Light burned MgO of technical grade (≥97%, VWR Chemicals BDH^®, United Kingdom) and high reactivity (citric acid neutralisation time of 45 ± 6 s) was used. Fresh human urine (20 persons, age 25–65) was collected using 500 ml sterile high-density polyethylene bottles, pooled, and used within 7 hours of donation. The samples represented urine collected over a working day (FU₁ and FU₃), first-morning urine (FU₂), and a mixture of first-morning urine and day urine (FU₄). Synthetic fresh urine (SU₁-SU₄) that mimicked the composition of real fresh urine was prepared by dissolving urea and inorganic compounds (NaCl, Na₂SO₄, KCl, MgCl₂.6H₂O, NaH₂PO₄, CaCl₂, and NH₄Cl) in Milli-Q water and adjusting the pH of the solution with NaOH (Table 1). When preparing synthetic dephosphatised fresh urine (SDU₁-SDU₄), NaH₂PO₄ was substituted with NaCl, to have the same sodium concentration as that measured for fresh human urine. To make concentrated fresh human urine, a sample of fresh human urine was dried in a CO₂-free drying chamber till the urine weighed 1/8th of its original weight. The concentrated urine (CFU_×8) was diluted with Milli-Q water to prepare CFU_×2 and CFU_×4. To make concentrated synthetic urine (CSU_×2, CSU_×4 and CSU_×8), the same procedure as that for making fresh synthetic urine was followed but the concentration of urea and inorganic compounds in Milli-Q water was increased by two, four or eight times, respectively.

To study the dissolution of Mg(OH)₂ in urine, flasks containing 250 ml fresh urine were dosed with 2 g MgO L⁻¹, covered with parafilm, and placed at room temperature (23 ± 2°C) over a magnetic stirrer set to 700 rpm for 60 min. Pre-trials indicated that at these experimental conditions (MgO dosage, mixing speed and duration), less than 15 min was required for electrical conductivity (EC) of urine to increase and equilibrate. The pH, electrical conductivity, and temperature of urine were monitored at 60 s intervals for the first 15 min, and thereafter at every 15 min interval. The pH was measured using a single junction gel electrode (13-620-AE6, Fisher Scientific United States) connected to a benchtop pH meter (AE150 accumet, Fisher Scientific, United States), while the EC and temperature were monitored with a probe (TetraCon 325, WTW, Germany) connected to a handheld meter (Cond 340i, WTW, Germany). After 60 min, the urine was filtered using a 0.45 μm pore size filter paper (Merck KGaA, Germany) placed in a vacuum filtration system (Uni-Crown, Taiwan) that was set to a pressure of 1.5 atm. A representative sample of the filtered urine was acidified to a pH of < 2 by adding 1 M H₂SO₄ and stored at 4°C for further analysis.

To determine the effect of organic substances and soluble phosphate present in urine on the solubility of Mg(OH)₂, the dissolution experiments were repeated using synthetic fresh human urine and synthetic dephosphatised fresh human urine, respectively.

To determine the effect of water removal (i.e., concentrating urine) on the solubility of Mg(OH)₂, the dissolution experiments were repeated with concentrated real fresh urine and concentrated synthetic fresh urine. All the experiments were performed in triplicate and average values along with their standard deviation are reported.

Flasks containing 250 ml fresh human urine or fresh human urine dosed with 2 g MgO L⁻¹ were contaminated with 7.3 mg urease L⁻¹ (lyophilised urease from Canavalia ensiformis with activity of ≥5 U mg⁻¹; 108,489 urease, Merck, Germany), covered with parafilm, and placed over a magnetic stirrer set to 700 rpm at room temperature (23 ± 2°C). The flasks were monitored for 14 days, and daily measurements were made for pH and total ammonia concentration in urine. As control, flasks containing fresh urine and fresh urine saturated with Mg(OH)₂, both without any urease contamination were also monitored. The concentration of urease was fixed based on the enzymatic activity reported by the manufacturer (5 µmol ammonia mg⁻¹ min⁻¹), a total hydrolysis time of 14 days, and assuming that fresh urine contained 10 g urea L⁻¹.

