## 4 Conclusions  
The PN emissions of three different oil formulations were examined in a 1.0 L gasoline direct injection engine under 15 steady-state load and speed conditions. Unlike most studies that focus on transient driving cycles, this research investigates oil impact on total particulate number (TPN) emissions under stable operating conditions, with particular emphasis on sub-23 nm particles. To simulate the detection efficiency of a condensation particle counter, two digital filters were applied to the raw PN data from a DMS500. F1-PN > 23 had a detection efficiency of d50 = 23 nm and d90 = 41 nm, while F3-PN > 10 had a detection efficiency of d50 = 10 nm and d90 = 15 nm. The three tested oil formulations included a mid-ash baseline, a low-ash low-volatility (LoLo) formulation, and a high-ash high-volatility (HiHi) formulation. The main findings included:  
* Depending on the condition, the baseline oil exhibited higher PN emissions with both digital filters, except at low loads. LoLo generally produced the lowest PN. Using the weighted arithmetic mean, HiHi had a higher F1-PN > 23 than LoLo by 9.7%, while F3-PN > 10 was higher by 3.6%.
* Over the full test matrix, a three-way ANOVA analysis revealed that load and speed were the dominant factors influencing TPN emissions. However, under specific conditions, the impact of oil on particulates is still clear and relevant.
* Particle size distributions (PSDs) and filtered PNs showed that HiHi had a higher sub-23 nm fraction than LoLo due to its greater volatile content. All PSD nucleation modes were observed around 8-12 nm, confirming that most emissions were in the sub-23 nm region.
* Oil formulation did not significantly impact the nucleation mode diameter of PSDs, as no lateral shift in the distributions was observed. However, nucleation modes shifted to larger diameters when the catalytic stripper was used, as it effectively removed volatile particles in the 5-10 nm region.  
In conclusion, this study highlights the critical need for further research on oil-related particulate emissions under steady-state conditions, particularly for sub-23 nm particles, as upcoming Euro 7 regulations tighten measurement thresholds to 10 nm, and emphasises the importance of exploring non-carbon fuels like ammonia (NH\({}_{3}\)) or hydrogen (H\({}_{2}\)) to fully understand the real impact of oils on particulate emissions.  
Conceptualization, S.A.P.; methodology, S.A.P.; software, S.A.P.; investigation, S.A.P. and E.H.-S.; data curation, S.A.P.; formal analysis, S.A.P. and S.L.; validation, S.A.P. and S.L.; visualization, S.A.P. and S.L.; writing--original draft, S.L. and E.H.-S.; writing--review and editing S.L., S.A.P., E.H.-S. and A.L.R.; supervision, A.L.R. and A.C.; funding acquisition, A.L.R. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This work was supported by the Engineering and Physical Sciences Research Council through the scholarship provided by EPSRC for [PERSON] [grant number EP/T517902/1].  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The raw data supporting the conclusions of this article will be made available by the authors on request.  
**Acknowledgments:** The authors thank [PERSON] and [PERSON] for their technical support with the engine setup. The authors further thank Lubrizol Limited for funding and supply of the fuel and lubricating oils.  
**Conflicts of Interest:** The authors declare no conflicts of interest.