeliners, and sunscreen [1016]. The estimated market value for phycobilin-based products is about $60 billion worldwide while this number was$1.24 billion in 2016 for carotenoids [17,18].

In many industrial applications and in environmental conditions, the above mentioned photosynthetic micro-organisms are suspended in a medium fluid; the suspension is often called “living” or “active” fluid, in which cells act as microstructural elements of the fluid and convert the chemical energy of nutrients into mechanical energy for driving the flow [19]. Therefore, living fluids can develop complex spontaneous motions in the absence of external pressure or velocity gradients. In this work, we focus on the suspensions of the bacterium Synechocystis as an active fluid.

In industrial applications, photosynthetic micro-organisms are cultivated in dedicated reactors, referred to as photobioreactors (PBRs). The design of a PBR, operating with an active fluid, involves the interplay between fluid flow, microbe biokinetics, and radiative transport, in which the physical and rheological properties of the active fluid intermingle with the biological response of micro-organism and play a crucial role. The intensity of hydrodynamic stress in active fluids can affect the growth of micro-organisms and can change the rheological properties of their suspensions [20]. The efficiency of a micro-organism's cultivation in a PBR is influenced by proper mixing inside the reactor, which is directly related to the hydrodynamic stress applied to the microbial suspension [20,21]. Mixing guarantees sufficient nutrient distribution, prevents thermal stratification and cell settling, and ensures better exposure to light at the illuminated surfaces [21]. However, high levels of shear stress can damage or kill micro-organisms. Therefore, for optimal mixing, it is crucial to study the effects of shear on the behavior and productivity of micro-organisms. The hydrodynamic stress in PBRs is usually applied by stirring in agitated PBR or by bubbling air in draft tube airlift PBR [3].

Although photosynthetic micro-organisms suspensions have attracted a large amount of attention in recent years as sources of high-value chemical products and biofuels, their physical properties, especially under flow conditions that occur in practical bioreactors, have not been sufficiently studied. Recent studies show that some fundamental physical properties of active suspensions, such as the diffusion coefficient, exhibit unexpected behavior and have therefore prompted extensive research [2224]. Because individual bacterial motions have a large random component, it seems plausible to search for the origin of these unexpected physical properties of active fluids in bacterial locomotion and signal transduction. Vourc'h et al. [22] observed a time-dependent slow-down in the diffusion rate of Synechocystis in biofilms. They showed that there exists an intimate correlation between the diffusive dynamics of Synechocystis and the propensity of the micro-organism to secrete exopolysaccharide (EPS) on the one hand and the properties of surface material on the other hand [23]. They indicated that the observed dynamical slowdown is in fact due to the evolution of the motility of Synechocystis and the characteristic times (run and tumble) that contribute to the diffusion coefficient, rather than to enhanced dissipation during the “run” periods of bacterium motility. Vourc'h et al. [22] proposed a mathematical model for the decrease in diffusion coefficient based on the secretion of EPS by the micro-organisms. It has also been shown that surface hardness [23] as well as light intensity and direction [24] affect the diffusion dynamics of Synechocystis.

The rheological properties of suspensions of micro-organisms must be understood to develop more efficient downstream processes in biomass production. In a recent study by Hu et al. [25], a basic rheological analysis was employed to provide a possible technical basis for choosing the agitation speed in suspensions of the red micro-alga Porphyridium cruentum. It was shown that the biomass growth and high-value chemical formation were affected by the agitation speed in PBRs [25]. Different rheological models such as the power-law model, Quemada model, Simha model, Herschel–Bulkley model, Cross model, Krieger–Dougherty (K–D) model, and Einstein's equation have been employed to describe the rheological behavior of suspensions of various micro-algae in different studies [2630]. However, the conventional rheological models are developed for suspensions of nondeforming, spherical, passive particles whereas active suspensions are constituted of deformable, motile, and mostly nonspherical particles. Moreover, different classes of bacteria use diverse motility mechanisms; twitching, pulling, and pushing are just a few examples. The type of the micro-organisms' motility could therefore affect their effective viscosity and characteristic organization time under shear. To design PBRs effectively, more detailed assessments of the potential rheological models are required to facilitate the development of models that more accurately describe bacterial suspensions. For this purpose, Souliés et al. [27] studied suspensions of Chlorella vulgaris CCAP 211-19. They observed Newtonian rheological behavior at low volume fractions. The Quemada model was used to describe the dependence of the relative viscosity with respect to volume fraction. At higher volume fractions, shear-thinning behavior was observed, and the volume-fraction-dependent viscosity was described by the Simha model. They attributed this behavior to the flocculation of algae under shear. At the highest values of the volume fraction, the suspension exhibited yield-stress behavior characterized by a divergence of the viscosity at lower stresses and also thixotropy. Shear-thinning behavior was also observed in slurries of Chlorella pyrenoidosa in [28]; this behavior could be successfully described by the Herschel–Bulkley model [28]. These authors also reported that increasing the temperature of the active suspension from 343 to 737 K caused the surface of C. pyrenoidosa to become rougher, as revealed in scanning electron micrographs. The apparent viscosity of C. pyrenoidosa slurries between 293 and 343 K followed the Arrhenius model.

