# Rheological characterization and modeling of freshwater and marine microalgae and cyanobacteria mixed cultures

Conor Button, Nature Poddar, Tom Lacassagne, Mathieu Pernice, Vishal

Gupta, Lisa Aditya, Unnikrishnan Kuzhiumparambil, Peter J Ralph

► To cite this version:

Conor Button, Nature Poddar, Tom Lacassagne, Mathieu Pernice, Vishal Gupta, et al.. Rheological characterization and modeling of freshwater and marine microalgae and cyanobacteria mixed cultures. Algal Research - Biomass, Biofuels and Bioproducts, 2025, 88, pp.103988. 10.1016/j.algal.2025.103988. hal-04989413

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# Rheological characterization and modeling of freshwater and marine microalgae and cyanobacteria mixed cultures

Conor Button<sup>a</sup>, Nature Poddar<sup>a, *, ID</sup>, Tom Lacassagne<sup>c, ID</sup>, Mathieu Pernice<sup>a, ID</sup>, Vishal Gupta<sup>a, ID</sup>, Lisa Aditya<sup>b</sup>, Unnikrishnan Kuzhiumparambil<sup>a, ID</sup>, Peter J. Ralph<sup>a, ID</sup>

## ARTICLE INFO

### Keywords:

Algae

Cyanobacteria

Mixed cultures

Mixed species rheology

Viscosity model

## ABSTRACT

Rheology is crucial for algal cultivation, affecting mixing efficiency and biomass productivity. There is limited research on the rheological aspects of mixed cultures of algae and cyanobacteria. The study aimed to investigate the rheological properties of microalgae and cyanobacteria mixed cultures (*Chlorella vulgaris* and *Microcystis aeruginosa*; *Nannochloropsis oceanica* and *Prochlorococcus* sp.). While all species were spherical and non-motile with similar aspect ratios, *Prochlorococcus* sp. exhibited meaningful cell-cell repulsion, increasing its apparent effective volume fraction by 20–40 %. Mixed suspensions of *C. vulgaris* and *M. aeruginosa* demonstrated shear thinning at all concentrations, accurately described by a power law model across the explored shear-rate range. The conventional Einstein and Krieger-Dougherty models confirmed that viscosity increased with cell concentration, with *Prochlorococcus* sp. having the greatest impact. However, these models did not effectively account for mixed suspensions. A novel model, based on Pal (2023) [1] and incorporating two independent parameters, provided a greater reflection of the viscosity in mixed suspensions. Interestingly, parameters for this new mixed culture model could be derived from mono-culture rheological models within the studied concentration range. This first-of-its-kind study highlighted the significance of rheology in optimizing mixed cultures and identifies the need for further research to address rheological challenges, notably towards higher industrial-scale biomass densities.

## 1. Introduction

The on-going exploitation of fossil fuels and increasing atmospheric carbon dioxide levels necessitate a shift to renewable energy sources. Microalgae, as a third-generation feedstock, provide a promising solution by offering alternative biomass sources for fuels and other high-value products [2], although achieving economically viable production at commercial scale requires ongoing research efforts [3]. Recent work has highlighted the potential of co-culturing algae and bacteria for enhanced biomass productivity [4,5] or integrated wastewater treatment [6], resulting in reduced cost of algal production systems.

In industrial settings, microalgae are typically cultivated at very low cell densities, around 0.05 % w/w [7], due to shading effects in photo-autotrophic growth. However, advanced photo-bioreactors can

improve light distribution, increasing biomass concentrations approximately 10-fold [8]. The in-depth knowledge of rheological behavior of algal suspensions is key to improving mixing efficiency and reducing power requirements in bioprocesses such as algal cultivation, harvesting, and biomass processing. Understanding parameters like viscosity, shear-thinning behavior, and flow properties is crucial in enhancing process scalability and energy efficiency in these applications. The microalgae culture process shows time-varying rheology, starting as a low-viscosity Newtonian medium. As biomass concentration increases, it transitions to a higher viscosity Newtonian fluid at intermediate levels and ultimately becomes a non-Newtonian fluid at high biomass concentrations [9]. These transitions and the ultimate rheological properties are highly dependent on the multiple parameters (such as volume fraction, pH of media, cell charge, extracellular polymeric substance)

<footnote><sup>a</sup> Climate Change Cluster, Faculty of Science, University of Technology Sydney, NSW, Australia</footnote>

<footnote><sup>b</sup> Centre for Technology in Water and Wastewater, School of Civil and Environmental Engineering, University of Technology Sydney, NSW 2220, Australia</footnote>

<footnote><sup>c</sup> IMT Nord Europe, Institut Mines Télécom, Univ. Lille, Center for Energy and Environment, F-59000 Lille, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail addresses: conor.button@student.uts.edu.au (C. Button), nature.poddar@uts.edu.au (N. Poddar), tom.lacassagne@imt-nord-europe.fr (T. Lacassagne), mathieu.pernice@uts.edu.au (M. Pernice), vishal.gupta@uts.edu.au (V. Gupta), lisa.aditya@student.uts.edu.au (L. Aditya), unnikrishnan.kuzhiumparambil@uts.edu.au (U. Kuzhiumparambil), peter.ralph@uts.edu.au (P.J. Ralph).</footnote>
[10,11] and the specific species (such as cell diameter, cell wall rigidity, motility, morphology) [12–14] involved and remain largely unexplored. Dense suspensions vary in shear stress with shear rates, fitting a power-law model to determine the consistency (K) and flow behavior (n) indices [15]. While several studies have reported specific biomass concentrations at which pure algal suspensions transition from Newtonian to non-Newtonian behavior, these thresholds vary depending on the algal strain, medium composition, and experimental conditions [10,16–18]. For instance, *Nannochloropsis* sp. transitions at approximately 40 g/L, while *Chlorella vulgaris* transitions at 60 g/L under similar conditions. This variability underscores the importance of context-specific considerations in rheological studies. Viscosity models like the Einstein [19] and Krieger-Dougherty [20] equations predict the effective viscosity based on particle volume fraction (φ) and medium viscosity (μ<sub>eff</sub>), effectively applied for dilute and concentrated suspensions, respectively.

