Shape and stability of doubly connected axisymmetric free surfaces in a cylindrical container

Slobozhanin, Lev A.; Alexander, J. Iwan D.; Fedoseyev, A. I.

doi:10.1063/1.870230

Cited by 31 publications

(8 citation statements)

References 13 publications

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“…As the curve OK is crossed, not only do the annular solutions have a higher energy, but at some contact angle above the curve OK, the annular solutions become unstable to small perturbations. This linear stability at contact angles above the curve OK was shown by Slobozhanin et al 3 When solving for the curve IK, it is also found that for at least some region to the right of IK ͑and necessarily left of JH͒ annular solutions of energies greater than plug energies are stable to small perturbations. Similarly, nonsymmetric droplets are found to be stable to small perturbations in all cases examined to the right of CK that are not on the segment CEF of the maximum volume curve for the nonsymmetric solution.…”

Section: -7mentioning

confidence: 77%

“…Clearly, for some larger perturbation, the annular distribution of fluid will change to the minimum energy state. Linear stability is addressed by Slobozhanin et al 3 The energies of the annular solutions are presented in Fig. 8 for contact angles from =0°͑bottommost line͒ to = 170°͑uppermost line͒ in steps of 10°.…”

Section: B Annulusmentioning

confidence: 99%

“…2 Historically an axisymmetric plug and axisymmetric annulur solutions have been studied, such as to evaluate the linear stability of the solutions. 3 Now a three-dimensional analysis of the relative energies of solutions for all contact angles is possible. As illustrated in Fig.…”

Section: Introductionmentioning

confidence: 99%

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Zero-gravity liquid-vapor interfaces in circular cylinders

2006

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The zero-gravity problems of a liquid volume sealing a circular tube of gas and a gaseous volume in a circular tube of liquid both involve one phase obstructing another. The two problems differ only in contact angle. From pulmonary research there is a history of axisymmetric analyses for liquid droplets in circular tubes of gas. These analyses consider only axisymmetric solutions-an annulus and an axisymmetric plug. Only recently have nonsymmetric solutions for nonzero contact angle wetting liquids ͑0°-90°contact angle͒ been realized by the authors with the use of the Surface Evolver code. Similar to the problem of droplets in a gas filled tube, a bubble in a liquid-filled tube is of interest to the commercial satellite industry and in vascular physiology. Further analysis by the authors now fills in the other half of contact angle range, i.e., either a nonwetting liquid in a tube of gas ͑contact angles of 90°-180°͒, or equivalently, a gaseous bubble in a liquid that wets the tube wall. Conditions for the existence and stability of solutions of three topologies are examined.

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Section: -7mentioning

confidence: 77%

Section: B Annulusmentioning

confidence: 99%

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Zero-gravity liquid-vapor interfaces in circular cylinders

2006

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“…This has been investigated, in the absence of gravity, for the trapping between pairs of vertical plates [22,23], spheres [24] and solid objects with other geometries [25]. The work by Slobozhanin et al [26] on the stability of a liquid trapped inside a solid cylinder is an example of an analysis taking gravity into account. The stability analysis was not a focus of this paper and a comprehensive account of this subject can be found in reference [27].…”

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confidence: 99%

Maximal liquid bridges between horizontal cylinders

2016

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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.

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“…The liquid containment in microgravity presents a special problem: ordinary open containers such as cups simply do not work, as without gravity they are difficult to drain and tend to leave stray fluid volumes (Thulasiram et al 1992;Mittelmann & Zhu 1996;Concus & Finn 1998;Slobozhanin et al 1999). Contact processes involving droplets are even more problematic in microgravity, as gravity is routinely assumed for phase separations (cf.…”

Section: Introductionmentioning

confidence: 99%

Microgravity/microscale double-helical fluid containment

May

Lowry

2008

Proc. R. Soc. A.

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Double-helical containment is a novel approach to open containment in microgravity (or at microscale). In contrast to axisymmetric containers, there is no length restriction on properly designed double-helical containers. Use of a double helix permits drainage to zero volume, an uncommon feature in microgravity; near-complete drainage is a key feature for any practically useful container. The fact that double-helical containers are open and tubular makes possible a broad range of applications that rely on accessible fluids.The double-helical fluid containment and the stability of such volumes are examined in detail. Helical supports permit filamentary containers of infinite extent, but only doublehelical containers are stable down to zero volume. The base case of symmetric supports (separation angle 1808) is considered in terms of symmetric volumes as well as asymmetric helicatenoid volumes. The distinct symmetric and asymmetric cases are then related by perturbing the angle of separation between the supports. The helicatenoid volumes may combine to form a dual helicatenoid volume. The dual helicatenoid is interesting in that it permits multiphase tube-like geometries.Double-helical behaviours such as drainability are found to vanish at a critical separation angle 246.488. With larger separation angles, double-helical containers behave like single-helical containers (3608), due to the dominance of the longer-span interface. A second shift in behaviour occurs at the limit angle 209.128, where the regions of stability including the cylinder and the helicatenoids become more connected. The common structures of DNA appear to coincide with the limiting geometry at 209.128. The most robust double-helical containers are therefore those with separation angles between approximately 2108 and 2408. Experimental results roughly verify the volume maximum for near-symmetry, and more importantly verify stability to zero volume.

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Shape and stability of doubly connected axisymmetric free surfaces in a cylindrical container

Cited by 31 publications

References 13 publications

Zero-gravity liquid-vapor interfaces in circular cylinders

Zero-gravity liquid-vapor interfaces in circular cylinders

Maximal liquid bridges between horizontal cylinders

Microgravity/microscale double-helical fluid containment

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