The concentration of total ammonia nitrogen, total nitrogen, and chemical oxygen demand was determined colorimetrically using Spectroquant^® test kits according to the instructions of the manufacturer (Merck KGaA, Germany) and a Spectroquant^® photometer (NOVA 60 A, Merck KGaA, Germany). The concentration of phosphorus, potassium, calcium, magnesium, sodium, and sulphur was determined by inductively coupled plasma-optical emission spectrometry (Optima Avio 200, PerkinElmer, United States), prior to which urine samples were digested with 65% HNO₃ and diluted with Milli-Q water.

The solubility of Mg(OH)₂ in urine was calculated using Eq. 1, whereas the MgO dosage required to saturate fresh human urine with Mg(OH)₂ was calculated using Eq. 2. Solubilit y Mg ( OH ) 2 = [ M g aq 2+ ] × M M Mg ( OH ) 2 M M M g 2+ (1) Saturation   dos e MgO = { [ M g 2+ ] aq + [ M g 2+ ] s - [ M g 2+ ] i } × M M MgO M M M g 2+ (2) where [ M g 2+ ] aq and [ M g 2+ ] s   are the concentration of Mg²⁺ in the filtered urine and in the precipitated solids, [ M g 2+ ] i is the concentration of Mg²⁺ initially present in the fresh urine, and M M Mg ( OH ) 2 , M M MgO and M M M g 2+ are the molar mass of Mg(OH)₂, MgO and magnesium, respectively.

The concentration factor, which can be defined either as the ratio of volume of water present in urine initially to the volume of water left after evaporation (Randall and Nathoo, 2015), or the proportion of ion concentration in urine after evaporation versus the ion concentration in fresh urine (Pronk et al., 2006), was calculated using Eq. 3. CF= wate r i   wate r f  or  ∑ ( C C,f + C A,f ) ∑ ( C C,i + C A,i ) (3)

The subscripts i and f refer to fresh urine and concentrated urine, respectively, whereas C and A refer to cations and anions.

To determine the pH of human urine as function of time, the experimental data was fitted to the pseudo second order kinetic model (Eq. 4). p H t = k 2 p H e q 2 t 1 + k 2 p H e q t (4) where k₂ (min⁻¹) is the rate constant, and pH _t and pH _eq are the pH of urine at time t and at equilibrium, respectively. To evaluate goodness of fit of the model, the correlation coefficient (R ²; Eq. 5) and normalised standard deviation ΔpH (%; Eq. 6) were calculated. R 2 = ∑ ( p H t , c a l − p H ¯ t , c a l ) ( p H t , e x p − p H ¯ t , e x p ) ∑ ( p H t , c a l − p H ¯ t , c a l ) 2 ∑ ( p H t , e x p − p H ¯ t , e x p ) 2 (5) ΔpH=100× ∑ [ ( p H t,exp - p H t,cal ) / p H t,exp ] 2 ( n - 1 ) (6) where pH _t,cal and pH _t,exp are the calculated and experimental pH of urine at time t, p H ¯ _t,exp is the average of pH _t,exp and n is the number of data points (Lin and Wang, 2009).

The software OLI Stream Analyzer (OLI Systems Inc., 2020) was used (using the Mixed Solvent Electrolyte model option) to simulate the pH, chemical speciation, and major solids formed in urine at thermodynamic equilibrium. The pH predicted by the software was matched with the experimentally determined pH using Eq. 4, and used to estimate the kinetics of chemical speciation, i.e., time required for Mg(OH)₂ to dissolve and for major solids to form in urine. The simulations were made for different compositions of real and synthetic urine used in this study (FU₁-FU₄), as well as for urine compositions taken from literature (FU₅-FU₁₁).