Our thorough literature review (Supplementary Table S1) highlights that, in mono-species cultures, viscosity consistently increases with higher cell concentrations, validating the models used in this study [11,16,21–23]. This increase in viscosity depends on various cell properties such as morphology [13,14,16,18], zeta potential [11], cell rigidity [18], viability [14], and motion [24]. The predictive viscosity models mentioned above are primarily developed for mono-species suspensions. For suspensions with mixed species, the Pal23 model [1] offers a novel approach using two independent volume fraction terms (φ₁ and φ₂) for particles of differing sizes, allowing for a more accurate modeling of viscosity compared to mono-species models.

Despite the fundamental role bacteria can play in algae processes, a significant gap exists in research exploring the complex fluid dynamics and influences of bacterial involvement on rheology. The presence of bacteria in algae cultures can significantly alter the rheological properties such as viscosity, yield stress, and flow behavior, due to interactions between bacterial cells and algae or their extracellular polymeric substances (EPS). These changes in rheology can impact process efficiency, such as mixing and pumping in bioreactors, highlighting the need for further investigation into the effects of bacteria on the fluid properties of mixed algal-bacterial cultures [25]. Previous research [18,25] has focussed largely on monoalgal systems, with some preliminary investigations into mixed cultures involving bacteria. However, these studies have not systematically controlled for bacterial concentrations or algal-to-bacterial ratios, leaving a significant knowledge gap regarding the algae-cyanobacteria interplay, particularly in less dense media, where interactions may differ [26]. This research on the rheology of mixed microalgae and cyanobacteria cultures is vital for optimizing large-scale production systems in industries such as biofuels, bioproducts, and agricultural biostimulants. Understanding the viscosity and shear-thinning behavior of these cultures is key to improving bioreactor design, enhancing processing efficiency, and reducing energy consumption, ultimately increasing productivity in large-scale applications.

The current study for the first time examined the rheology and flow behavior of two algae-cyanobacteria mixed cultures - freshwater *Chlorella vulgaris* and freshwater *Microcystis aeruginosa*; and marine *Nannochloropsis oceanica* and marine *Prochlorococcus* sp. under controlled conditions. This study offers valuable insights into how species interactions in mixed culture systems influence rheological properties, providing a more comprehensive understanding of viscosity behavior compared to traditional monoculture-based studies. The findings highlight the importance of considering species dynamics in bio-processes and introduce the new Pal23 model as a tool for more accurate rheological characterization of mixed species. These results are critical for optimizing algal cultivation systems and advancing industrial-scale algae-based biotechnologies. However, in this study, we decided to mix two cultures instead of growing them together in a co-culture to keep the species-specific interactions consistent and avoid growth factors that could affect the rheology. This approach was chosen due to the

limited research on the rheology of algae-cyanobacteria mixed cultures, and aims to provide a baseline for future studies in this area.

Various concentrations of algae and cyanobacteria cells are examined in test samples, providing insight into how rheology is affected by different cell culture conditions. The study focuses on algae:cyanobacteria mixed cultures and their potential impact on rheological predictions. Rheological properties are investigated across monoalgal cultures, mono-cyanobacteria cultures, and predefined algae and cyanobacteria mixed culture ratios. Non-Newtonian rheological properties were modelled using the power-law equation (Section 2.5.1), and predictive viscosity models (Section 2.5.2) were fitted using non-linear regression. Additionally, morphological properties (Section 2.2) were studied and correlated with viscosity, while the zeta potential properties (Section 2.4) were analysed and correlated to the power-law model and viscosity behaviors.

## 2. Materials and methods

### 2.1. Microalgae and cyanobacteria growth conditions

Two microalgae strains were used in this study. The freshwater microalgae *Chlorella vulgaris* (CS-41) the marine *Nannochloropsis Oceanica* (CS-179) were obtained from the Australian National Algae Culture Collection (CSIRO). The freshwater *C. vulgaris* was grown in MLA medium (Algaboost; Wallaroo, SA, Australia), comprising approximately 49 mg/L of MgSO₄·7H₂O, 170 mg/L of NaNO₃, 35 mg/L of K₂HPO₄, and 2 mg/L of H₃BO₃, respectively [27]. On the other hand, the marine *N. oceanica* was grown in marine f/2 media [28], and prepared using autoclaved seawater collected from Sydney Harbour (with a salinity of 33–35 g/L). All the seed cultures for the experiments were grown to high density in air-sparged 2 L Schott bottles and were exposed to a constant photoperiod with a light intensity of 60–70 µmol photons m⁻²s⁻¹. The cultures were maintained at an ambient temperature of 25 ± 4 °C and were sealed with 0.2 µm vented caps to prevent airborne contamination. Two strains of cyanobacteria selected in this study were obtained from the Australian National Algae Culture Collection (CSIRO). The freshwater *Microcystis aeruginosa* (CS-558) and marine *Prochlorococcus* sp. (CS-965) grown in MLA media [27] and marine Pro 99 media [29], respectively under the same growth conditions as the microalgae cultures.