Cagney et al. [29] studied the rheological properties of suspensions of Tetraselmis chuii, Chlorella sp. and Phaeodactylum tricornutum at shear rates ranging from 20 to 200 s−1 and volume fractions ranging from 5% to 20% in a rotational rheometer. The choice of three different strain rates was motivated by an interest in assessing the effects of motility and morphology of the micro-organisms on the effective viscosity of active suspensions. The alga T. chuii is oval (approximately 10 × 14 μm), flagellated, and highly motile, while Chlorella sp. is a nonmotile, nonflagellated, almost spherical unicellular alga. P. tricornutum is a nonmotile, unicellular diatom species, which can display oval or triradiate morphology. The rheological measurements were fitted to the Herschel–Bulkley model. Einstein's equation and the K–D model were employed to estimate the intrinsic viscosity at low concentrations; the agreement between the data and models was modest. At high shear rates, the viscosity of T. chuii was less sensitive to cell concentration. Low viscosity and lack of shear-thinning behavior for nonmotile cell suspensions of T. chuii showed that motility of the cells could be the reason for the observed resistance to flow. Contrary to T. chuii, Chlorella sp. suspensions demonstrated shear-thickening behavior and, as a result of their small aspect ratio, had a small intrinsic viscosity, while P. tricornutum, with a larger aspect ratio, had a larger intrinsic viscosity [29].

The focus of the present work is on the effects of shear, which was applied during cell growth, on the viscosity, biomass production, growth rate, doubling per day, pigments, and lipid production for dilute suspensions of Synechocystis sp. CPCC 534. Experiments are carried out at three different stirring rates under well-controlled conditions, and the results are compared with results for cells grown under stationary conditions, where only molecular diffusion and cell motility govern the transport phenomena and biomass production. This work also endeavors to understand the effects of cell concentration and cell motility on the rheological behavior of suspensions of Synechocystis.

## 2 Materials and Methods

### 2.1 Experimental Culture.

In this work, Synechocystis sp. CPCC 534 (hereafter Synechocystis) was used as the working micro-organism. Synechocystis sp. CPCC 534 is a prokaryote freshwater unicellular bacterium that is widely used as a model micro-organism for studying photosynthesis, energy metabolism, and environmental stress. The genome of Synechocystis was sequenced in 1996 [31]. Synechocystis is an almost spherical, small size (1–3 μm diameter) micro-organism whose locomotion on solid surfaces relies on the twitching action of type IV pili with an average speed of around 1–3 μms−1. In twitching motility, the pili extend, bind on the solid surface, and then retract causing the micro-organism's motion forward. Synechocystis is not a swimmer micro-organism.

The initial liquid suspension of Synechocystis sp. CPCC 534 was primarily obtained from the Canadian Phycology Culture Center (CPCC) and maintained in BG-11 medium [32] in an incubator at 20±1 °C and 50±10 μmol photons·m−2·s−1 light intensity for 12:12 h light-dark cycle. Experiments were performed in 500-mL Erlenmeyer flasks containing 250 mL culture and incubated at 20±1 °C under a light–dark cycle of 12:12 h and photon flux of 70±10 μmolphotons·m−2·s−1. Prior to the experiments, cells were grown for 5–6 days (midexponential growth phase based on the growth curve), and a constant inoculum of 500,000 cells·mL−1 was transferred to each experimental flask.

### 2.2 Experimental Apparatus.

Shear was applied to the working fluid (active suspensions, as described in Sec. 2.1) by generating a vortical flow in the experimental reactor vessels. Magnetic stirring bars with a diameter of 7.9 mm and a length of 19.8 mm were used to generate the flow in the active suspensions using a digitally controlled magnetic stirrer (VWR Canada) . The agitation speeds were set at 0, 450, 900, and 1,500 rpm corresponding to 0, 7.5, 15, and 25 Hz, respectively (Table 1). To determine the average shear stress induced on the working fluid by rotation of the stirring bars, we used the theoretical procedure developed by Pérez et al. [33] and Rushton et al. [34] (see Appendix). This procedure gives the average shear rate as a function of rotation speed, fluid properties, and the geometrical parameters for turbulent flows as
$γ˙=N32(4Npρd227πd)12=βN32$
(1)
where
$Np=PρN3d5$
(2)
Table 1

Correspondence between stirring rates (rpm), rotation speeds (Hz), and shear rates (s−1)

Stirring rate (rpm)Rotation speed (Hz)Shear rate (s–1)
000
4507.523
9001563
150025134
Stirring rate (rpm)Rotation speed (Hz)Shear rate (s–1)
000
4507.523
9001563
150025134
The Reynolds number Re is given by
$Re=ρNd2η$
(3)

Here, γ̇ is the average shear rate, N is the rotation speed (Hz), Np is the power number, P is the input power, d is the impeller diameter (in this case, the length of the magnetic stirring bars), η and ρ are, respectively, the dynamic viscosity and density of the fluid. In this calculation, we used the density and dynamic viscosity of de-ionized water at 20 °C (used in the preparation of the medium), 998.2 kg·m−3, and 1.002 × 10−3 Pa·s, respectively.

