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Analysis of the shape of a capillary liquid bridge in a gap between large diameter spheres

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Thermophysics and Aeromechanics Aims and scope

Abstract

The results of experimental studies on the properties of a capillary liquid bridge in the gap between two glass spheres of an equal diameter are presented. It is shown that for the case when the diameter of the spheres is much larger than the capillary scale of liquid, the shape of the capillary liquid bridge can be described as a figure formed by two “drops”, touching the spheres, and the central catenoid. The contact angle between the “drop” and the sphere depends on the effective mass of the “drop”, and the relative position of the catenoid and the “drops” is set by the condition that the contact angle between them is equal to zero. In the field of gravity, the position of the minimum cross section of the catenoid does not coincide with the middle of the gap between the spheres and is determined by the magnitude of the surface energy and the way how the mass of liquid in the bridge is distributed over the “drops” and the catenoid.

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Abbreviations

A :

parameter in the catenary equation, m

Bo:

Bond number

D :

diameter of sphere, m

E σ and E g :

surface and potential energy, J

g :

acceleration of gravity, m/s2

H :

value of a gap between the spheres, m

L :

characteristic size, m

M :

mass of liquid layer, kg

r 1 :

radius of minimum cross section of the liquid bridge, m

r L, r m :

azimuth and meridian curvature radii, m

S :

area of the liquid bridge surface, m2

V :

volume of the liquid bridge layer, m3

x :

horizontal coordinate, m

y :

vertical coordinate, m

y* :

base point of reference of the fluid layer height for calculation of Eg, m

y 0 :

vertical coordinate of “drop top”, m

y 1 :

vertical coordinate of minimum cross section, m

δ :

linear scale (Laplace constant), m

θ :

contact angle, degree

ν :

coefficient of kinematic viscosity, m2/s

ρ 1, ρ g :

densities of liquid and gas, kg/m3

σ :

surface tension, N/m

φ :

azimuth angle, degree.

av:

average

b:

bottom

c:

central

u:

upper.

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Authors and Affiliations

  1. Kutateladze Institute of Thermophysics SB RAS, Novosibirsk, Russia

    B. V. Perepelitsa, E. Yu. Sukhorukova & V. V. Ovchinnikov

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  1. B. V. Perepelitsa
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  2. E. Yu. Sukhorukova
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  3. V. V. Ovchinnikov
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Correspondence to B. V. Perepelitsa.

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The research is fulfilled in the framework of the state contract with the IT SB RAS.

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Perepelitsa, B.V., Sukhorukova, E.Y. & Ovchinnikov, V.V. Analysis of the shape of a capillary liquid bridge in a gap between large diameter spheres. Thermophys. Aeromech. 28, 677–687 (2021). https://doi.org/10.1134/S0869864321050085

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  • DOI: https://doi.org/10.1134/S0869864321050085

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