At the onset of the early stationary phase, the cultures were centrifuged (Multifuge X4 Pro, Thermo Scientific) at 4200 rpm for 15 min to obtain a cell pellet and supernatant, individually. The obtained freshwater and marine pellets were resuspended in a known volume of MiliQ and 3 % NaCl, respectively to prepare stock solutions of each species, individually. The pellets and supernatant were stored at -20 °C until further use. 20 mL samples of algal and cyanobacteria cultures were taken. Cell concentration was estimated by measuring the absorbance of diluted samples (Abs<sub>680</sub>) using a 96-well plate reader (Varioskan™ LUX spectrophotometer, Thermo Scientific). Cell density (cells/mL) for each species suspension was measured using a FACS instrument (Cytoflex LX Flow Cytometer, Beckman Coulter). Separate linear correlations (R² > 0.93) between cell concentrations (cells/mL) and absorbance were established for each species. This allowed the conversion of Abs<sub>680</sub> readings of the suspensions into cell densities (cells/mL) throughout the experiments. We used cell count for biomass assessment, as dry weight can be influenced by species morphology and introduce experimental error in dilute cultures, making cell count a more reliable method for evaluating rheological behavior of low-density mixed cultures.

### 2.2. Cell morphology

Cell morphology measurements of each species suspension were conducted using a light microscope (Nikon Eclipse Ci-L plus, Nikon) in conjunction with ImageJ software [30]. Briefly, a small drop (~10 µL) of each sample was placed onto a microscopic slide and covered with a
coverslip. Subsequently, images were captured at 100× magnification using a DP72 digital camera from Olympus (Australia). ImageJ was used to study the various parameters such as cell shape, cell diameter, cell volume, and aspect ratio of each species. Multiple fields of view (at least 30) were randomly selected to ensure a representative sample. From the minor and major axes provided by ImageJ, the cell volume (V, µm³) was calculated according to Eq. (1).

$$V = \frac{4}{3} \pi \times \frac{r_1}{2} \times \frac{r_2}{2} \times \frac{r_2}{2} \qquad (1)$$

where, $r_1$ is the major axis of the cell, and $r_2$ is the minor axis. The cell is assumed to rotate around its minor axis; therefore, the volume of prolate spheroid formula is used [31].

## 2.3. Rheological measurements

Rheology tests were all performed using biomass that was freshly prepared for each experiment. The centrifuged biomass from each experiment was stored at -20 °C overnight prior to analysis. While freezing can influence rheological characteristics, this method was essential to ensure consistency and reproducibility across experiments. The freshwater and marine mixed culture combinations were prepared by mixing microalgae and cyanobacteria suspensions in fixed volume ratios (1:1, 1:10, 10:1, 1:5, 5:1, v/v) to achieve the desired cell concentrations ranging from $10^8$ to $10^6$ cells/mL. These ratios were selected to investigate a range of cell concentrations suitable for co-culture systems. The volume fraction range tested varied between species due to differences in cell concentrations in each culture.

The volume fraction ($\phi$, dimensionless) of each of the individual suspensions was determined by the following formula (Eq. (2)):

$$\phi = (v_c \times C_n) \qquad (2)$$

where, $v_c$ is the volume of an individual cell in µm³, and $C_n$ is the number of cells/mL in the suspension. The volume of 1 mL of water was converted to µm³ for calculations to obtain a dimensionless unit. To calculate the total volume fraction of the mixed suspension, the volume fractions of the two component suspensions were added together.

C. vulgaris suspensions had volume fractions ($\phi$) ranging from 0.0029 to 0.027, N. oceanica from 0.0015 to 0.015, M. aeruginosa from 0.00026 to 0.0044, and Prochlorococcus sp. from $9.3 \times 10^{-7}$ to $1.21 \times 10^{-5}$. The much lower values are attributed to the significantly smaller size of Prochlorococcus sp. However, as will be demonstrated in the results section, the effective volume fraction, when considering for zeta potential effects, is much higher. The controls (mono-algal, mono-cyanobacterial cultures, supernatants, and fresh media) were also tested to provide a comprehensive understanding of the mixed culture system dynamics. A strain-controlled rheometer (Discovery Hybrid Rheometer 1, TA Instruments) with a 40 mm parallel plate and a gap height of 600 µm was used, equipped with (TRIOS, TA instruments) software to automatically calculate shear rate, and shear stress, based on the measured torque and displacement data [13]. Briefly, shear rates $\dot{\gamma}$ from 0.5 s⁻¹ to 225 s⁻¹ were tested for each sample. The recorded measurements were averaged after a 2.5 s equilibration time for each shear rate applied to a sample. Shear stress values were averaged after an equilibration period, and samples were maintained at 25 °C using a Peltier plate attachment. Each sample was tested in triplicate. The viscosity ($\mu$, Pa.s) for each shear rate was calculated according to Eq. (3).

$$\mu = \frac{\tau}{\dot{\gamma}} \qquad (3)$$

where, $\dot{\gamma}$ is the shear rate (s⁻¹), and $\tau$ is the shear stress (Pa).

## 2.4. Zeta potential

Suspensions of all microalgae, cyanobacteria, and mixed microalgae

and cyanobacteria were prepared using the same cell concentrations and blanking mediums as those used for the rheology measurements. The zeta potential of algal cells was measured using a Zetasizer Nano ZS Zen 3600 instrument (Malvern, UK). To prevent charge screening, samples were diluted twofold. A 3 mL aliquot of each sample was transferred into DTS1070 disposable folded capillary cells. The refractive index used for the measurements was 1.347, deemed most suitable for assessing the surface charge of microalgae [32]. With a dielectric constant of 78.5, water was used as the dispersant. The measurements were conducted at a controlled temperature of 25 °C. For each sample, three measurements were performed, each consisting of 100 runs, ensuring that standard errors were maintained below 2.0 %. Zeta potentials were calculated and selected for precision, considering the cell size and ionic strength of the media.

## 2.5. Data analysis

### 2.5.1. Power-law

The flow behavior was quantified by fitting the appropriate range of shear rate and shear stress data collected for each species to the Power-Law model (Eq. (4)) [15], from which the flow behavior index (n) and the consistency index (K) was determined.

$$\tau = K \times \dot{\gamma}^n \qquad (4)$$

This model was fit using the curve_fit function from the Python package Sci-Py [33].

