Surface-area to volume (S/V) has central place in STEM syllabuses, explaining the relation between structure and function governed by the heat equation, such as in diffusion and heat transfer by conduction. However, teaching the abstract S/V quotient faces many difficulties, due to the need for high reasoning abilities and visual-spatial skills. Surprisingly, an exploratory survey among 64 high school biology teachers revealed that 12.5% of them teach the relation between structure and function in diffusion by one dimensional, tangible, quotient free, explanation: small and non-spherical structure results in short diffusion length, which results in fast diffusion. Those teachers tend to hold higher academic degree (p= 0.002) and be more experienced (p=0.045). A plausible explanation for the limited usage in the 'diffusion length' model may be the lack of mathematical framework and graphical illustration to support it. Here I link the diffusion length, volume (V) and surface-area (S) and show that the average diffusion length = 3V/S and present an illustration of V/S. Therefore, the small, non-spherical shapes of structures adopted for fast diffusion can be equivalently explained by the short diffusion length in these structures. Having the necessary mathematical framework and graphical illustration should help other teachers adopt this simple explanation.
Analysis of dengue model with fractal-fractional Caputo–Fabrizio operator