A 500-mL Erlenmeyer flask with an inner diameter D =80 mm was used as the reactor vessel in these experiments. The liquid height was H =35 mm. The Reynolds number Re, calculated from Eq. (3) for the rotation speeds applied here (450–1500 rpm), varies between 10,000 and 30,000. The flow is therefore turbulent, consistent with the assumptions of Eq. (1).

To determine the magnitude of the average shear rate, γ̇, in Eq. (1), the power input to the fluid by the stirrer (called power consumption hereafter), P, is required. Since the actual power input to the reactor was unknown, empirical correlations developed by Kato et al. [35] and Furukawa et al. [36] for propeller and Pfaudler-type impellers in agitated reactors were employed (see Appendix). After calculating β for different values of Np corresponding to each rotation speed N, the average shear rate was determined by using Eq. (1). Then, the average shear stress was calculated as
$τ=ηγ˙$
(4)

where $η$ is the fluid viscosity, $τ$ is the shear stress, and $γ̇$ is the shear rate. The relationship between the average shear stress and rotation speed determined in this correlation is plotted in Fig. 1.

Fig. 1
Fig. 1

### 2.3 Measurement of Bacterial Growth Rate (Ke).

To measure the culture growth, the optical density of the suspension, which is correlated with the particle density [37], was measured using a spectrophotometer at an absorbance wavelength of 750 nm. A calibration curve was established between the measured optical density and cell concentration (cells·mL−1) using a hemocytometer count.

Growth rate (Ke) is defined as the increased rate of cell density during the exponential growth phase and is calculated using the Gillard [38] equation
$Ke=(ln(Nt)−ln(N0))/(tt−t0)$
(5)

where $N0$ is the population of cells at the initial time ($t0$) and $Nt$ is the population of the cells at the final time ($tt$).

The growth rate, Ke, can be used to calculate the number of cell divisions per day, known as doubling per day ($k$), using the following Eq. [38]
$k=Ke/ln2=Ke∕0.6931$
(6)

The cell yield of Synechocystis sp. CPCC 534 was determined as the average biomass in the early stationary phase of the growth curve, where the maximum biomass was produced. The results are presented as a cell count per unit volume.

### 2.4 Pigment Measurement

#### 2.4.1 Chlorophyll and Carotenoid Measurement.

Chla and carotenoid (Carot) were extracted using a modified version of the protocol described in Lichtenthaler and Buschmann [39]. Five milliliter aliquots of cells were centrifuged at 2700 g for 30 min at 4 °C. The pellets were resuspended in 5 mL of 95% ethanol and homogenized using vortex in dim-light conditions. Then, the tubes were sonicated in a water bath for 20 min and incubated in dark conditions at 45 °C for 45 min. To remove the cell debris, the extracts were carried out through centrifugation at 2700 g for 20 min. After that, the supernatant was transferred into a 1-cm path length quartz cuvette and the optical absorption for Chla and carotenoid were measured at 470, 648, and 664 nm wavelengths. The amount of Chla and carotenoid were calculated using Eqs. (7) and (8), respectively [39]
$Chla=13.36 OD664−5.19 OD649$
(7)
$Carot=(103OD470−2.13 Chla)/209$
(8)

where $Chla$ and $Carot$ are the Chla and carotenoid concentrations, respectively, given in mg·L−1, and $ODλ$ is the optical density at the wavelength λ.

#### 2.4.2 Phycocyanin Measurement.

PC was analyzed using a modified version of the technique described by Lawrenz et al. [40]. Five milliliter aliquots for each treatment were centrifuged at 2,700 g for 30 min. The supernatants were discarded, and the pellets were stored at –80 °C prior to analysis. After samples were thawed at room temperature, 2 mL phosphate buffer (0.1 M, pH = 6.8) was added to each sample. The samples were homogenized using a vortex mixer, followed by sonication in a water bath for 20 min. Samples were stored at 4 °C for 24 h then centrifuged at 2,700 g for 10 min prior to measurement with a spectrophotometer at 750 and 620 nm. To correct the absorbance values, the absorbance value at 750 nm was subtracted from the PC peak at 620 nm, and the PC concentration (in μg·L−1) was calculated as
$Phycocyanin=Aεd×MW×VsampleVbuffer×106$
(9)

where A, ε, d, and MW are absorbance, PC molar extinction coefficients (1.9 × 106 L·mol−1·cm−1), path length, and PC molecular weight (264,000 g·mol−1). $Vsample$ and $Vbuffer$ are the volumes of sample and buffer, respectively.