When $n = 1$, the flow is Newtonian, and the viscosity does not change with varying shear rate. Conversely, when $n < 1$, the flow is shear-thinning, and the viscosity decreases with increasing shear rate. This shear-thinning behavior is typically observed as cell concentration increases above a threshold value, where cell-cell interactions begin to occur. The threshold value varies across species and depends on various factors such as rigidity [18], morphology [16], zeta potential [11], and EPS production [25], typically the threshold lies somewhere between $\phi = 0.015-0.1$ (Supplementary Table S1).

### 2.5.2. Viscosity models

The relationship between viscosity (at $100 s^{-1}$) and volume fraction was analysed by fitting the Einstein model (1905, Eq. (5)), as presented by Barnes (2000) [19], and Krieger-Dougherty model (1959, Eq. (6)) [20] to the data.

$$\mu_r = \mu_0 (1 + \alpha \phi) \qquad (5)$$

$$\mu_r = \mu_0 \left( 1 + \frac{\phi}{\phi_m} \right)^{-\alpha} \qquad (6)$$

where, $\mu_r$ is the relative viscosity, $\mu_0$ is the viscosity of the cell-free suspending medium, $\phi_m$ is assumed to be around 0.62, as in previous studies on the viscosity of microalgae [22]. However, this value depends on the shape and morphological distribution of the cells within the suspension [34,35].

The novel viscosity model Pal23 [1] was used to calculate the viscosity of suspensions with multiple distinct particle types (Eq. (7)). This model is like the Krieger-Dougherty model but uses two independent volume fraction terms: $\phi_1$ for the volume fraction of the first species (here algae) and $\phi_2$ for the volume fraction of the second one (here cyanobacteria) within the suspension.

$$\mu_r = \mu_0 \left( 1 - \left( 1 + \left( \frac{1 - \phi_m}{\phi_m^2} \right) \phi_1 \right) \phi_1 \right)^{-\alpha} \left( 1 - \left( 1 + \left( \frac{1 - \phi_m}{\phi_m^2} \right) \phi_2 \right) \phi_2 \right)^{-\alpha} \qquad (7)$$

In all the viscosity models, $\alpha$ corresponds to the suspension's intrinsic viscosity, representing the impact of suspending material on the effective viscosity increase. It is the fitted parameter and is determined using
the *curve_fit* function from the Python package SciPy [33].

## 2.6. Statistical analysis

Unless otherwise stated, all measurements were performed in triplicate, and the reported values are the averages of these replicates. The standard deviation was calculated using Pandas in Python [36]. The R² score, calculated using scikit-learn [37], is reported for each model fit. The Pal23 model has an overall R² score calculated using all the data, an algae R² score for algae-only suspensions, a bacteria R² score for bacteria-only suspensions, and a mixed R² score for mixed suspensions. This approach allows to compare the Pal23 model fit quality to the mono-culture models (Einstein and Krieger-Dougherty).

While R² values were used as the primary measure of model fit to evaluate the trends in rheological behavior, we acknowledge that additional metrics, such as Root Mean Squared Error (RMSE), could provide a more comprehensive assessment of model accuracy. However, due to the exploratory nature of this study and the limited dataset, our focus was on establishing baseline trends rather than predictive accuracy, which will be addressed in future investigations.

# 3. Results

## 3.1. Algae and cyanobacteria morphology

The morphology of the selected algae and cyanobacteria strains, as studied by microscopic image analysis (Supplementary Fig. S1), is reported in Table 1. All species were approximately spherical, with aspect ratios ranging from 1.08 to 1.20. *Prochlorococcus* sp. had the smallest diameter of 0.72 µm, while *N. oceanica*, *C. vulgaris*, and *M. aeruginosa* had diameters of 2.77 µm, 3.99 µm, and 4.13 µm, respectively.

All strains except *Prochlorococcus* sp. have diameters large enough that Brownian motion is negligible. The smaller size of *Prochlorococcus* sp. suggests that physico-chemical interactions, rather than size, influence its rheological properties [38,39]. In freshwater conditions, the size ratio between the two species is close to unity, so any rheological interplay is not attributable to conventional polydisperse suspension mechanisms [40].

## 3.2. Zeta potential

These mono- and mixed-species suspensions were used to investigate zeta potential measurements to understand cell-cell interactions (Supplementary Fig. S2A and S2B). The monocultures of each species in the defined ratios using their respective diluents were also tested. The two microalgae species, *C. vulgaris* and *N. oceanica*, maintained stable zeta potential values regardless of cell concentration, ranging from -20.2 mV to -21.9 mV and -13.9 mV to -16.0 mV, respectively. The cyanobacteria species, *M. aeruginosa* and *Prochlorococcus* sp., showed a decrease in zeta potential with increasing cell concentration. *M. aeruginosa* decreased from -33.03 mV to -24.5 mV, while *Prochlorococcus* sp. decreased from -17.9 mV to -12.8 mV. The zeta potential of mixed suspensions was primarily influenced by the concentration of cyanobacteria. In marine mixed suspensions

(*N. oceanica* and *Prochlorococcus* sp.), the zeta potential resembled that of *N. oceanica* due to the relatively low cell count of *Prochlorococcus* sp. in all the concentrations tested (Supplementary Table S2). In freshwater mixed suspensions (*C. vulgaris* and *M. aeruginosa*), high concentrations of *M. aeruginosa* (>40 % *M. aeruginosa*/*C. vulgaris* volume) resulted in higher zeta potential compared to *C. vulgaris* and mixed suspensions with lower *M. aeruginosa* concentrations (≤10 % *M. aeruginosa*/*C. vulgaris* volume).

## 3.3. Rheology of mono- and mixed-cultures

Cell pellets for each species were obtained by centrifuging the cultures. The resulting supernatants were also stored to investigate viscosity as a function of the applied shear rate (Supplementary Fig. S3), tested against fresh media (MLA, Pro99, and F/2) and diluents (MilliQ and 3 % NaCl). The viscosity of MilliQ and 3 % NaCl stabilized at a shear rate of 15 s⁻¹. Therefore, all values below this shear rate were removed from the analysis, as any viscosity variation before this point was attributed to experimental error, which is typically expected when measuring the viscosity of low-viscosity fluids in plate-plate geometries [41].

