  We investigate two-dimensional liquid bridges trapped between pairs of
identical horizontal cylinders. The cylinders support forces due to surface
tension and hydrostatic pressure which balance the weight of the liquid. The
shape of the liquid bridge is determined by analytically solving the nonlinear
Laplace-Young equation. Parameters that maximize the trapping capacity (defined
as the cross-sectional area of the liquid bridge) are then determined. The
results show that these parameters can be approximated with simple
relationships when the radius of the cylinders is small compared to the
capillary length. For such small cylinders, liquid bridges with the largest
cross sectional area occur when the centre-to-centre distance between the
cylinders is approximately twice the capillary length. The maximum trapping
capacity for a pair of cylinders at a given separation is linearly related to
the separation when it is small compared to the capillary length. The meniscus
slope angle of the largest liquid bridge produced in this regime is also a
linear function of the separation. We additionally derive approximate solutions
for the profile of a liquid bridge making use of the linearized Laplace-Young
equation. These solutions analytically verify the above relationships obtained
for the maximization of the trapping capacity.
