Empirical prediction of maximum spreading factor of diesel/n-butanol droplets impacting heated substrates

This study experimentally investigates the maximum spreading behaviour of diesel/n-butanol binary fuel droplets impacting a heated substrate. The effects of n-butanol volume fraction, Weber number ( We = 13–66) and substrate temperature ( T w = 25–350 ℃) on droplet spreading behaviour are systematically analysed using high-speed imaging. The results show that the maximum spreading factor β max increases with increasing Weber number, indicating the dominant role of impact inertia during the spreading process. The addition of n-butanol enhances the early-stage spreading tendency by reducing surface tension, while the variation of fuel volatility and thermophysical properties may influence the spreading behaviour under elevated-temperature conditions. Accordingly, the spreading behaviour is further characterised by considering the combined influences of impact inertia and substrate temperature. A temperature-dependent empirical correlation incorporating the dimensionless temperature T* and Weber number is proposed to predict β max . The proposed correlation is established based on D80B20 droplets under the investigated conditions ( We = 13–66, T* =0–1.17), and the maximum deviation between predicted and experimental values is 5.28 %. Comparison with selected literature data shows relative errors within 8.7 %, indicating good consistency between the correlation and reported experimental results. These findings provide a reference for predicting β max of diesel/n-butanol (specifically D80B20) droplets under similar heated-wall conditions.