The supernatants of freshwater species *C. vulgaris* and *M. aeruginosa* had constant viscosities of 0.829 mPa·s and 0.841 mPa·s, respectively, similar to MilliQ and MLA (0.817 mPa·s and 0.824 mPa·s). The supernatants of *N. oceanica* and *Prochlorococcus* sp. were more viscous (0.879 mPa·s and 0.878 mPa·s) than their suspending diluents (3 % NaCl, 0.846 mPa·s) and respective media (F/2 at 0.869 mPa·s and Pro99 at 0.809 mPa·s).

Fixed quantities of cyanobacteria and microalgae cells were mixed to assess their combined impact on viscosity, compared to controls using MilliQ and 3 % NaCl. Cell concentrations varied: *C. vulgaris* (8.61 to 81.27 × 10⁷ cells/mL), *M. aeruginosa* (0.69 to 8.0 × 10⁷ cells/mL), *N. oceanica* (13.29 to 136.4 × 10⁷ cells/mL), and *Prochlorococcus* sp. (0.47 to 6.1 × 10⁷ cells/mL). Supplementary Table S2 detailed cell concentrations, volume fractions, power-law model parameters (Eq. (3)), and viscosity at 100 s⁻¹ shear rates. *C. vulgaris* (Supplementary Fig. S4A), *N. oceanica* (S4C), and *Prochlorococcus* sp. (S4D) exhibited Newtonian behavior across shear rates. Although a slight decrease in the flow behavior index below 1.00 was observed at higher cell concentrations, it did not indicate significant shear-thinning behavior. *M. aeruginosa* (S4B) showed obvious shear-thinning behavior as cell concentration increased above 4.30 × 10⁷ cells/mL (φ = 0.001590), with the flow behavior index decreasing from 0.88 to 0.70 at 11.77 × 10⁷ cells/mL (φ = 0.004351).

All suspensions of microalgae and cyanobacteria were fitted with the Einstein and Krieger-Dougherty models (Fig. 1). As cell concentration increased, the viscosity of freshwater *C. vulgaris* and *M. aeruginosa* suspensions also increased. *C. vulgaris* viscosity increased from 0.81 mPa·s to 0.97 mPa·s at 100 s⁻¹ across the tested concentrations, while *M. aeruginosa* viscosity increased more significantly from 0.85 mPa·s to 2.24 mPa·s at the same shear rate.

Fig. 1A depicted the relative viscosity as a function of the total volume fraction occupied by both species, fitted with the Einstein and Krieger-Dougherty models. The intrinsic viscosities were 7.28 and

<table><caption>**Table 1**

Morphological properties of algae and cyanobacteria species.</caption><thead><tr><th>Species</th><th>Minor axis (µm)</th><th>Major axis (µm)</th><th>Cell volume (µm³)</th><th>Aspect ratio</th><th>Effective diameter (µm)</th><th>Mixed culture size ratio</th></tr></thead><tbody><tr><td>Freshwater mixed culture</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td><i>C. vulgaris</i></td><td>3.87</td><td>4.24</td><td>33.33</td><td>1.10</td><td>3.99</td><td>0.97</td></tr><tr><td><i>M. aeruginosa</i></td><td>4.03</td><td>4.34</td><td>36.96</td><td>1.08</td><td>4.13</td><td></td></tr><tr><td>Marine mixed culture</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td><i>N. oceanica</i></td><td>2.60</td><td>3.13</td><td>11.07</td><td>1.20</td><td>2.77</td><td>3.85</td></tr><tr><td><i>Prochlorococcus</i> sp.</td><td>0.69</td><td>0.80</td><td>0.1989</td><td>1.16</td><td>0.72</td><td></td></tr></tbody></table>
<figure><img src="image_4.png" /><figcaption>Fig. 1. Relative viscosity of freshwater species (A, *C. vulgaris* and *M. aeruginosa*) and marine species (B, *N. oceanica* and *Prochlorococcus* sp.) suspended in MLA and 3 % NaCl, respectively. The results are represented as average and standard deviation of three replicates.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>B</figcaption></figure>

310.05 for the Einstein model, and 6.56 and 210.51 for the Krieger-Dougherty model, representing *C. vulgaris* and *M. aeruginosa*, respectively. The Krieger-Dougherty model suggested that *M. aeruginosa* viscosity could increase exponentially as the volume fraction exceeds the tested range, whereas *C. vulgaris* viscosity did not significantly deviate from the linear behavior predicted by the Einstein model within the explored range.

In case of marine species, both *N. oceanica* and *Prochlorococcus* sp. exhibited increasing viscosity with higher cell concentrations, measured from 0.87 mPa·s to 1.05 mPa·s and 0.914 mPa·s to 1.06 mPa·s respectively, at a shear rate of 100 s⁻¹. The relative viscosity, compared to NaCl (3 %) at 100 s⁻¹, varied with the total volume fraction occupied by each species (Fig. 1B). *Prochlorococcus* sp. demonstrated significantly higher intrinsic viscosity compared to *N. oceanica* and freshwater species across tested concentrations. The Einstein and Krieger-Dougherty models provided intrinsic viscosity values, highlighting differences between *N. oceanica* (17.71 and 15.64) and *Prochlorococcus* sp. (23,093.66 and 20,439.85). The cell concentrations, volume fractions, viscosity at a shear rate of 100 s⁻¹, and power-law parameters for mixed suspensions are detailed in Supplementary Table S2.

The rheology of both marine and freshwater mixed suspensions was found to be influenced more by the combination of microalgae and cyanobacteria rather than by their individual concentrations (Fig. 2).

