Structure of adhesive pad cuticle and model for fluid secretion. (a) SEM image of a freeze-fractured Nauphoeta cinerea arolium showing the branched fibrous structure of the procuticle (IRL, inner rod layer; ORL, outer rod layer; EP, epicuticle). (b) Schematic of the discrete-step compartmental model, which includes a storage volume V, a steady influx Q and an efflux (footprint deposition) that linearly depends on volume and step frequency. The dotted arrow shows a hypothesized positive effect of step frequency on influx rate (not confirmed by our experiments); the solid arrow indicates an overflow feedback mechanism limiting the influx when the storage volume is full. The model predicts an exponential decay of droplet volume down to a non-zero steady state (see appendix A).