### 2.5 Neutral Lipid Measurement.

To determine the amount of neutral lipid in our bacterial samples, a Nile Red fluorescence assay was used. One milliliter aliquots from the stationary phase (day 16) were centrifuged at 16,300 g for 10 min. The pellets were stored at –80 °C for 24 h and then thawed at room temperature. This freeze-thaw cycle was repeated twice. Then, 1 mL phosphate buffer (0.1 M, pH = 6.8) was added to each sample. The samples were homogenized with a vortex mixer followed by water bath sonication for 20 min. Using a black 96-well microplate (BD Falcon, USA), 100 μL of the bacterial sample was pipetted into each well. A fresh daily working solution of 1 μg·mL−1 Nile Red, a lipid-soluble fluorescent dye, was prepared in 50% dimethyl sulfoxide (DMSO), and 100 μL was added to each well. The plate was incubated in the dark at 40 °C with shaking. After 10 min, the fluorescence was measured at an excitation wavelength of 530 nm and an emission wavelength of 570 nm. A standard curve of lipid standard Triolein (Sigma-Aldrich) was generated by dissolving the analytical grade of Triolein in anhydrous ethanol, followed by twofold serial dilutions using assay buffer.

### 2.6 Viscosity Measurement of Bacterial Cell Suspensions.

In this work, “viscosity” shall be used to refer to the “effective viscosity,” which is the global rheological measure of a suspension sample's properties; the local viscosity experienced by a bacterium is equal to the viscosity of the surrounding culture medium in the suspension. A Cannon-Ubbelhode viscometer (Cannon Instrument Company) was used to measure the viscosity of the bacterial samples. The glass tube was filled with a 12 mL sample at 20 °C and placed into the holder. Suction was applied until the sample reached the center of the top bulb, and the time of the descent between two sets of fiduciary lines was measured. During the experiments, care was taken to ensure that no air bubbles were created. The suspension viscosity was calculated using the following equation
$η=Kρt$
(10)

where η is the viscosity (cp) of the cell suspension, ρ is the density of bacterial cell suspension, and it is equal to 1.005875 (g·mL−1), $t$ is the time of descent (s), and K is viscometer constant (0.004447 (cST·s−1)).

To evaluate the effects of cell concentration on the rheological behavior (Newtonian or non-Newtonian) of the suspensions of Synechocystis sp. CPCC 534, the viscosity for samples of different volume fractions was also measured by an Anton-Paar Modular Compact Rheometer (MCR302, Austria) with a concentric cylinder geometry. The diameters of the inner and outer cylinders were 22 and 26 mm, respectively. The temperature was maintained at 20 °C during all experiments. Samples of cell suspensions were centrifuged at 2,700 g for 20 min, and supernatants were collected for diluting the pellets in the next step. The viscosity of suspensions was studied in two series of experiments, called experiment series 1 and 2, which were carried out on two different cultures of Synechocystis sp. CPCC 534, prepared according to the same protocol. In each series, suspension samples with known volume fractions (1.25, 2.5, 5, 7.5, 10, 12.5, 15, 17.5, and 20%) were prepared by diluting the pellets with the collected supernatant. To perform the experiments, approximately 20 mL of samples with different volume fractions was poured into the cylinder. Measurements were carried out for shear rates in the range of 50–100 s−1. The rheometer was insensitive below 50 s−1 since the suspension viscosity was very close to that of water.

### 2.7 Cell Size Measurement.

To determine the size of Synechocystis cells following exposure to shear, cells were observed using an Imager Z1 Zeiss Microscope, and the data were analyzed using digimizer software.

### 2.8 Statistical Analysis.

A one-way anova was used to investigate the significant differences in growth, doubling per day, yield, and lipid production, and a two-way anova was used for pigments. Statistical analyses were performed using originpro 2017 (OriginLab Corporation, Northampton, MA, USA), and p <0.05 was considered as significant.

## 3 Results and Discussion

### 3.1 Effects of Shear on Biomass Production.

During the exponential growth phase and in the presence of sufficient light, cell density increases because of nutrient uptake [41]. The growth rate and doubling per day were calculated during this phase for samples subjected to different stirring rates and are plotted in Figs. 2(a) and 2(b). The results revealed a significant difference between the cultures grown under stationary conditions and those grown under shear (p < 0.05). Exerting turbulent shear on the cultural system, causing the suspension to be mixed, improved the growth rate as well as doubling per day in comparison with the stationary condition where only molecular diffusion and cell motility govern the transport phenomena and nutrient up-take. The data suggest that adding stirring causes a change but increasing the stirring rate does not. Therefore, if there is mixing, the cells grow faster, but the amount of mixing does not make a significant change in the growth rate and doubling per day. However, it was previously reported [41] that Synechocystis sp. cell growth collapsed when cells were subjected to shear stress over 0.35 Pa. It should be mentioned that the maximum shear stress attained in the present study was 0.14 Pa. Increasing the stirring rate in the aforementioned study did not show any significant variation in the growth as well as doubling per day, suggesting that Synechocystis cells are highly shear resistant micro-organisms, which can be attributed to the fact that their pseudo-spherical shape, small size (1–3 μm), and low motility (1–3 μm·s−1), make them less sensitive to friction forces and shear stress [42]. Similar results were reported for Synechocystis sp. PCC 6803 for stirring rates up to 900 rpm [42].