The experiment data was tested for normality and homogeneity of variance, after which one way analysis of variance at 95% confidence interval was performed to assess whether the initial composition of fresh urine and the type of urine (fresh, synthetic or concentrated) had a significant influence on the pH, EC and elemental composition of the saturated urine as well as the solubility of Mg(OH)₂. When significant differences were found, a post-hoc test (Tukey’s honest significant difference) was performed at 95% confidence interval. In addition, exploratory principal component analysis was conducted to identify variables that explained the variance in the solubility data, following which linear regression analysis was performed on the variables of interest. All the statistical analyses were carried out in RStudio version 1.2.5042 and R version 4.0.0 (RStudio Team, 2016).

The effect of introducing urease to fresh urine, with and without alkalisation by Mg(OH)₂ are shown in Figure 1. Without any Mg(OH)₂, urea is quickly hydrolysed to ammonia (1860 mg L⁻¹ after 14 days), which increases the pH of urine to 8.6. In fresh urine treated with Mg(OH)₂, the concentration of total ammonia nitrogen increased from 100 mg L⁻¹ to 128 mg L⁻¹ after 14 days. This corresponds to a urea hydrolysis rate of just 0.5%. As fresh urine was dosed with excess MgO (2 g L⁻¹), it was saturated with Mg(OH)₂ and maintained a pH of >10.5 for 14 days.

When MgO is added to fresh urine, it hydrates to Mg(OH)₂. As Mg(OH)₂ dissolves in urine, the concentration of Mg²⁺(aq) and OH⁻(aq) increases (Eq. 7), resulting in a corresponding increase in the urine pH (Figure 2). Depending on the composition of urine, when the pH is between 6.8 and 7.4, the concentration of Mg²⁺(aq) and P O 4 3- (aq) starts decreasing, whereas the concentration of Mg²⁺(s) starts increasing, suggesting that the precipitation of struvite is triggered. This trend continues until pH 8.6, when the majority of the soluble phosphate is precipitated. MgO ( s ) + H 2 O↔Mg ( OH ) 2 ( s ) ↔M g 2+ ( aq ) +2O H - ( aq ) (7)

At 25°C, between 80 and 700 mg Mg(OH)₂ L⁻¹ dissolves, depending on the composition of urine (Figure 3A). The average simulated Mg(OH)₂ solubility is 365 mg L⁻¹, making it sparingly soluble in fresh human urine. The dissolution of Mg(OH)₂ increases the pH of urine to 10 ± 0.15 at 25°C (Figure 3B). The overall dosage of MgO needed to saturate fresh urine with Mg(OH)₂ at 25°C varies between 250 and 970 mg L⁻¹ (Figure 3C).

The dissolution of Mg(OH)₂ is exothermic, so it has retrograde solubility in fresh urine. Increasing the temperature decreases Mg(OH)₂ solubility (Figure 3A) as well as the pH of urine (Figure 3B). The solubility of Mg(OH)₂ in concentrated fresh urine is higher than its solubility in fresh urine (Figure 4A) and there is a linear relationship between solubility and urine concentration factor (Figure 5). At 25°C and CF = 32, the solubility of Mg(OH)₂ in concentrated fresh urine is 16,240 mg L⁻¹, which is 27 times higher than the solubility in fresh urine (Supplementary Figure S1). As a result, at a given temperature, the higher the concentration factor, the lower is the pH of fresh urine when it is saturated with Mg(OH)₂ (Figure 4B). Only when >98% of the water is removed from urine, i.e., concentration factors above 60, the minerals arcanite and halite are predicted to precipitate (Figure 5).