The freshwater mixed suspensions (Fig. 2A) consistently showed shear thinning behavior, even at the lowest concentration of *M. aeruginosa*. The flow behavior index decreased from 0.96 to 0.72, while the consistency index increased as the flow behavior index decreased, ranging from 1.22 mPa·sⁿ to 8.18 mPa·sⁿ. In contrast, the viscosity of marine mixed suspensions depended on the overall mixture of *N. oceanica* and *Prochlorococcus* sp., rather than on the specific ratio of these species (Fig. 2B). The marine mixed suspensions exhibited rheological behavior like their individual components, with a minor decrease in the flow behavior index (−0.01). However, proper shear thinning behavior was not observed due to the low volume fractions tested. The consistency index ranged from 1.15 mPa·sⁿ to 1.26 mPa·sⁿ.

### 3.4. Modified model for rheology parameters

While the Einstein and Krieger-Dougherty models are commonly used to describe the viscosity-concentration relationship in microbial suspensions [16], we opted to test both models due to the dilute nature of our systems. While the Krieger-Dougherty model is often favored for more concentrated systems, the Einstein model can still be sufficient for dilute systems. However, our data indicated that neither model adequately fit the viscosity data for both freshwater and marine mixed suspensions, as evidenced by the negative R² values. This suggests that

<figure><img src="image_6.png" /><figcaption>Fig. 2. Flow behavior of freshwater species (A, *C. vulgaris* and *M. aeruginosa*) and marine species (B, *N. oceanica* and *Prochlorococcus* sp.) prepared in a known ratio of cell concentration. The flow behavior index (n) for each combination is also provided in the legend. The results are the average and standard deviation of three replicates, fitted using the power-law model.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>B</figcaption></figure>
these classical models may not fully capture the complex rheological behaviors of mixed microbial suspensions, especially considering the diverse species and their interactions in our systems. This also indicated that viscosity was not solely dependent on the total volume fraction but instead on a combination of both microalgae and cyanobacteria. While we were within the dilute concentration range where the Einstein model is applicable to individual suspension viscosities, we considered mixed models based on a Krieger-Dougherty structure for several reasons: the existing Pal23 model in the literature already uses this approach, it accounts for possible non-linear behavior when combining species, and it allows for further generalization of our work to larger volume fractions that deviate from Einstein behaviors.

Therefore, we used a novel Pal23 model (Eq. (7)) to understand the rheological parameters of mixed particle types. However, the original

Pal23 model also proved to be a poor fit for the data, as shown in Fig. 3A and B, with negative R² values for both freshwater and mixed suspensions. The poor performance was due to the model’s constraint of equal intrinsic viscosity for both species, which failed to capture the substantial differences in viscosity sensitivity to volume fractions among the various species, as shown in the monoculture results in Fig. 1.

Thus, a modified Pal23 Model was developed, incorporating two independent intrinsic viscosity terms (α₁ and α₂), as depicted in Fig. 3C and D, and Eq. (8).

$$ \mu_r = \mu_0 \left( 1 - \left( 1 + \left( \frac{1-\phi_m}{\phi_m^2} \right) \phi_1 \right) \phi_1 \right)^{-a_1} \left( 1 - \left( 1 + \left( \frac{1-\phi_m}{\phi_m^2} \right) \phi_2 \right) \phi_2 \right)^{-a_2} \quad (8) $$

<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /><figcaption>Fig. 3. Relative viscosity of freshwater species (A, C. vulgaris and M. aeruginosa) and marine species (B, N. oceanica and Prochlorococcus sp.) using the Pal23 model (Eq. (7)). A modified version of the Pal23 model (Eq. (8)) was also applied to both freshwater (C) and marine (D) species. The results represent the average and standard deviation of three replicates.</figcaption></figure>
This model showed improved fitting for both freshwater and marine mono-species suspensions. The incorporation of the intrinsic viscosity term in the Pal23 model improves predictions by accounting for the individual contributions of each microorganism, considering their diverse size, shape, and structural properties, which is particularly important for mixed microbial suspensions where species interact differently and influence viscosity in distinct ways. In the freshwater suspension, both mono- and mixed-species showed a good $R^2$ value. However, for marine suspensions, while an overall positive $R^2$ was attained for mono-species, the mixed-species data still showed a negative $R^2$ value.

Visual examination of the freshwater model revealed that it failed to predict the viscosity reduction observed in the three most *M. aeruginosa* dense mixed suspensions, although it effectively accounted for viscosity increases in *C. vulgaris* dense suspensions. In contrast, the marine model consistently overpredicted viscosity for mixed suspensions. The intrinsic viscosity values from the modified Pal23 model, $\alpha_1$ and $\alpha_2$, did not exactly match those from the Einstein model but were similar to those from the Krieger-Dougherty model. For the freshwater suspension, $\alpha_1$ and $\alpha_2$ were 6.69 and 203.51, respectively, while for the marine suspension, $\alpha_1$ and $\alpha_2$ were 14.70 and 18,240.23, respectively. The proximity of the intrinsic viscosity values determined from the Krieger-Dougherty model to those of the modified Pal23 model suggests that the viscosity of suspensions containing two cells with different particle-fluid interactions could be predicted using this modified Pal23 model, at least in the dilute range as was investigated in this study.

## 4. Discussion

The lack of shear thinning observed in *C. vulgaris*, *N. oceanica*, and *Prochlorococcus* sp. in this study (Supplementary Figs. S4A, 4C, 4D) is most likely attributable to the low volume fractions tested. These low volume fractions would have limited the effects of particle-particle interactions on the flow behavior of these suspensions. Previous research has reported shear thinning in suspensions containing *C. vulgaris* and *Nannochloropsis* sp., but only at higher concentrations ($\phi$ > 0.06 and $\phi$ > 0.04, respectively) [18] than those tested here. In such cases, the concentration typically exceeds the dilute limit defined by Einstein [19], where particle-particle interactions begin to significantly influence rheological behavior [13]. Although the study does not investigate the non-Newtonian rheology of denser suspensions found in advanced PBRs [8], it is noted that current industrial settings typically operate with very dilute suspensions densities [7], making the findings highly relevant to existing industrial applications.

