Direct Measurement of Capillary Attraction between Floating Disks

Two bodies resting at a fluid interface may interact laterally due to the surface deformations they induce. Here we use an applied magnetic force to perform direct measurements of the capillary attraction force between centimetric disks floating at an air-water interface. We compare our measurements to numerical simulations that take into account the disk’s vertical displacement and spontaneous tilt, showing that both effects are necessary to describe the attraction force for short distances. We characterize the dependence of the attraction force on the disk mass, diameter, and relative spacing, and develop a scaling law that captures the observed dependence of the capillary force on the experimental parameters.

Figure 1

(a) Schematics of the experimental setup for direct measurements of the attraction force between floating disks. Relevant forces which lead to vertical equilibrium (floating) are highlighted on the disk on the right. The capillary attraction force ${\overrightarrow{F}}_x$, which is balanced by the imposed magnetic force ${\overrightarrow{F}}_M$, is depicted on the disk on the left. (b) Photograph of two disks in the experimental apparatus as they deform the free surface and attract one another. See the video in Supplemental Material for a typical experimental run [46].

Figure 2

(a) Capillary attraction force $F_x$ vs distance $d$ between disks as measured in experiments and compared to numerical simulations. Disks have radius $R=1.0\mathrm{cm}$ and mass $m=0.90\mathrm{g}$. Inset: Schematic of the geometrical configuration considered in the numerical simulations. (b) Side view of disks at $d=0$ (top) and $d=0.78\mathrm{cm}$ (bottom) demonstrating presence of inward tilt for $d=0$. $\alpha =1.22°$ inward tilt is numerically predicted for $d=0$, as indicated by the red dashed line.

Figure 3

Ensemble of experimental (points) and numerical (lines) data for pairs of disks with different mass $m$ and radius $R$. (a) Dimensional capillary force $F_x$ vs distance $d$ between disks. (b) Dimensionless capillary force $F_x/F_0$ vs dimensionless distance between the disks $d/l_c$. $F_0$ is defined in Eq. (13).