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Fig. 3 Pressure equilibration timescales of double emulsion droplets.a Sketch showing a double emulsion droplet of initial inner pressure and volume (or radius ) and initial oil volume , reducing its volume to the equilibrium values over a timescale . b Inner droplet volume relaxation (normalized to the initial volume ) for double emulsion droplets of different initial sizes: = 37.9 ± 0.7 µm (green, N = 20); = 27.3 ± 0.4 µm (red, N = 20); = 20.9 ± 0.3 µm (blue, N = 47). Initial PEG concentration (5% w/w) and fixed . Mean ± SD (represented by an error band). Black lines are exponential fits to the data (Methods). c–f, Dependence of the measured equilibrium relaxation timescale, , on the initial inner droplet size, (c initial PEG concentration (5% w/w) and fixed ; N = 20 (green), 20 (red), 47 (blue) droplets), the initial internal pressure, (d fixed and , N = 13 (5% w/w),18 (10% w/w), and 20 (20% w/w) droplets), the externally imposed osmolarity, (e initial PEG concentration (5% w/w) and fixed , N = 11 (0.25 MPa), 15 (0.5 MPa), 12 (0.75 MPa), 14 (1.5 MPa) and 16 (5.0 MPa) droplets), and the initial oil volume fraction, (f initial PEG concentration (10% w/w), fixed and ; N = 10 droplets), with being the initial total droplet volume. Inset in (f) shows z-x imaging plane of a droplet relaxing to the equilibrium state (fluorocarbon oil, cyan; fluorescent PEG, purple). Continuous blue lines in d and e are fits to the data with the form: . Scale bar, 25 µm. Mean ± SD for c–e. Mean ± error from exponential fit for f. Source data are provided as a Source Data file.