Fig. 2
Fig. 2

Biomass production is a proxy for autotrophic cultivation in the bacteria system, while it is often limited by light deficiency because of the shading of the cells, which leads to low biomass yield [43]. Light as a source of energy for photosynthesis is required for the cell's maintenance and growth [44]. Mixing intensification is an efficient strategy for enhancing cell exposure to light and therefore increasing biomass yield from solar radiation [45]. Moreover, sufficient mixing of the continuous phase fluid (medium) assists each cell to have more access to nutrients and CO2 [46]. Our results presented greater biomass and therefore, yield production due to the stirring of the cultures (p < 0.05), as is shown in Figs. 3(a) and 3(b). These results suggest that the better mixing that results in the cases with increased shear led to improved nutrient uptake, along with light and CO2 utilization by the cells. Due to experimental limitations, the impact of other parameters, such as light, temperature, nutrients, and CO2 concentration, was not measured in this study, although it is known that each of these parameters, and their interaction with one another can affect the production of biomass and other valuable chemical products [47].

Fig. 3
Fig. 3

### 3.2 Effects of Shear on Pigment Production.

Pigments play a crucial role in the development of cyanobacteria as well as their color [48]. The pigment content was measured at day 6 (midexponential phase) and day 10 (early stationary phase). The total amount of Chla (Fig. 4(a)) and Carot (Fig. 4(c)) showed an increase in the early stationary phase compared to the exponential growth phase and enhanced the total content of Chla and Carot significantly. These results are consistent with Fadlallah et al.'s [42] work, although the actual concentration of these pigments varied due to differences in cell growth [10]. Unlike the increase in the total content of Chla and Carot, no statistically significant differences were detected for PC under the defined conditions (Fig. 4(e)).

Fig. 4
Fig. 4

The amount of cellular Chla for the static culture revealed an increase at the early stationary phase in comparison with the exponential stage (Fig. 4(b), 0 rpm) where cell growth caused a slow increase in Chla. No significant change was observed at the cellular level for the cultures grown under different stirring rates (Fig. 4(b)). Similar results were also detected for cellular Carot content (Fig. 4(d)). This suggests that the total pigment enhancement improved because of biomass production and the amount of pigment per cell remained insensitive to stirring [45,46,49]. Alternatively, the cellular content of PC decreased as the cell growth continued into the stationary phase (Fig. 4(f)). PC acts as internal nitrogen storage that can be degraded under nitrogen and iron limitations [11,50]. Therefore, the depletion in the external nitrogen reserves due to cyanobacteria uptake in the stationary phase can impose PC degradation [51].

### 3.3 Effects of Shear on Lipid Production.

In addition to biomass productivity, high lipid accumulation is required for biofuel production from cyanobacteria. These two parameters are not necessarily correlated [4,49]. However, the highest amount of lipid accumulates under nitrogen starvation, which occurs during the stationary phase [52]. Our results demonstrated that the shear induced by stirring had a negative impact on the lipid production of Synechocystis sp. CPCC 534 (Fig. 5). The production of total lipids and the amount of lipid per cell showed a significant reduction in stirred samples. As before, stirring has an effect, but the amount of stirring does not make any significant difference. This suggests that the uptake of nitrogen by Synechocystis cells that grew without any stirring stress is much faster in comparison with cells that grew under various stirring rates. Nitrogen starvation paused the cell division while triggering lipid production [52].

Fig. 5
Fig. 5

### 3.4 Effects of Shear on the Cell Size.

The cellular size of micro-organisms can impact the ecophysiological traits of the cell such as metabolic rate, growth, nutrient uptake, and light absorption [5355]. To investigate the impact of stirring rate on the size of Synechocystis sp. CPCC 534, the cells were imaged under a 20× objective lens. Analysis of the images demonstrated two features. First, shear reduced the size of Synechocystis cells compared to those grown in the static culture (Fig. 6), but all the sizes for nonzero shear rate are the same within the experimental uncertainty. Second, as the cells aged, there was no statistically significant shrinkage in the cell size. Moreover, as is shown in Fig. 7, the culture with the highest growth rate presented the smallest size of cells; this observation is directly in line with the previous finding that reported a negative correlation between cell size and growth rate [56]. The nutrient uptake in smaller cells is more efficient due to their higher specific surface area, while the addition of mixing may increase the advective transport of nutrients to the cell surface, which improves the nutrient uptake rate [53].

Fig. 6
Fig. 6
Fig. 7
Fig. 7

### 3.5 Rheology of Synechocystis Suspensions.

In this section, we focus on the rheological behavior of dilute cell suspensions of Synechocystis with an interest in the effects of cell shear history, cell concentration, and cell motility on this behavior. For this purpose, Synechocystis suspensions of different concentrations were presheared by vortex stirring at 450, 900, and 1500 rpm, corresponding to average shear rates of 23, 63, and 134 s−1 (Table 1), until the cell growth reached the stationary state. Then suspension viscosity was measured. Measured viscosity, η, did not show an effect of shear history within the accuracy of measurements, implying that shearing had not changed the cell characteristics which could affect the rheological properties of the Synechocystis suspensions (data not shown).

