Extended Data Fig. 3: Simulation of magnetic pressure and fine-tuning of the balance between magnetic and capillary pressure to create or conceal the micro-topography of FLIPS.

a, Simulated magnetic field B = μ₀H₀ in free space surrounding a 0.5-inch-tall and 0.5-inch-diameter NdFeB magnet. b, Magnetization curve of ferrofluid 1 (from Ferrotec). The ferrofluid rapidly reaches its saturation magnetization μ₀M_s ≈ 0.04 T. The saturation magnetization is regarded as a linear function of ferrofluid concentration in the following estimate. c, Magnetic pressure of ferrofluid 1 in the region above the magnet. The magnetic pressure (in kPa) can be considered as the magnetic energy density (in kJ m⁻³). Ferrofluid flows from a high pressure (energy) region to a low pressure (energy) region. d, Turning on the micro-topographical response; |p_m| ≈ 10⁴ Pa > 10³ Pa ≈ p_γ. e–g, Turning off the micro-topographical response. e, Response when the ferrofluid is diluted to 4% by volume; |p_m| ≈ 10² Pa < 10³ Pa ≈ p_γ. f, Response using a weaker magnet (Alnico); |p_m| ≈ 10³ Pa ≈ 10³ Pa ≈ p_γ. g, The distance between the repeating units of the microstructure is reduced so that the capillary pressure increases; |p_m| ≈ 10⁴ Pa ≈ 10⁴ Pa ≈ p_γ. The microstructure is pattern 5, which is a hexagonal array of posts of 1.5 μm in diameter and about 10 μm in height. The spacing between posts is 1.4 μm. The bottom panels in d–g show the corresponding 3D profiles of the ferrofluid–air interface near the magnet. Only in d is the interface pulled down towards the bottom of the microstructure.