Droplet-based microfluidics at the femtolitre scaleElectronic supplementary information (ESI) available: S1: mixing inside femtolitre droplets produced by step-emulsification, S2: mixing inside picolitre droplets produced by step-emulsification, S3: dielectrophoretic sorting of femtolitre droplets, S4: electrocoalescence of femtolitre droplets, S5: splitting of femtolitre droplets, S6: parallelized production of femtolitre droplets, S7: reinjection of femtolitre droplets. S8: fabrication of the

We have built a toolbox of modules for droplet-based microfluidic operations on femtolitre volume droplets. We have demonstrated monodisperse production, sorting, coalescence, splitting, mixing, off-chip incubation and re-injection at high frequencies (up to 3 kHz). We describe the constraints and limitations under which satisfactory performances are obtained, and discuss the physics that controls each operation. For some operations, such as internal mixing, we obtained outstanding performances: for instance, in 75 fL droplets the mixing time was 45 μs, 35-fold faster than previously reported for a droplet microreactor. In practice, in all cases, a level of control comparable to nanolitre or picolitre droplet manipulation was obtained despite the 3 to 6 order of magnitude reduction in droplet volume. Remarkably, all the operations were performed using devices made using standard soft-lithography techniques and PDMS rapid prototyping. We show that femtolitre droplets can be used as microreactors for molecular biology with volumes one billion times smaller than conventional microtitre plate wells: in particular, the Polymerase Chain Reaction (PCR) was shown to work efficiently in 20 fL droplets. Standard operations of droplet-based microfluidic were miniaturized down to the femtolitre scale. The level of control is maintained despite the three order of magnitude reduction in droplet volume.