From Scale to Energy:A Semi-Empirical Model for Residue Effects in Combustion

This study originates from a common observation: carbonated beverages like Sprite dissolve limescale (calcium carbonate). This phenomenon sparks an exploration into chemical reactions, abstraction of principles, and their application to energy release in combustion and explosive materials. We propose a semi-empirical model linking residue mass fraction ($r$) to key performance metrics: total energy release ($E$), rise time ($\tau_{\text{rise}}$), impulsiveness ($\Phi$), and instability ($I$). Using an expanded dataset from verified literature (e.g., black powder, smokeless powder, composite propellants), we optimize the model via least-squares fitting. Results confirm a negative correlation between $r$ and $E$, a positive correlation with $I$, and a competitive effect on $\Phi$. Validated through Python-based fitting, the model highlights trade-offs in energy systems, offering insights for engineering design and education. While not a first-principles derivation, it integrates disparate knowledge into a testable framework, demonstrating value in unifying residue impacts across combustion domains.