Figure 3.

Flow-limited and diffusion-limited regimes in the presence of metabolism. The curves show for all four specimens the location where flow-limited and diffusion-limited regimes balance (which we define by Da⁻¹ = F/G), as a function of the non-dimensional uptake parameter $\mathcal{U}$. For weak uptake ($\mathcal{U}\ll 1$), Da⁻¹ ≈ 1; for strong uptake ($\mathcal{U}\gg 1$), ${\text{Da}}^{-1}\approx \mathcal{U}$. The boundary between flow-limited and diffusion-limited regimes should be understood as a smooth transition, indicating where contributions of both regimes are of comparable strength. The curves for all four specimens collapse appreciably. The inset illustrates how, when uptake is weak, the boundary between flow- and diffusion-limited uptake is approximated more precisely by ${\text{Da}}^{-1}\approx 1+\mathcal{W}$ (dashed line), highlighting $\mathcal{W}$ as a significant dimensionless measure of uptake in this regime. Geometric parameters are reported in table 3. (Online version in colour.)