The solubility of Mg(OH)₂ in real fresh urine at 23 ± 2°C was measured to be between 495 mg L⁻¹ (FU₁) and 940 mg L⁻¹ (FU₂), varying with urine composition (Figure 6). According to the mass balance (Supplementary Figure S2), 60% (±2) of the total ammonia initially present in fresh urine, which accounted for 10% (±5%) of the total nitrogen, precipitated when the urine was saturated with Mg(OH)₂. In addition, 94% (±3) of the total phosphorus, 69% (±23) of the calcium, and 55% (±9) of the sulphur also precipitated. The solubility of Mg(OH)₂ in real fresh urine increased when the urine was concentrated by evaporation (Figure 5). At CF = 8, the solubility was 3,980 mg L⁻¹ or about seven times higher than the solubility in unconcentrated fresh urine, whereas the pH of urine decreased from 10.6 to 9.8. The relative increase in Mg(OH)₂ solubility for concentrated fresh synthetic urine was lower than the relative increase in solubility for real urine. The pH of synthetic fresh urine saturated with Mg(OH)₂ was >11, but the pH dropped to 10.3 (±0.1) at CF=16 (Supplementary Figure S3).

The deviation between the Mg(OH)₂ solubility determined in experiments and the thermodynamic simulations were less than 5% (Figure 6), suggesting that the thermodynamic model accurately predicted the chemical speciation in urine. In fact, the experimentally measured EC in urine and the simulated Mg(OH)₂ solubility curve had the same trend–increasing at first, then decreasing, and finally equilibrating. In comparison to real fresh urine, the solubility of Mg(OH)₂ at 23 ± 2 °C was less in synthetic (393 ± 180 mg L⁻¹) and dephosphatised synthetic urine (452 ± 126 mg L⁻¹), and the deviation between the simulated and experimental values was much larger (>28%).

By matching the experimentally determined pH with the thermodynamically simulated pH of urine, we could also simulate the kinetics of Mg(OH)₂ dissolution. We found that it took between 6 and 16 min for brucite (Mg(OH)₂) to dissolve (Figure 7), which compares well with the time required for the pH to increase to >10 (Figure 8) and EC to equilibrate (Supplementary Figure S4). In addition to brucite, struvite and hydroxyapatite were the only two minerals predicted to form. All the urine solutions were supersaturated with respect to struvite in 10 min, while hydroxyapatite supersaturation required less than 2 min. It is likely that both the minerals precipitated in 15 min as the change in EC of urine is less than 5% after this (Supplementary Figure S4).

In experiments, after 60 min of mixing at 700 rpm, the pH of real fresh urine treated with Mg(OHJ₂ reached >10.5 (Figure 8A) and remained stable during 14 days of storage in a closed flask (Figure 1). To reach pH 10, the average time required was 8.9 ± 5.7 min. Increasing the urine concentration factor reduced the pH but increased the time required to achieve saturation (Table 2). The Mg(OH)₂ dissolution kinetics in both fresh urine and concentrated fresh urine was well described (R ² = >0.99 and ΔpH = <5%) by the pseudo-second order rate equation (Figures 8A,B) (Table 2). Similar trends were seen when the experiments were repeated with synthetic fresh urine and synthetic concentrated urine, although the pH of urine was higher, and the time required to reach equilibrium was less in comparison to real fresh urine.

The results of our study demonstrated that Mg(OH)₂, an alkaline Earth metal compound, is sparingly soluble in freshly excreted human urine. Despite a low solubility of < 1 g Mg(OH)₂ L⁻¹ at 25°C, fresh urine saturated with Mg(OH)₂ has pH > 10.5, which we also demonstrated as being sufficient alkalinity to inhibit the enzymatic degradation of urea (Figure 1). Yet, many factors determine the solubility of this compound in human urine. First, fresh urine with different compositions had different solubilities. According to descriptive principal component analysis, it is the concentration of magnesium (R ²=0.95; p < 0.0001) and phosphate (R ²=0.93; p < 0.0001) and to a lesser extent calcium (R ²=0.89; p < 0.001) and total ammonia (R ²=0.88; p < 0.001) that is initially present in urine that explain this variability (>94% of total variance) and has the largest influence on Mg(OH)₂ solubility (Supplementary Figure S5). This is apparent because Mg(OH)₂ solubility is a direct reflection of the concentration of Mg²⁺(aq) (Eq. 1), which is influenced by the concentration of Mg²⁺ removed from urine as a precipitate (Figure 2).

