A Floating Cylinder on an Unbounded Bath

Chen, Hanzhe; Siegel, David

doi:10.1007/s00021-018-0372-7

Cited by 4 publications

(6 citation statements)

References 18 publications

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“…The meniscus on a circular cylinder with the radius (figure 2 c ) has been well studied (see e.g. Chen & Siegel 2018), where the relationship between and the height of the centre of the circular cylinder is given by It is noted that (2.7) is also derived from (2.3 b ) and the geometric constraint (2.4). Thus, (2.7) is equivalent to (2.5) for a circular cylinder.…”

Section: Multiple Possible Menisci and Their Stabilitiesmentioning

confidence: 99%

“…After determining the equilibrium positions, their stabilities can be investigated by the sign of the slope of : the equilibrium will be stable if the slope , and unstable if (see e.g. Chen & Siegel 2018). In this case, all the equilibrium positions are stable at .…”

Section: Hysteresis Effect and Force Analysis On A Concave Cylindermentioning

confidence: 99%

“…The meniscus on a circular cylinder with the radius R (figure 2c) has been well studied (see e.g. Chen & Siegel 2018), where the relationship between ϕ c and the height h of the centre of the circular cylinder is given by…”

Section: Concave Shapes With Cornersmentioning

confidence: 99%

“…Rapacchietta et al. 1977; Bhatnagar & Finn 2006; Chen & Siegel 2018). The former provides a more intuitive but less rigorous interpretation of the stability.…”

Section: Introductionmentioning

confidence: 99%

“…Assuming that two equilibria exist, their stabilities can be examined either by force analysis or by energy analysis (see e.g. Rapacchietta et al 1977;Bhatnagar & Finn 2006;Chen & Siegel 2018).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Surface tension force on a partially submerged horizontal concave cylinder

Tan

Zhang²,

Zhou³

2022

J. Fluid Mech.

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A horizontal cylinder with a concave cross-section partially submerged in a liquid at a given position may permit multiple menisci around itself. The number and stabilities of the menisci are analysed, and how the menisci change during the processes of gradually hoisting and lowering the cylinder is explained by bifurcation theory. The restoring force on the concave cylinder and the rebounding potential energy (defined as the work done by the restoring force during the whole hoisting process to represent the potential rebounding capacity of a cylinder on water) are also investigated. The results show that, when the radius of the concave arc is smaller than the critical value, the concave cylinder at a given position permits multiple possible menisci. The equilibria form fold bifurcations with the position of the cylinder as the bifurcation parameter, and two successive fold bifurcations can form a one-fold hysteresis loop. The force–distance curve representing the relation between the restoring force and the position of the cylinder also has corresponding hysteresis loops, where the restoring force will jump (i.e. change discontinuously) at the bifurcation points. In contrast to a convex cylinder, a concave cylinder can have different values of the restoring force at the same height because of multiple menisci, and the values depend on whether it is hoisted or lowered. Under the condition of a fixed cross-sectional area, the optimal cross-sectional shape is determined when the maximum rebounding potential energy is reached, and it is close to the shape with the critical concave arc angle for the existence of multiple possible menisci. The cross-sections with concave parts are preferable to circular, laterally planed and corner-concave cross-sections. This paper provides an effective method of enhancing the restoring force and potential rebounding height of a robotic water strider insect or particles on the surface of water.

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Section: Multiple Possible Menisci and Their Stabilitiesmentioning

confidence: 99%

Section: Hysteresis Effect and Force Analysis On A Concave Cylindermentioning

confidence: 99%

Section: Concave Shapes With Cornersmentioning

confidence: 99%

“…Rapacchietta et al. 1977; Bhatnagar & Finn 2006; Chen & Siegel 2018). The former provides a more intuitive but less rigorous interpretation of the stability.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Surface tension force on a partially submerged horizontal concave cylinder

Tan

Zhang²,

Zhou³

2022

J. Fluid Mech.

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Effects of surface tension on a floating body in two dimensions

2018

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A model for calculating the force profile and the moment profile of a floating body in two dimensions with an arbitrary cross-section is proposed. Three types of cross-sections with different contact angles and densities are calculated by using the model to determine the vertical and rotational equilibria and their stabilities. Results show that the model can be applied to convex floating bodies with finitely many sharp edges. The study is then extended to investigate the surface tension effects on the vertical and rotational stabilities by varying the following parameters: the radii of curvature of the solid surface at the contact lines and the size of floating body. In general, the smaller the radii of curvature the better the vertical and rotational stabilities. However, for the contact angle $\unicode[STIX]{x1D703}=0$ (or $\unicode[STIX]{x1D703}=\unicode[STIX]{x03C0}$) the radii of curvature have no effect on the vertical stability of the floating body. By varying the size of the floating body, it is found that the vertical and rotational stabilities of mesoscale floating bodies vary continuously between the stabilities of the macroscale and microscale floating bodies with other parameters remaining unchanged.

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Equilibria and stabilities of a confined floating cylinder

Zhang

Zhou

2023

J. Fluid Mech.

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A two-dimensional system with a floating cylinder confined between two parallel vertical stationary plates partially immersed in an infinite liquid bath in a downward gravity field is considered. The equilibrium states of the system are investigated using the Young–Laplace equation in two dimensions. According to the symmetry of menisci at both sides of the cylinder, the equilibrium states are classified into three types: the equilibria of fully symmetric menisci, the equilibria of partially symmetric menisci and the equilibria of asymmetric menisci. The study is then extended to investigate the stabilities of the confined cylinder with bifurcation theory. Results show that there can be at most two stable regions in the bifurcation diagram. For different plates’ contact angles, there are five representative types of bifurcation behaviours for either the case of one stable region or the case of two stable regions. In comparison with the case of an unconfined cylinder, the confinement by two hydrophobic plates with a small spacing can assist the stable interfacial floatation of the confined cylinder with a large weight.

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A Floating Cylinder on an Unbounded Bath

Cited by 4 publications

References 18 publications

Surface tension force on a partially submerged horizontal concave cylinder

Surface tension force on a partially submerged horizontal concave cylinder

Effects of surface tension on a floating body in two dimensions

Equilibria and stabilities of a confined floating cylinder

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