Very-Long-Range Nature of Capillary Interactions in Liquid Films

Micron-sized objects confined in thin liquid films interact through forces mediated by the deformed liquid-air interface. These capillary interactions provide a powerful driving mechanism for the self-assembly of ordered structures such as photonic materials or protein crystals. We demonstrate how optical micro-manipulation allows the direct measurement of capillary interactions between mesoscopic objects. The force falls off as an inverse power law in particles separation. We derive and validate an explicit expression for this exponent whose magnitude is mainly governed by particle size. For micron-sized objects we found an exponent close to, but smaller than 1, making capillary interactions a unique example of strong and very long ranged forces in the mesoscopic world.

Figure 1

Wetting geometry. The liquid film wraps the particle inside a spherical cap of radius $r_c$. For $r>r_c$ the liquid-air interface is freestanding and slowly falls to the large distance height $h$. The local height of the interface measured from $h$ is indicated by the function $\zeta (r)$, whose gradients are assumed to be small everywhere (${\psi }_c\ll 1$).

Figure 2

Schematic view of the experimental setup described in text.

Figure 3

Film thickness profile around an isolated particle. (b) Monochromatic light reflected off the film displays interference fringes centered around an isolated trapped particle. A period in the fringe pattern corresponds to 240 nm thickness variation. (a) Film height $\zeta (r)$ versus distance from particle center $r$ (open circles), red line is a logarithmic fit.

Figure 4

Capillary force law. (a) Open circles are experimental determinations and black solid line represents a fit to the predicted power law (12). Red dashed line is the full Kralchewsky theory. (b) Same plot on a double-log scale. A $1/s$ law is added for reference, as a black dashed line.