The shear rates imposed on the bacterial suspension in this work are quite high compared to other studies. To quantify the comparative effect of shear and bacterial motility on the rheological properties of suspensions we have calculated a motility Péclet number based on the flow average time-scale (average shear rate) and bacterium average motility time-scale (average motility speed/flow length-scale). The maximum motility Péclet number calculated with the highest bacterium speed (3 μm·s−1) and the lowest imposed shear rate (23 s−1) result in a motility Péclet number of Pe = 16 × 10−7, which is very small and therefore supports the fact that the micro-organism motility should not play a role in sheared suspension viscosity.

#### 3.5.1 Effects of Cell Volume Fraction.

We then investigated the dependency of viscosity on the bacterial volume fraction of suspensions. Volume fractions ranged between 0% (culture medium) and 20% corresponding to cell densities ranging from 0 to ∼550 × 106 cell·mL−1 for unsheared suspensions. In the following, where it is justified, cell density is used instead of cell volume fraction for making it possible to compare the viscosities of suspensions with live and dead bacteria; this will be elaborated upon later. In Fig. 8, the viscosity, η, normalized by the viscosity η0 of the culture medium, is plotted as a function of the cell density. This figure shows that suspension viscosity is an increasing function of cell density, as it is for a suspension of rigid passive particles. The linear dependence of normalized viscosity on cell density in Fig. 8 is fitted to a linear function expressed below
$η=η0(1+βω)$
(11)

where η and η0 are the suspension and culture-medium viscosities respectively,ω is the cell density (expressed in a cell·mL−1), and β is the linear proportionality factor.

Fig. 8
Fig. 8
It has been shown that suspensions of dilute (ω < 1–2%) passive spherical rigid particles have a concentration-dependent viscosity. Einstein (1906, and corrected 1911) [57,58] derived an analytical solution for the flow of solvent around the spherical particles, which yields
$η=η0(1+αω)$
(12)

where η and η0 are the suspension and the solvent viscosity, respectively, ω is the solid fraction (expressed in volume fraction, %), and α is called “Einstein's intrinsic viscosity,” which takes on a value of 2.5 for rigid spherical particles. In the present experiments, we found β (the equivalent of α in Einstein's equation) between 0.3 and 0.4 for different volume fractions, which are lower than Einstein's intrinsic viscosity value. The smaller increases in viscosity with cell volume fraction (or cell density), compared to the one predicted for a suspension of hard spheres, can be attributed to the fact that particles in this study are soft, deformable, and non-spherical; thus, some of the flow energy could be dissipated through deformation of the cells, so the viscosity is less than it would be for hard spheres. However, there can be other possible causes. In fact, recent studies have shown that shape dynamics also affects the rheology of soft elastic particles in shear. Gao et al. [59] investigated theoretically the shape dynamics of soft elastic particles in an unbounded simple shear under stokes flow conditions. The particle is considered as an incompressible neo-Hookian solid of shear modulus S and aspect ratio L, surrounded by a Newtonian fluid of viscosity η0. The ratio of viscous forces in the fluid to elastic forces in the elastic solid can be represented by a non-dimensional number G = η0γ̇/S. If for an initial aspect ratio L0, the hydrodynamic forces exerted by the fluid on the particle are not sufficiently strong in comparison with elastic forces in the particle; which tend to preserve its initial shape; the particle will then tumble; otherwise, it will tremble, or reach a steady-state if the particle is initially spherical. The initial aspect ratio L0 of the particle is a determining parameter for tumbling, trembling, or steady-state motion. Using the single-particle dynamics, these authors calculated the rheological properties of dilute suspensions (volume concentrations < 1%) of elastic particles. They showed that the intrinsic viscosity of suspensions of deformable particles generally decreases with G and even can become negative for sufficiently large G; although the effect becomes less noticeable with decreasing initial aspect ratio L0.

#### 3.5.2 Newtonian or Non-Newtonian?

To assess the Newtonian or non-Newtonian behavior of Synechocistis suspensions, the suspension viscosity was measured as a function of the imposed shear rate, for different cell volume fractions by the Anton-Paar rheometer, the results of which are shown in Fig. 9.

Fig. 9
Fig. 9

The viscosity shows no variation under the imposed shear rate which implies Newtonian behavior of the suspensions. To the authors' knowledge, there is no rheological data on the behavior of Synechocystis suspensions in the open literature for comparison. However, rheological behavior of several algal slurries such as Chlorella sp. [28,29,59], T. chuii [29], P. tricornutum [27,60], and Nannochloris sp. [60] have been studied. Among those species, the alga Chlorella sp. has more similarities to Synechocystis; it is almost spherical, nonflagellate, low motility (though higher than Synechocystis) but three to four times larger than Synechocystis. Cagney et al. [29] examined suspensions of C. vulgaris at very low shear stress (10–100 mPa). They observed that the rheology was Newtonian, like the present study, for cell volume fractions ω = 8.2%, and shear thinning for ω = 16.5%. Souliès et al. [27] found a suspension of Chlorella sp. (ω =10% and 20%) was shear-thinning at low shear rates and shear-thickening at higher shear rates. The underlying physical mechanism for the rheological behavior of micro-organism suspensions is not clear yet and needs more local viscosity measurements under shear and also microscopic observation of the micro-organism orientation with implied shear field direction, see the section below for more discussion.

