Sébastien Neukirch
Institut Jean le Rond d'Alembert
Centre National de la Recherche Scientifique
Sorbonne Université, Campus Pierre et Marie Curie
Paris, France

tel: +33 1 44 27 72 61
e-mail: sebastien.neukirch (-atat-) upmc.fr


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The heavy windlass: Buckling and coiling of an elastic rod inside a liquid drop in the presence of gravity

H. Elettro, A. Antkowiak, and S. Neukirch

Mechanics Research Communications, vol. 93 (2018) 58-61

Abstract : A liquid drop sitting on an elastic rod may act as a winch, or windlass, and pull the rod inside itself and coil it. This windlass effect has been shown to be generated by surface tension forces and to work best for small systems. Here we study the case where the drop is large enough so that its weight interferes with surface tension and modifies the windlass mechanics.

DOI: 10.1016/j.mechrescom.2018.01.008

download the journal version : PDF


Submitted (Oct, 2017)
Reports (received Jan, 2018)

Reviewer 1

The paper presented by Elettro et al. deals with the windlass effect that results in the buckling and coiling of a thin elastic rod inside a drop. The aim of the study is to characterize the effect of the weight of the drop on the windlass effect. The theoretical work is based on the potential energy minimization of the system, under constraints enforced through Lagrange multipliers. The results are summarized in a bifurcation diagram: at high tension, the thread simply sags under the weight of the drop, at low tension, the thread buckles and coils inside the drop. The authors also present experimental results obtained with droplets of varying radius. The experimental characterization recovers the bifurcation diagram obtained theoretically and the linear evolution of the plateau sagging angle. The authors provide satisfactory explanations for the overshooting of the sagging angle as the plateau is reached, and for the variations of Branch II. The slope of the linear dependence of the sagging angle on the weight over Tp is lower than expected. The authors suggest that this is due to the deformation of the drop under its own weight, modifying its geometry and the meniscus points.

Although I have not derived all the equations, the approach is similar to the one developed by the authors in the absence of gravity and detailed in H. Elettro, P. Grandgeorge, and S. Neukirc in the Journal of Elasticity 127 (2), 235-247 (2017). The theoretical work seems carefully done and the experiments are rigorously conducted and presented. This manuscript deserves publication in Mechanics Research Communications, provided that the following points are addressed.

My biggest concern is with Reference [13] which is not necessary since the work has not been published or even submitted. In addition, it seems to indicate that the authors can explain the discrepancy between the theoretical model presented here and the experimental results. If the authors can describe the effect of the weight on the shape and meniscus points, why not start with the complete story? Why publish a model that is not the best they can do? This is quite awkward. I would suggest that the authors give us the full story in a single paper, or at least, have the common sense to not tell the readers to skip ahead to a more complete paper.

The authors should correct typos and missing spaces. Mistakes include:

  1. “the systems behaves” on page 4 and missing space between numbers and units.
  2. The sentence leading to Hessian matrix (equation 7) and the one after do not make sense.
  3. The notation for Lout in Figure 1 is unclear, at first sight it looks like the authors are defining an angle.
  4. There are not enough references to the extensive work on elastocapillary effects. I am thinking of the work of Duprat et al. in Nature (2012), Sauret et al. in Soft Matter (2017) and many others.

Reviewer 2

- This paper deals with the effect of gravity on the elasto-capillary windlass phenomenon that was recently reported by the same group. The paper is well-written, the proposed analytical model is simple yet allows for the computation of a bifurcation diagram, and the experiments and analysis are carefully conducted. I therefore recommend this paper for publication, with minor changes.

The main focus of the paper is to look at the effect of gravity on the windlass mechanism. However, the comparison with the case without gravity is left for the very end of the paper, and a number characterizing the effect of the drop weight is only introduced in the experimental part. It could be interesting to discuss the effect of gravity specifically from the beginning, i.e. from Figure 2. For instance, there could be several curves for different values of Cgrav, from the limit of no weight to the curve presented here for a finite value of the weight. The number Cgrav is introduced but not really discussed; the relevant parameter is not directly Cgrav, but Mg/2Tp, and although Tp is indeed related to Cgrav, the term EI/2R^2 also changes since the drop radius changes. This should be discussed. Small comment: the experiments are said to be for Cgrav ranging from 0.01 to 0.46, but an experimental bifurcation curve is shown for Cgrav=0.6?

The effect of gravity is seen on the first branch of the bifurcation diagram. The model suggests that without gravity, this branch is a portion of the vertical axis. However, in the experiments presented in previous papers without gravity, there is a finite range of end-shortening distances were the tension decreases linearly before reaching the plateau; how is this compatible with the presented model ?

Without gravity, the regime of constant tension where the fiber buckles inside the drop is followed by a « coiling » regime. This regime is never observed here? Would it be observable? Would the sagging angle then increase? My understanding is that the expression of the bending energy in the model (the assumption that the curvature is 1/R), and thus the model, is only valid in the buckling regime. However, experimentally one could see an increase of the angle/decrease of tension at small end-shortening distances. The title does specify « buckling and coiling » of the elastic rod, although this is not discussed further in the text where « coiling regime » is used to describe the plateau (buckling?) regime. This should be clarified in order to be consistent with the previous studies.