The shape of two-dimensional liquid bridges

Abstract

We have studied a single vertical, two-dimensional liquid bridge spanning the gap between two flat, horizontal solid substrates of given wettabilities. For this simple geometry, the Young-Laplace equation can be solved (quasi-)analytically to yield the equilibrium bridge shape under gravity. We establish the range of gap widths (as described by a Bond number Bo) for which the liquid bridge can exist, for given contact angles at the top and bottom substrates (θ t c and θ b c , respectively). In particular, we find that the absolute maximum span of a liquid bridge is four capillary lengths, for θ b c = 180 • and θ t c = 0 • ; whereas for θ b c = 0 • and θ t c = 180 • no bridge can form, for any substrate separation. We also obtain the minimum value of the cross-sectional area of such a liquid bridge, as well as the conditions for the existence and positions of any necks or bulges and inflection points on its surface. This generalises our earlier work in which the gap was assumed to be spanned by a liquid film of zero thickness connecting two menisci at the bottom and top substrates.

Dynamics of two-dimensional liquid bridges

“…We have simulated the motion of a two-dimensional liquid bridge sandwiched between flat horizontal substrates of tunable wettability, using the lattice Boltzmann method. This was validated by comparison with quasi-analytic results for equilibrium (static) bridges [11], and found to be reliable except for Bond numbers very close to the maximum above which an equilibrium bridge breaks.…”

“…where ∆ρ is the density difference between the bridge and the surrounding medium, and F ext is the force applied in the vertical direction (perpendiculat to the substrates). The shape of the right-hand surface bounding the bridge is then [11] x ′ (y…”

“…This paper is organized as follows: in section 2 we describe our general simulation method (2.1), how we implement two-phase flows (2.2), tune the wettabilities of substrates (2.3) and compute the drag force exerted by the moving liquid bridge on the solid substrates (2.4). Our results are presented in section 3: first we validate our method by comparing the shapes it yields for static bridges with the semianalytical solutions of the Young-Laplace equation [11] (3.1); then we establish how the drag force (3.2) and contact angles (3.3) scale with the bridge velocity, for different combinations of Bond numbers and substrate wettabilities; finally, we investigate the stability of many types of bridges (i.e., the maximum velocity needed to break them) (3.4). We conclude in section 4.…”

Capillary Bridges on Hydrophobic Surfaces: Analytical Contact Angle Determination

“…18 Liquid transfer between solid surfaces was also studied 19,20 because of its central role in various printing processes. 21 The capillary force was calculated, and the profile of the liquid bridge was described according to various approaches: finite element methods 14,17 and numerical 16 and (quasi-)analytical solutions 15,22,23 were also applied. The capillary bridge probe method was introduced recently.…”

Решение Задачи О Форме Вертикального Жидкого Моста Между Выпуклыми Поверхностями С Учетом Силы Тяжести

“…В первой из этих работ дается классификация форм мостов, а во второйприводятся их фотографии, полученные в эксперименте. Подробная библиография работ, посвященных решению задач о форме жидких мостов и возможным приложениям этих исследований, приведена в [7].…”