Magnetic manipulation of diamagnetic droplet on slippery liquid-infused porous surface

Magnetic control is a feasible way to manipulate droplets in various applications. For actuating nonferromagnetic droplets, embedded magnetic particles or marbles that contact the droplet directly have been widely used; however, such strategies tend to result in departure, substrate contamination, and infection of biological samples. Herein we propose a portable and noncontact method for magnetic manipulation of water droplets on slippery liquid-infused porous surfaces by a single magnet. The migration velocity of the water droplet reaches 1 mm/s, which correlates positively with the droplet volume and negatively with the viscosity of the lubricating oils. The effects of droplet volume, viscosity of lubricating oil, and vertical spacing on the critical migration velocity of water droplet are investigated. Combined with experiments, numerical simulations, and theoretical analysis, the migration mechanism of the droplet is analyzed thoroughly. In addition, this method exhibits great potential for transporting low-surface-tension fluids, bubbles, and magnetic nanofluids. The present findings offer potential benefits for the design and application in droplet microfluidics.

Figure 1

Schematic of the experimental setup of the migration of water droplet actuated by magnet.

Figure 2

(a) Migration of 10-μl water droplet driven by the uniform moving magnet under vertical spacing $h=1.2\mathrm{mm}$. The contact angle of droplet is 100° and the wet radius is 1.56 mm; $t=0–5\mathrm{s}$: the droplet remains stationary ($a=6.24\mathrm{mm}$), $t=5–12\mathrm{s}$: the droplet accelerates and the horizontal spacing reduces from 5.18 to 4.28 mm, $t=12–24\mathrm{s}$: the droplet remains in relative motion with the magnet, $a=4.30\mathrm{mm}$, as seen in Supplemental Material Movie S1 [28]. (b) Real-time positions of the magnet and droplet during the motions. (c) Relations of the relative horizontal spacing and moving speed of magnet with respect to droplet volume and vertical spacing.

Figure 3

(a) Critical migration velocity of water droplet as functions of vertical spacing between droplet and SLIPS. The insets donate the cases that the vertical spacing between droplet and magnet is a1: $h=0.5\mathrm{mm}$; a2: $h=1.64\mathrm{mm}$ and a3: $h=2.4\mathrm{mm}$. The symbol θ represents the angle between magnetic force and horizontal plane. The dash lines are magnetic flux generated by magnet. (b) Relations of the critical migration velocity of water droplet to the square of droplet radius under various vertical spacings and viscosity of lubricating oil. The slopes of the plotted lines are around 0.05.

Figure 4

(a) Dimensionless migration velocity of water droplet as functions of magnetic driving force when the wetting ridge is ignored. (b)–(d) Correction process of the nondimensioned magnetic driving force acting on water droplet and wetting ridge under vertical spacing $h=0.5$, 1.2, and 2.4 mm. The hollow and solid symbols represent data ignoring and considering the wetting ridge respectively. The symbols are measured in experiments and the dash line represents linear fits using the Levenberg-Marquardt algorithm. The magnetic force distributions are calculated under corresponding vertical spacings and magnet velocity $U_{\mathrm{mag}}=0.2\mathrm{mm}/\mathrm{s}$.

Figure 5

(a) Migration of a 5-μl SDS water droplet actuated by a magnet moving at a velocity of 0.1 mm/s. The scale bar in the figure is 1 mm (see Supplemental Material Movie S3 [28]). (b) Dimensionless migration velocity of SDS water droplet as functions of magnetic driving force under various vertical spacings and droplet volumes. The symbols are measured in experiments and the dash line represents linear fits using the Levenberg-Marquardt algorithm. The inset donates the experimental observations of the outline of a 5-μl DI water and SDS water droplet and its corresponding wetting ridge.

Figure 6

Migration of (a) water droplet on slightly titled surface, (b) the magnetic droplet, and (c) bubble actuated by magnet. The sliding angle of SLIPS beneath DI water is 2°. The magnetic droplet used here is the water droplet with ${\mathrm{Fe}}_3{\mathrm{O}}_4$ 10-nm nanoparticles with concentration of 4 mg/ml. The moving velocity of magnet is 0.1 mm/s for DI water and magnet droplet while it is 0.05 mm/s for bubble. The scale bar in figure is 1 mm.

Figure 7

(a) SEM imagine of the micronanoscale structures of copper surface. (b) Wetting status of water droplet on PTFE coated surface. (c) Wetting status of water droplet on oil impregnated SLIPS. (d)–(f) Sliding behavior of a water droplet on an inclined SLIPS surface.

Figure 8

Schematic diagram of geometric model adopted in simulations. The dimensioned unit is in millimeters.

Figure 9

(a) Comparison of the magnetic flux intensity along the axis of magnet measured by gaussmeter and numerical results. (b) The surrounding magnetic flux distribution of magnet on the $z$-o-x slice obtained by numerical simulations. (c) The magnetic flux distribution inside water droplet. The arrows indicate the magnetic force induced by magnet.

Figure 10

The outlines of DI water droplet deposited on SLIPS.

Figure 11

Surface morphology of water droplet (a),(b) and SDS water droplet (c),(d) on lubricant-impregnated surface before spraying and after spraying. The scale bar in figure is 0.5 mm.