**Capillary forces on a small particle at a liquid-vapor interface: Theory
and simulation**

YF Tang and SF Cheng, PHYSICAL REVIEW E, 98, 032802 (2018).

DOI: 10.1103/PhysRevE.98.032802

We study the meniscus on the outside of a small spherical particle with
radius R at a liquid-vapor interface. The liquid is confined in a
cylindrical container with a finite radius L and has a contact angle
pi/2 at the container surface. The center of the particle is placed at
various heights along the central axis of the container. By varying L,
we are able to systematically study the crossover of the meniscus from
nanometer to macroscopic scales. The meniscus rise or depression on the
particle is found to grow as ln(2L/R) when R << L << K-1 with K-1 being
the capillary length and saturate to a value predicted by the Derjaguin-
James formula when R << K-1 << L. The capillary force on the particle
exhibits a linear dependence on the particle's displacement from its
equilibrium position at the interface when the displacement is small.
The associated spring constant is found to be 27 pi gamma ln(-1) (2L/R)
for L << K-1 and saturate to 2 pi gamma ln(-1) (3.7K(-1)/R) for L >>
K-1. At nanometer scales, we perform molecular dynamics simulations of
the described geometry and the results agree well with the predictions
of the macroscopic theory of capillarity. At micrometer to macroscopic
scales, comparison to experiments by Anachkov et al. **Soft Matter 12,
7632 (2016).** shows that the finite span of a liquid-vapor or liquid-
liquid interface needs to be considered to interpret experimental data
collected with L similar to K--(1).

Return to Publications page