Fig. 5.

Bending and branching does not affect the resistance $K$ and scalar exchange efficiency $\mathcal{E}$ significantly. Shown are the prefactors $C_K$ (orange) and $C_{\mathcal{E}}$ (blue) of (Left) bent and (Right) branched shapes normalized to the respective values for the corresponding rectangular shape with sides $a$ and $b$ as a function of its aspect ratio $a/b$. $C_K$ follows from a numerical solution of Eq. 1, while $C_{\mathcal{E}}$ has been calculated from Eq. 4 using the first 16 eigenmodes of Eq. 5 as described in SI Appendix. Parameters are given in Table 2, and the dashed blue line in Right shows $C_{\mathcal{E}}$ for channels that are elongated by a factor of $100$, emphasizing the influence of the junction in longer channels.