#### 3.5.3 Effects of Cell Motility.

Samples of different volume fractions (0–20%) were prepared, and the viscosity was measured for both live and dead cell suspensions using Anton-Paar and Cannon-Ubbelhode rheometers. Dead suspensions were obtained by adding 10% of H2O2 to live suspensions of the same volume fraction. Experiments were run twice with the Anton-Paar rheometer and four times with Cannon-Ubbelhode for each concentration. Before experiments, the dead-cell and live-cell suspensions were observed under a 20× objective lens microscope to verify the difference between the morphology of samples; Fig. 10 shows microscopic images of a live-cell and a dead-cell sample.

Fig. 10
Fig. 10

Figure 10 shows that cells shrink after bleaching, and therefore, for the same cell population per unit volume of suspension (cell density), the cell volume fraction is smaller for the dead samples. Thus, for comparing the variation of the viscosity of live cell and dead cell samples we use “cell density” rather than “cell volume fraction” as a variable. Figure 11 shows the variation of the normalized viscosity with shear rates for live-cell and dead-cell suspensions. Each data point is the average of two assays.

Fig. 11
Fig. 11

Figure 11 shows that in both cases (live and dead cells), the suspension behaves as a Newtonian fluid, and the normalized viscosity of live and dead suspensions is equal within the measurement accuracy. Rafaï et al. [61] measured the viscosity of suspensions of live and dead Chlamydomonas reinhardtii as a function of cell volume fraction. They showed that the relative viscosity ((η – η0)/η0) of live suspensions was quantitatively higher than that of dead suspensions; this observation is different from ours for suspensions of Synechcists. While the viscosity of dead suspensions, in Rafaï et al.'s [61] experiments, followed Kreiger and Dougherty's [62] semi-empirical law for suspensions of passive rigid particles, the viscosity of the live suspensions did not. These authors attributed the difference to the effects of C. reinhardtii motility. By imaging the cells, while they were subjected to a shear flow, they showed dead cells follow a regular rotation, as would passive spherical particles. However, live cells resisted the flow rotation most of the time and eventually flipped very rapidly. In the present study, Synechcists is a low motility twitching (moving by sticking to solid surfaces and pulling by contraction) cell that has no means (flagella) to resist the flow rotation. Therefore, it behaves as soft deformable passive particles and thus shows no difference between the viscosity of live and dead suspensions.

In Fig. 12, the normalized viscosity is plotted as a function of cell density for live and dead cell suspensions (from experiment series 2) as well as the averaged values of the normalized viscosity for presheard live-cell suspensions from experiment series 1; the latter series was already plotted in Fig. 8. The data show that within the accuracy of measurements; live, dead, sheared, and unsheared suspensions all have the same normalized viscosity value for a given cell density. Also, they show the same Newtonian trend of viscosity increase with cell density.

Fig. 12
Fig. 12
To obtain the general trend of the viscosity variation with cell density, the data in Fig. 12 are averaged and plotted against the cell density in Fig. 13. It is fitted to a linear correlation, which yields
$η=η0(1 + 0.0001β)$
(13)

where η and η0 are the suspension and the culture-medium viscosities, respectively, expressed in (mPa·s), and β is the suspension cell density given in (cell·mL−1).

Fig. 13
Fig. 13

A final note with respect to the effects of motility on the viscosity of suspensions of self-propelled particles needs to be mentioned here. It is noted that time-reversal symmetry breaking and the flow field associated with self-propulsion can have an influence on the viscosity of suspensions of self-propelling particles. In this regard, two classes of self-propelled particles can be distinguished among the flagellar bacteria (microswimmers): “pushers”, such as Escherichia coli bacterium, which propels itself using a helical flagellar bundle powered by rotary motors, and “pullers”, such as C. reinhardtii alga, which swim by beating two flagella at the front of each cell [63].

For a suspension of puller-like microswimmers (C. reinhardtii), an increase in the viscosity has been observed. This increase has been attributed to the fact that the algae affect the surrounding flow vorticity when they are perpendicularly oriented to the axis of gravity. To verify this effect, Mussler et al. [64] measured the suspension viscosity in a cone-plate and a Couette–Taylor cell. The two set-ups yielded the same increase in viscosity as a function of volume fraction, although the vorticity direction in the Couette–Taylor cell is parallel to the axis of gravitation. These results led the authors to conclude that gravitational effects are not sufficient to describe this viscosity increase.

For a suspension of pusher-like microswimmers (E. coli) at very low shear (0.04 s−1) [65], a Newtonian plateau characterized by a viscosity decreasing with bacterial concentration; called negative viscosity increase; was observed. In the semidilute regime, at around 0.75% volume fraction, the suspension displayed a vanishing viscous resistance to shear; a “super-fluid” like behavior. On the contrary, for Chlamydomonas, which is a puller-like microswimmer, an increasing viscosity with concentration was measured [61]. It was shown [65] that the decrease of viscosity to zero at bacterial volume fractions above the critical value of 0.75% in suspensions of E. coli was the result of the emergence of a collective motion in the quiescent state, when the flow became nonlinear. However, NIV behavior has not been reported for nonflagellar micro-organisms, such as Synechocystis studied here.

