  Deformation of a fluid interface caused by the presence of objects at the
interface can lead to large lateral forces between the objects. We explore
these fluid-mediated attractive force between partially submerged vertical
cylinders. Forces are experimentally measured by slowly separating cylinder
pairs and cylinder triplets after capillary rise is initially established for
cylinders in contact. For cylinder pairs, numerical computations and a
theoretical model are found to be in good agreement with measurements. The
model provides insight into the relative importance of the contributions to the
total force. For small separations, the pressure term dominates, while at large
separations, surface tension becomes more important. A cross-over between the
two regimes occurs at a separation of around half of a capillary length. The
experimentally measured forces between cylinder triplets are also in good
agreement with numerical computations, and we show that pair-wise contributions
account for nearly all of the attractive force between triplets. For cylinders
with equilibrium capillary rise height greater than the height of the cylinder,
we find that the attractive force depends on the height of the cylinders above
the submersion level, which provides a means to create precisely-controlled
tunable cohesive forces between objects deforming a fluid interface.
