Maximal liquid bridges between horizontal cylinders

Abstract

We investigate two-dimensional liquid bridges trapped between pairs of identical horizontal cylinders. The cylinders support forces owing to surface tension and hydrostatic pressure that 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 with 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 with 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, using the linearized Laplace–Young equation. These solutions analytically verify the above-mentioned relationships obtained for the maximization of the trapping capacity.

Numerical study of the formation and drying kinetics of a capillary bridge of trehalose solution between two parallel hydrophilic fibres

“…Eq. 26 where the contact angle ( ) of liquid on fibre was set to and the distance of two fibres ( ) was 1 . The diameter of fibre is 3 .…”

“…Since Young studied the surface tension of the capillary bridge in 1805 16 , much work has been done to investigate the shape and stability of capillary bridges between surfaces with differences in wettability, rugosity and geometry, principally focusing on spherical particles [17][18][19][20][21][22][23][24][25] . Less attention has been paid to the capillary bridge in fibre matrices and the majority of these studies have analysed the wetting morphologies experimentally 8,[26][27][28][29] . Boulogen et al 30 presented experimental results on the evaluation of the viscous liquid evaporation at the cross point of two nylon fibres aligned with different angles (column, drop and mixed) and compared the evaporation rate with a simplified predication.…”

“…Capillary bridge structure in fibre matrices determines the wetting, the degree of liquid retention and the drying rate 26,31 . The bridge geometry is a principle parameter in the drying dynamic defining either the break point or solidification point.…”