## 4 Conclusions

In this study, effects of shear on the growth, doubling per day, biomass production, pigments, lipid production, and rheological properties of Synechocystis sp. CPCC 534 suspensions in agitated vessel reactors were investigated. The data revealed a significant increase in biomass, doubling per day, yield production, and the total amount of Chla and Carot because of induced flow in comparison with the nonagitated suspension. Meanwhile, mixing had a negative impact on lipid production and cell size.

On the other hand, the rheological behavior in terms of the viscosity of cell suspensions, which experienced various shear rates during growth, was studied. The viscosity, normalized at a constant biovolume fraction, showed Newtonian behavior at all cell concentrations. This behavior was observed for both presheared and unsheared samples, implying the shear history does not have an influence on the rheological behavior of suspensions. Concerning the effect of cell motility, experiments showed no difference between the viscosity of live-cell and dead-cell suspensions. This behavior is attributed to the low and twitching nature of the motility of Synechocystis sp. CPCC 534, in contrast to the high motility of swimmers such as C. reinhardtii.

Cell concentration showed a noticeable influence on the viscosity of cell suspensions. We observed that viscosity is a linearly increasing function of the cell volume fraction, as it is for passive rigid particles; a correlation is given for this variation. However, this increase is smaller than the one observed in suspensions -of rigid particles. The smaller observed increase in viscosity with cell volume fraction could be attributed to the fact that in the present study elastic soft particles (Synechocystis sp. CPCC 534) can deform; thus, some of the energy of the flow is dissipated in deforming the cells. This decreases the amount of energy dissipated by hydrodynamic interactions compared to rigid particles, so the viscosity is less than it would be for rigid particles. Another (or concomitant) cause can be the effect of the shape dynamics of soft elastic particles discussed in Gao et al. [59].

## Acknowledgment

The authors would like to thank Dr. Charles G. Trick for providing Synechocystis strain for this study, and Dr. Lars Rehman for fruitful discussions. They also thank reviewers for their thoughtful comments.

## Funding Data

• NSERC (RGPIN-2019-05156) which partially funded ZH and Western Research Chair in Urban Resilience and Sustainability starting fund which funded MMA (Funder ID: 10.13039/501100000038).

• NSERC (RGPIN-2017-04078) (Funder ID: 10.13039/501100000038) .

## Nomenclature

• b =

width of magnetic bar (mm)

•
• d =

length of magnetic bar (mm)

•
• D =

reactor inner diameter (mm)

•
• G =

the ratio of shear forces over elastic forces

•
• H =

liquid height in a vessel (mm)

•
• Ke =

growth rate (d–1)

•
• K =

doubling per day (d–1)

•
• L =

elastic particle aspect ratio

•
• n =

speed of rotation (rpm)

•
• N =

rotation speed (Hz)

•
• Np =

power number

•
• P =

power (W)

•
• Pe =

motility Péclet number

•
• Re =

Reynolds number

•
• PBR =

photobioreactor

•
• S =

shear modulus of soft elastic particles

### Greek Symbols

Greek Symbols

• η =

viscosity (cp)

•
• η' =

viscosity history (cp)

•
• τ =

shear stress (Pa)

•
• γ̇ =

shear rate (s–1)

•
• ω =

volume fraction

### Appendix

Np was determined using the following empirical correlations developed by Kato et al. [35] and Furukawa et al. [36] for propeller and Pfaudler-type impellers in agitated reactors
$Np={[1.2π4β2]/[8d3/(D2H)]}f$
(14)
$f=CL/ReG+Ct{[Ctr/ReG+ReG]−1+(f∼/Ct)1m}m$
(15)
$ReG={[π η ln(D/d)]/(4 d/β D)}Re$
(16)
$CL=0.215 η np (d/H)[1−(d/D)2]+1.83 (b sin θ/ H)(np/ 2 sin θ)13$
(17)
$Ct=[(3X1.5)−7.8+(0.25)−7.8]−1/7.8$
(18)
$m=[(0.8X0.373)−7.8+0.333−7.8]−1/7.8$
(19)
$Ctr=23.8 (d/D)−3.24 (b sin θ/D)−1.18X−0.74$
(20)
$f∼=0.0151(d/D)Ct0.308$
(21)
$X=γ np0.7 b sin1.6θ/H$
(22)
$β=2 ln(D/d) [(D/d)−(d/D)]$
(23)
$γ=[η ln(D/d)/(β D/d)5]1/3$
(24)
$η=0.711 {0.157+[np ln(D/d)]0.611}/{np0.52 [1−(d/D)2]}$
(25)

where np corresponds to the number of the blades which is 2 in our experiment; θ is the pitch angle of the blade that is equal to π/2 in our case since we used a flat magnetic agitation bar that is analogous to the paddle mixing impeller without a central axis. ReG is the modified Reynolds number and Re is the Reynolds number as defined in Eq. (3).

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