Fig. 2: Experimental demonstration and numerical simulation of the physical processes underlying DBDR.

a Schematic plot of the sequential change in the supply voltage and pressure required to drive the physical process underlying DBDR. The voltage supply is used to manipulate the bead and the droplet in the reaction chamber. The pressure pulse dispenses a droplet on-demand into the reaction chamber. \({T}_{{ENC}}\) represents the time for which the bead remains encapsulated within the droplet. b A single bead in the vicinity of the electrode is dielectrophoretically trapped by raising the voltage to \({V}_{S} \, \approx \, 40\,{{\rm{V}}}\). c The voltage is lowered, and a pressure pulse is exerted on the microchannel to dispense a single droplet into the reaction chamber. d The pressure pulse is stopped and a voltage \({V}_{{DD}} \, \approx \, 20 \, {{\rm{V}}}\) is applied to trap the generated droplet adjacent to the trapped bead. e (i) Experimental implementation and (ii) numerical electrohydrodynamic phase field simulation depicts the encapsulation of the bead by the droplet under high supply voltage (\({V}_{s}\approx \, 120 \, {{\rm{V}}}\)) and its ejection from the droplet under low supply voltage (\({V}_{s} \, \approx \, 0.1\,{{\rm{V}}}\)). The phase field variable (\({{{{\rm{\phi }}}}}\)) has a value of \(-1\) in the silicone oil suspension medium (phase 1) and a value of \(1\) in the reagent droplet (phase 2). \({{{{\rm{\phi }}}}}\) transitions from \(-1\) to \(1\) at the droplet-medium interface. The bead is represented in white. (iii) Electrocapillary potential energy representation of the engulfing and (iv) ejection process. The frames in e(i) are extracted from Supplementary Movie 1 which was recorded at \(30 \, {{\rm{fps}}}\). The scale bars in these frames represent \(50 \, \upmu {{\rm{m}}}\).