This PDF file includes:

• fig. S1. Fabrication process flow for the radial undercut patterns with TiO₂ and polymer coatings.
  
• fig. S2. SEM images and contact angles of TiO₂ and fluoropolymer-coated surfaces and merely fluoropolymer-coated surfaces.
  
• fig. S3. Optical images of residual liquid on sample B3 after droplet transport.
  
• fig. S4. The outward spreading of an oil droplet of 1 μl on the A1 pattern.
  
• fig. S5. The effect of D and Φ on the driving force for droplet motion.
  
• fig. S6. Self-transportation of water-ethanol mixture droplets of different compositions on sample B3.
  
• fig. S7. Self-transportation of an ethanol droplet on sample A5.
  
• table S1. Geometrical parameters of different patterns and their contact angles, wettability gradients, and breakthrough pressure equations.
  
• table S2. Effect of pattern parameters on droplet speed.
  
• table S3. Effect of liquid type on droplet speed.
  
• Legends for movies S1 to S3

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Other Supplementary Material for this manuscript includes the following:

• movie S1 (.mov format). Demonstration of three modes of oil droplet motion on various sample surfaces.
• movie S2 (.mov format). Self-transportation of ethanol-water mixture droplets with different compositions on sample B3.
  
• movie S3 (.mov format). Self-transportation of an ethanol droplet on sample A5.