Investigation of Single and Binary of “Sandwich” Type Convex Liquid Capillary Bridges, Stretched between Two Flat Surfaces (Experimental Approach)

Plamen V Petkov,Boryan Radoev

doi:10.3390/colloids3040068

Abstract

The interest to monophasic liquid capillary bridges (CB) has a long history. These shapes are attractive not only because of their interesting surface properties but also because of the possibility of their behavior to be analytically predicted by the equations of differential geometry. In the current paper we extend our previous studies by implementation of an approach for prediction of liquid gravityless CB behavior during their quasi-static stretching. It was found, that a simple linear relation, h r m ~ ln R r m , is valid the case of good wetting, 0° ≤ θ ≤ 90°, where h is the height of CB, R is the radius at the contact surface, rm is the CB waist radius, and θ is the solid/liquid (static, receding) contact angle. We experimentally studied the geometrical properties evolution of monophasic cedar oil and water CBs between two glass plates during their quasi-static (stepwise with equilibration after each step for 1–2 min.) stretching. In addition, we investigated a binary CB of a new type, resembling “sandwich”. There, due to the stronger glass wetting by the water, the oil phase is adhered at the water/gas interface, partially engulfed with a tendency to stand in the zone around the waist (minimal surface energy). During the stretching, it tends to replace the water in the CB waist region. A simple mechanism for interaction of the two immiscible liquids leading to creation of “sandwich” like binary structures, is proposed. Experiments of capillary bridges (CB) stretching between two flat surfaces have been carried for all liquids at different volume proportions. The investigation is extended also to identification of CB profile generatrix shape. We experimentally found that for monophasic CB, it can be described by a circle during the quasi-static stretching. If the CB height is increased, before the rupture, the shape evolves consecutively to an ellipse, parabola, or possibly to a hyperbola. The investigated binary CB evolves a similar way. Conclusions are drawn and directions for further investigations are given.

Highlights

The capillary structures that are subject to our analysis belong to a class of axially symmetrical surfaces of constant mean curvature [1]
We experimentally found that for monophasic capillary bridges (CB), it can be described by a circle during the quasi-static stretching
We developed a set of curves for CB constant solid/liquid static receding contact angles, called isogones

Summary

Introduction

The capillary structures that are subject to our analysis belong to a class of axially symmetrical surfaces of constant mean curvature [1]. The elliptic integrals are discussed in computing the lengths of basic plane curves F(φ m) for Bernoulli’s lemniscate and E(φ m) for an ellipse, [3]. Despite their practical importance, the solutions involving linear combination of these integrals always is exposed to problems because of complex relations, resulted from F(φ m) and relation to Jacobian elliptic functions, [4]. According to [4], there are three groups of methods for computing of these integrals: series expansion formulas, implementation of Landen transformations, and methods using duplication theorems. All of these methods have their advantages and disadvantages. It was presented in detail in [5]

Methods

Results

Discussion

Conclusion