## 2 Materials and Methods
### Indoor Batch Cultivation of microalgae Testing Various Digestate Dilution  
The purpose of these experiments was to evaluate the algal growth performances at different dilution rates of ALD. Dilution of ALD was considered as a necessary step in order to alleviate its toxicity due to high ammonium and turbidity content [8; 19]. a seeding of these cultures was carried out on ALD at different dilution concentrations (dilution of 1:20, 1:30 and 1:50 using distilled water). The culture was carried out on a laboratory scale, in a growth shelf, using 2-dm\({}^{3}\) bottles (cf. Figure S1). Cells were inoculated into the medium at a proportion of 20% (%). Each batch was performed in duplicate and started from an initial algae biomass concentration of 0.14 gTSS L\({}^{-1}\). The cultures were artificially illuminated (33.75 umol m\({}^{2}\) s\({}^{-1}\)) and bubbled with a mix of air and carbon dioxide (0.2%v\({}_{\text{CO2}}\)/v\({}_{\text{air}}\)) controlled by a mass flow meter from Aalborg(r). Temperature was kept at room values (21-23 \({}^{\circ}\)C). Irradiance was provided by warm-white fluorescent lamps. The light intensity was measured from the outer surface of the crystal bottles using a LX-105 Digital Light LUX meter RS232 and then converted into PAR flux (umol m\({}^{2}\) s\({}^{-1}\)) by multiplying the calibration factor (0.0135 in the case of cool white fluorescent lamps). Microalgae growth was daily followed by determining Optical Density (OD) at 680 nm with a UV-visible spectrometer (7315, Jenway, United Kingdom), after proper dilution with deionized water to obtain absorbance values between zero and one.  
The specific growth rate in the exponential phase of the algal growth was measured using Equation (1).  
\[\mu\left(day^{-1}\right)=\left(LnX_{2}-LnX_{1}\right)/\left(t_{1}-t_{2}\right) \tag{1}\]  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Values** & **Units** \\ \hline pH (25 \({}^{\circ}\)C) & 8.6 & \\ \hline
**Conductivity** & 3640 & \(\mu\)S cm\({}^{-1}\) \\ \hline
**TS** & 2.0 & \% raw matter \\ \hline
**VS** & 470 & g/kg TS \\ \hline
**COD** & 239 & g/kg TS \\ \hline
**NTK** & 216 & brut g N/kg TS \\ \hline
**NH\({}_{4}\)\({}^{+}\)** & 121 & g N/kg TS \\ \hline
**P** & 16.1 & g P\({}_{2}\)O\({}_{5}\)/kg TS \\ \hline
**K** & 252 & g K\({}_{2}\)O/kg TS \\ \hline
**Mg** & 7.1 & g MgO/kg TS \\ \hline
**Ca** & 33.8 & g CaO/kg TS \\ \hline
**S** & 17.2 & g SO\({}_{3}\)/kg TS \\ \hline
**As** & 2.1 & mg As/kg TS \\ \hline
**Cd** & 0.36 & mg Cd/kg TS \\ \hline
**Cr** & 5.5 & mg Cr/kg TS \\ \hline
**Cu** & 79.5 & mg Cu/kg TS \\ \hline
**Ni** & 10.0 & mg Ni/kg TS \\ \hline
**Zn** & 207 & mg Zn/kg TS \\ \hline \hline \end{tabular}
\end{table}
Table 1: Selected chemical properties of the liquid digestate used in this study.  
where \(X_{2}\) and \(X_{1}\) are the Cell numbers (Cells/\(\mu\)L) at time \(t_{2}\) and \(t_{1}\), respectively.  
In parallel, the nutrient removal efficiency was also calculated according the Equation (2) below:  
\[\text{NRE (\%)}=100-(100^{\circ}\text{Ct/C}_{0}) \tag{2}\]  
where \(\text{C}_{0}\) and \(\text{C}_{\text{t}}\) are the nutrient concentrations (mg/L) at the beginning of the experiment and end of the experiment respectively.