## 3 Results
### Nanofluid Stability  
Despite the good prospects of TiO\({}_{2}\)-based nanofluids reported in the literature to enhance the thermal properties of the base fluid, these nanoparticles tend to agglomerate probably due to their strong van der Waals and gravity [30]. Thus, the effect of one anionic surfactant (PSS), two cationic surfactants (PEI, CTAB), and one non-ionic surfactant (PVP) on the stability of a 0.50 wt% A-TiO\({}_{2}\)/PG:W 30:70 nanofluid at a 1:2 surfactant-to-nanodditive mass ratio was observed. The nanoadditives with PVP in the 0.50 wt% A-TiO\({}_{2}\)/PG:W 30:70 nanofluid precipitated almost immediately after preparation, leading to the exclusion of this surfactant for the proposed nanofluids. The remaining nanosized dispersions stabilized with PEI, PSS, and CTAB were observed over 7 days under static conditions. Figure 4 represents the three different nanofluids just after preparation and after the 7-day observation period. It was noted that the nanoadditives with CTAB in the 0.50 wt% A-TiO\({}_{2}\)/PG:W 30:70 nanofluid precipitated during the observation period, while the PEI and PSS surfactants maintained the particles in suspension. Thus, the stability of A-TiO\({}_{2}\)/PG:W 30:70 + PEI and A-TiO\({}_{2}\)/PG:W 30:70 + PSS nanofluids was evaluated by analysing the changes in their apparent size distribution through DLS during 25 days under both static and shaken conditions for different surfactant-nanoadditive mass ratios namely 1:1, 1:2, 1:3, and 1:4, as depicted in Figure 5. A-TiO\({}_{2}\)/PG:W 30:70 nanofluids without surfactant were monodisperse (one single narrow peak) after the preparation (Figure 5a). In contrast, the addition of surfactants caused the samples to become polydisperse, evolving to bimodal and trimodal distributions after preparation, except for the PEI:nanoadditive mass ratios of 1:1 and 1:2 (Figure 5b,d). A shift in the main peak from \(\sim\)1860 nm to smaller apparent sizes (between \(\sim\)1024 and \(\sim\)633 nm for PEI and  
Figure 3: XRD pattern of A-TiO\({}_{2}\) nanopowder, with the most representative crystalline planes for the identified space group I4I/amd. between \(\sim\)771 and \(\sim\)689 nm for PSS) was also observed (Figure 5b-i), which may indicate a reduction in the agglomeration of the A-TiO\({}_{2}\) nanoparticles. After 25 days, the sample without surfactant decreased in apparent size and showed a bimodal distribution with one narrow peak around \(\sim\)0.6 nm and another peak around \(\sim\)5400 nm in static conditions, which indicates complete sedimentation of the nanopowder. Likewise, the samples with PEI and PSS revealed lower apparent sizes in static conditions but only up to \(\sim\)140 nm and \(\sim\)120 nm, respectively. All A-TiO\({}_{2}\)/PG:W 30:70 + PEI nanofluids at the analysed surfactant-nanoadditive mass ratios evolved to trimodal distributions in shaken conditions (Figure 5b,d,f,h), whereas A-TiO\({}_{2}\)/PG:W 30:70 + PSS nanofluids showed bimodal and trimodal distributions after 25 days. These results suggest that the addition of PSS provides a more consistent distribution of the nanoparticles suspended in the base fluid compared to PEI and would indirectly provide information about the potential positive charge of the nanoparticle surfaces. Likewise, it is important to note that surface charge densities depend on both the particle size and the pH value, as stated by [PERSON] et al. [31] for TiO\({}_{2}\) nanoparticles, who report that determining size-dependent surface charging is challenging. It was observed that the main peak of the PSS 1:3 mass ratio evolved to higher apparent sizes under shaken conditions after 25 days, suggesting agglomeration of the nanoparticles. Consequently, this mass ratio was disregarded. Regarding PSS 1:2 under shaken conditions, a 12% decrease in the apparent size of the main peak was observed after 25 days compared to the first day. In contrast, PSS 1:1 and PSS 1:4 maintained the same apparent size of \(\sim\)689 and \(\sim\)771 nm, respectively, after 25 days in shaken conditions.