Secondly, the solubility is retrograde with respect to the temperature of urine, increasing significantly at lower temperatures (R ²=0.97; p < 0.001). The hydration of MgO(s) is exothermic, with reaction enthalpy of −81 kJ mol⁻¹ (Kato et al., 1996). The dissolution of Mg(OH)₂ is also exothermic, with solution enthalpy of −152 kJ mol⁻¹ (Tahiri et al., 2003). The overall enthalpy change is about eight times more if urine is dosed with CaO (Long et al., 2017) as the solubility of Ca(OH)₂ in fresh urine is 5 g L⁻¹ at 25°C (Randall et al., 2016). Due to the low solubility of Mg(OH)₂, the temperature of urine dosed with 2 g MgO L⁻¹ and kept in an uninsulated flask increases by just 2°C over 60 min (Supplementary Figure S6). The rate of increase in the urine temperature depends on the hydration kinetics of MgO and the dissolution kinetics of Mg(OH)₂. According to Kato et al. (1996), the hydration of MgO involves rapid physical adsorption of water to produce an intermediate (MgOH₂O), followed by chemical hydration which is the rate-controlling process. A fraction of MgO remains inert to hydration because of sintering during calcination (Strydom et al., 2005).

Thirdly, we found a large effect on solubility from organic substances present in urine. On average, the solubility of Mg(OH)₂ was 40% lower in synthetic fresh urine than in real fresh urine. The synthetic urine that we prepared contained only urea, which has no COD (Li et al., 2012), whereas in real human urine, the concentration of organic substances is about 10 g COD L⁻¹ (Udert et al., 2006) and there can be hundreds of metabolic breakdown products (Bouatra et al., 2013). Organic compounds in urine also have pH-dependent solubility. Increasing the pH of urine from < 7 to >10 increases the solubility of creatinine but decreases the solubility of uric acid. We also know that some organic substances in urine co-precipitate by adhesion to mineral colloids and that the sediment at the bottom of tanks storing hydrolysed urine contain 0.39–0.65 g VS. g TS⁻¹ (Höglund et al., 2000). On the other hand, Curtin et al. (2016) showed that solubility and degradation of organic matter increases when soil is treated with Ca(OH)₂. It seems that the presence and/or degradation of organic substances and the change in their solubility also affects the solubility of Mg(OH)₂ in urine.

Lastly, we found that the more concentrated the urine, the higher is the solubility of Mg(OH)₂. However, the relative increase in the Mg(OH)₂ solubility is lower at a higher concentration factor, as is the pH of the urine saturated with Mg(OH)₂. Increasing the temperature reduces the pH of urine further. For instance, at 50°C and concentration factor of 16, the pH of urine saturated with Mg(OH)₂ drops to < 9. To increase the urine pH to ≥10 and prevent ureolysis, the temperature must be < 30°C at CF=1 and < 22°C at CF=16, respectively (Supplementary Figure S7). In contrast, the solubility of Ca(OH)₂ and the pH of urine increase with concentration factor since soluble sulphate in urine precipitates as gypsum at CF < 60 and anhydrite at CF > 60. In contrast, no ammonia nitrogen can be recovered when fresh urine is alkalised using Ca(OH)₂ (Riechmann et al., 2021), since all of the phosphate in urine precipitates as hydroxyapatite (Ca₁₀(PO₄)₆(OH)₂) (Randall et al., 2016). At CF > 100 or when 99% water is removed from urine dosed with Mg(OH)₂, the fraction of soluble phosphate in urine that is precipitated as struvite increases and hydroxyapatite decreases (Supplementary Figure S8). This suggests that there is higher potential to recover ammonia nitrogen excreted in fresh urine as struvite at high concentration factors. Depending on the composition of urine, between 22 and 100% of the ammonia nitrogen can be recovered as struvite when fresh urine is alkalised using Mg(OH)₂ (Figure 9).