Our findings indicate that *M. aeruginosa* displayed shear thinning at cell concentrations exceeding $4.3 \times 10^7$ cells/mL (Supplementary Fig. S4B). This suggests that at higher concentrations, this organism begins to be affected by the shear rate, leading to a change in the particle-fluid interactions [42]. This behavior was also evident in mixed suspensions of *C. vulgaris* and *M. aeruginosa*, which exhibited shear thinning across all tested concentrations (Fig. 2A). This implies that at the lowest concentrations, interactions between *C. vulgaris* and *M. aeruginosa* cells promote non-Newtonian behavior, which does not occur in low concentrations of *M. aeruginosa* or in any concentration of *C. vulgaris*. No prior research on the rheology of *Prochlorococcus* sp. could be found, but since we tested concentrations below the dilute limit, shear thinning due to particle-particle interactions was not expected. The rheology of *Prochlorococcus* sp. can be compared to the closely related *Synechococcus* sp., which showed shear thinning at a volume fraction of 0.087 [14]. Nevertheless, the current study is limited to low volume fractions, and future research could investigate rheological behavior at various time points and growth phases, ranging from low to high biomass concentrations in a mixed culture system. This would offer valuable insights into shear thinning behavior and facilitate a more thorough comparison with monoalgal system, enhancing our understanding of rheological trends across a broader range of conditions.

Increased viscosity with increasing cell concentration was expected for all species tested. This is well-documented for microalgae like *C. vulgaris* [18,23] and *N. oceanica* [10,18]. Although this is the first study on the topic for the cyanobacteria, the increase in viscosity was expected since neither species is motile [43], and motility can increase the viscosity [16,22]. An increase in viscosity is expected when studying the rheology of microalgae due to factors such as zeta potential [11], morphologies [16], exopolymeric substance (EPS) characteristics [25], and cultivation conditions [44]. Previous research has shown that EPS production in *C. vulgaris* increases suspension viscosity and also causes shear thinning behavior [45]. EPS production and characteristics vary by species, strain, and conditions [46], with *Microcystis* sp. producing more viscous EPS than other cyanobacteria and microalgae [47]. The shear-thinning behavior of *M. aeruginosa* could be partly due to the bound EPS on the cells, which has been observed to be shear-thinning in other species [48].

The supernatants of *C. vulgaris* and *M. aeruginosa* had similar viscosities to media blanks (Supplementary Fig. S3), indicating low dissolved EPS. In contrast, *N. oceanica* and *Prochlorococcus* sp. supernatants were more viscous than their media blanks (Supplementary Fig. S3), suggesting significant dissolved EPS. With no published data available on rheology of *Prochlorococcus* sp., it is difficult to confidently explain the high intrinsic viscosity observed in this current study (Supplementary Fig. S3). A separate experiment was conducted to measure EPS concentrations in both freshwater and marine mixed suspensions (Supplementary Information). EPS concentrations, normalized to cell volume, showed a significant difference between *N. oceanica* and *Prochlorococcus* sp. bound EPS (0.056 and 77.20 $pg/\mu m^3$, respectively), which helps explain the variation in intrinsic viscosity (Fig. 1B). However, more studies are needed to confirm whether bound EPS is the main factor behind the high viscosity observed in *Prochlorococcus* sp. This study also represents the first quantification of EPS in *Prochlorococcus* sp., revealing higher bound EPS in cyanobacteria compared to microalgae, which may explain viscosity differences in the Einstein and Krieger-Dougherty models. The supernatants of *C. vulgaris* and *M. aeruginosa* showed low EPS concentrations, while *N. oceanica* and *Prochlorococcus* sp. had higher viscosities, suggesting more dissolved EPS. Dissolved EPS was higher in marine species, particularly *Prochlorococcus* sp., though variability in samples indicates the need for further testing. Future research should use larger sample volumes or more sensitive techniques to accurately measure dissolved EPS. Due to the variability of EPS production across different species, comparing results across studies can be challenging. Additionally, rheological behavior is influenced by EPS structure (composition, molecular weight, and branching; [46]), which was beyond the scope of this study but warrants further exploration to better understand species-specific rheological behaviors.

The zeta potential of these species was considered in this study. The Smoluchowski factor ($S_f$ Supplementary Equations SE1 and SE2) quantifies the increase in cell volume fraction ($\phi$) within a suspension [49]. This increased volume fraction can then be applied to the viscosity models to describe the effect of zeta potential. Due to the larger size (Table 1) and similar zeta potential (Supplementary Fig. S2) values of *C. vulgaris*, *M. aeruginosa*, and *N. oceanica*, there was little difference in the Smoluchowski factor (Supplementary Table S3). In contrast, due to the much smaller size of *Prochlorococcus* sp. (Table 1), the difference in the Smoluchowski factor was more pronounced compared to the other three species (Supplementary Table S3). This partially explains why *Prochlorococcus* sp. exhibited such a high intrinsic viscosity (Fig. 1B). However, the exact mechanism behind the viscosity increase in *Prochlorococcus* sp. remains unclear. Further research is necessary to understand *Prochlorococcus* sp. implications in co-culture systems fully.

