Capillary-scale solid rebounds: experiments, modelling and simulations

Galeano-Rios, Carlos A.; Cimpeanu, Radu; Bauman, Isabelle; MacEwen, Annika; Milewski, Paul A.; Harris, Daniel M.

doi:10.1017/jfm.2020.1135

Cited by 14 publications

(56 citation statements)

References 71 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Section: The Kinematic Matchmentioning

confidence: 99%

“…The model problem of the impact of a rigid sphere onto a deformable substrate has proven to be very useful in the study the dynamic behaviour of deformable bodies that undergo a collision [20,21,22,23,24,25]. Moreover, the transfer of energy to waves during contact was shown to be successfully captured with relatively simple models in the same set-up [25]. Furthermore, in [23,25], the use of moving meshes or variational methods, such as the finite element method, was not strictly necessary to solve these type of impacts (though there is, in principle, no impediment to use them); instead, it was sufficient to use the finite difference method, which is easier to program and, therefore, accessible to a larger community of modellers.…”

Section: The Kinematic Matchmentioning

confidence: 99%

“…The kinematic match (KM) method, introduced in [23] was first developed as a fully-predictive method to solve the impact and rebound of a rigid hydrophobic sphere onto the free surface of a bath, an application for which it has been successfully validated using experimental data (see figures 3a and 11 in [23]; figures 5, 7 and 9 in [24]; and figures 6a and 7 in [25]), as well as direct numerical simulations (see figures 6b, 7, 9 and 12 in [25]). However, the method has far more general applications.…”

Section: The Kinematic Matchmentioning

confidence: 99%

“…We note that, in prior formulations of the kinematic match [23,24,25], the condition given by equation (17) was not included. Instead, the implementation relied on including equations that satisfied this condition approximately.…”

Section: The Kinematic Matchmentioning

confidence: 99%

See 3 more Smart Citations

Impact of a rigid sphere onto an elastic membrane

A.¹,

Alventosa²,

Harris³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

We study the axisymmetric impact of a rigid sphere onto an elastic membrane theoretically and experimentally. We derive governing equations from first principles and impose natural kinematic and geometric constraints for the coupled motion of the sphere and the membrane during contact. The free-boundary problem of finding the contact surface, over which forces caused by the collision act, is solved by an iterative method. This results in a model that produces detailed predictions of the trajectory of the sphere, the deflection of the membrane, and the pressure distribution during contact. Our model predictions are validated against our direct experimental measurements. Moreover, we identify new phenomena regarding the behaviour of the coefficient of restitution for low impact velocities, the possibility of multiple contacts during a single rebound, and energy recovery on subsequent bounces. Insight obtained from this model problem in contact mechanics can inform ongoing efforts towards the development of predictive models for contact problems that arise naturally in multiple engineering applications.

show abstract

Section: The Kinematic Matchmentioning

confidence: 99%

Section: The Kinematic Matchmentioning

confidence: 99%

Section: The Kinematic Matchmentioning

confidence: 99%

Section: The Kinematic Matchmentioning

confidence: 99%

See 2 more Smart Citations

Impact of a rigid sphere onto an elastic membrane

A.¹,

Alventosa²,

Harris³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…which corresponds to the displacement of a small non-wetting sphere floating on a liquid bath [29,30].…”

Section: B Hydrostatic Region Matching and Sphere Displacementmentioning

confidence: 99%

Leidenfrost levitation of a spherical particle above a liquid bath: evolution of the vapour-film morphology with particle size

Brandão¹,

Schnitzer²

2021

Preprint

View full text Add to dashboard Cite

We consider a spherical particle levitating above a liquid bath owing to the Leidenfrost effect, where the vapour of either the bath or sphere forms an insulating film whose pressure supports the sphere's weight. Starting from a reduced formulation based on a lubrication-type approximation, we use matched asymptotics to describe the morphology of the vapour film assuming that the sphere is small relative to the capillary length (small Bond number) and that the densities of the bath and sphere are comparable. We find that this regime is comprised of two formally infinite sequences of distinguished limits which meet at an accumulation point, the limits being defined by the smallness of an intrinsic evaporation number relative to the Bond number. These sequences of limits reveal a surprisingly intricate evolution of the film morphology with increasing sphere size.Initially, the vapour film transitions from a featureless morphology, where the thickness profile is parabolic, to a neck-bubble morphology, which consists of a uniform-pressure bubble bounded by a narrow and much thinner annular neck. Gravity effects then become important in the bubble leading to sequential formation of smaller and smaller neck-bubble pairs near the symmetry axis. This process terminates when the pairs closest to the symmetry axis become indistinguishable and merge. Subsequently, the inner section of that merger transitions into a uniform-thickness film that expands radially, gradually squishing larger and larger neck-bubble pairs into a region of localised oscillations sandwiched between the uniform film and what remains of the bubble whose radial extent is presently comparable to the uniform film; the neck-bubble pairs farther from the axis remain essentially intact. Ultimately, the uniform film gobbles up the largest outermost bubble, whereby the morphology simplifies to a uniform film bounded by localised oscillations. Overall, the asymptotic analysis describes the continuous evolution of the vapour film from a neck-bubble morphology typical of a Leidenfrost drop levitating above a flat solid substrate to a uniform-film morphology which resembles that in the case of a large liquid drop levitating above a liquid bath.

show abstract

Surface tension force on a partially submerged horizontal concave cylinder

Tan

Zhang²,

Zhou³

2022

J. Fluid Mech.

View full text Add to dashboard Cite

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.

show abstract

Capillary-scale solid rebounds: experiments, modelling and simulations

Abstract: Abstract

Cited by 14 publications

References 71 publications

Impact of a rigid sphere onto an elastic membrane

Impact of a rigid sphere onto an elastic membrane

Leidenfrost levitation of a spherical particle above a liquid bath: evolution of the vapour-film morphology with particle size

Surface tension force on a partially submerged horizontal concave cylinder

Contact Info

Product

Resources

About