The Einstein and Krieger-Dougherty models describe the relationship between relative viscosity and volume fraction ($\phi$) within measurement uncertainty. The intrinsic viscosities of *C. vulgaris* and *N. oceanica* are relatively similar, while those of *M. aeruginosa* and *Prochlorococcus* sp.
are significantly higher (Fig. 1). C. vulgaris has the most similar intrinsic viscosity to the Einstein model [19], which aligns with its lack of significant EPS production, low Smoluchowski factor, and rigid cell wall, making it closest to suspensions of rigid spheres for which the theory was derived. The application of the Power Law model (Supplementary Fig. S4) to monocultures revealed no shear thinning for C. vulgaris, N. oceanica, and Prochlorococcus sp., further supporting that the volume fractions tested were below the threshold where particle interactions significantly impact viscosity. However, the viscosity in mixed suspensions did not correlate with total volume fraction (Fig. 2), highlighting the limitations of conventional models like Einstein and Krieger-Dougherty, which are optimized for mono-species scenarios. A novel Pal23 model (Eq. (7)) was used to fit the data in mixed-species scenario considering two different volume fractions ($\phi_1, \phi_2$) (Fig. 3A-D). However, one potential issue with this model is the assumption that both particle types have the same intrinsic viscosity and impact on viscosity with increasing volume fraction. This is not true for different microalgae species and strains, as shown by [11,16].

However, in our study, all three models (the Einstein, Krieger-Dougherty, and Pal23) failed to accurately predict the viscosity of mixed suspensions, primarily due to the disproportionate influence of low-volume-fraction cyanobacteria on overall suspension viscosity. In mixed suspensions with particles having different intrinsic viscosities, the Pal23 model would fail to predict the relative viscosity accurately. To overcome this limitation, the current study modified the Pal23 model (Eq. (8)), incorporating two independent volume fraction terms for different particle types, provided a more accurate understanding of the viscosity in mixed suspensions.

Cyanobacteria, with their inherently higher viscosity per unit volume fraction compared to microalgae (Fig. 1B), significantly affected suspension rheology when combined. This divergence from expected model predictions underscores the complex interplay of components in mixed suspensions, where simple volume fraction-viscosity relationships do not hold when one component dominates rheological behavior, such as observed with Prochlorococcus sp. (Fig. 3D).

Notably, in highly concentrated Prochlorococcus sp. mixed suspensions, rheological behavior mirrored that of pure Prochlorococcus sp. suspensions (Fig. 3D), indicating minimal impact from the added N. oceanica despite increased volume fraction. However, in less concentrated Prochlorococcus sp. cultures, the influence of N. oceanica on rheology became more apparent (Fig. 3D). This rheological behavior aligns with expectations that increasing volume fraction generally increases viscosity, yet it also highlights the significant role of dominant species in determining overall suspension viscosity.

Conversely, in freshwater mixed suspensions (Fig. 3C) with higher M. aeruginosa concentrations, viscosity decreased compared to pure M. aeruginosa (Fig. 1A) suspensions, even with the increase in volume fraction from the added C. vulgaris. This unexpected decrease challenges conventional rheological expectations, suggesting additional factors at play beyond volume fraction alone. Variations in zeta potential with changing concentration and the differential EPS characteristics of cyanobacteria likely contribute to these observed rheological complexities, suggesting further investigation into their specific impacts.

The Pal23 model assumes multiplicative interactions between species, which does not adequately capture the non-cumulative, non-monotonic trends observed in mixed suspensions of microalgae and cyanobacteria. As these systems are dominated by hydrodynamic forces rather than molecular interactions, the applicability of traditional colloidal models is limited. Future studies should explore incorporating interaction terms and considering factors such as particle size ratios, cell shape, and suspension density to improve model accuracy.

## 5. Conclusion

The current study investigated the rheological dynamics of mixed cultures of algae and cyanobacteria. The study aimed to bridge the gaps

in understanding for more efficient and scalable algal cultivations by investigating into species-specific morphology, zeta potential, and flow behavior and rheology of mixed-species suspensions. Traditional viscosity models (Einstein, Krieger-Dougherty) did not accurately predict mixed suspension viscosity. The modified Pal23 model provided a more accurate fit, highlighting the need for better designed rheological models. Overall, cyanobacteria applied a disproportionate influence on suspension viscosity in mixed cultures, challenging simple volume fraction-viscosity relationships. By addressing the complexities of mixed-species suspensions, our research highlights the need for better designed rheological models that account for species-specific interactions and concentration-dependent behaviors. Future research should aim to explore higher biomass densities and a broader range of shear rates to better understand the industrial-scale implications of these findings. Additionally, future work should focus on refining the Pal23 model by incorporating interaction terms and considering factors such as particle size ratios, cell shape, and suspension density. Additionally, exploring the impact of EPS, surface charge, and cell functional groups on viscosity and fluid dynamics in mixed cultures will be crucial for optimizing large-scale cultivation systems and improving bioreactor efficiency.

## CRediT authorship contribution statement

**Conor Button:** Writing – original draft, Methodology, Investigation, Formal analysis, Data curation. **Nature Poddar:** Writing – original draft, Supervision, Project administration, Methodology, Investigation, Formal analysis, Conceptualization. **Tom Lacassagne:** Writing – review & editing, Formal analysis. **Mathieu Pernice:** Writing – review & editing, Supervision. **Vishal Gupta:** Writing – review & editing, Supervision. **Lisa Aditya:** Writing – review & editing, Resources. **Unnikrishnan Kuzhiumparambil:** Writing – review & editing, Resources. **Peter J. Ralph:** Writing – review & editing, Funding acquisition.

## Declaration of Generative AI and AI-assisted technologies in the writing process

During the preparation of this work the authors used BioRender tool in order to create high quality graphical abstract. Publication licence is attached with this manuscript. Authors also used Chatgpt tool to improve the readability and language of the manuscript. After using this tool, the authors reviewed and edited the content as needed and take full responsibility for the content of the published article. No other tools or services were used for this manuscript.

## Declaration of competing interest

Authors declare no conflict of interest.

## Acknowledgements

The authors acknowledge the support of the Climate Change Cluster at the University of Technology Sydney for their assistance in supporting the Honours research program.

## Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.algal.2025.103988.

## Data availability

Uploaded data as excel file under supplementary
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