Elastocapillary Coiling of an Elastic Rod Inside a Drop

Abstract

Capillary forces acting at the surface of a liquid drop can be strong enough to deform small objects and recent studies have provided several examples of elastic instabilities induced by surface tension. We present such an example where a liquid drop sits on a straight fiber, and we show that the liquid attracts the fiber which thereby coils inside the drop. We derive the equilibrium equations for the system, compute bifurcation curves, and show the packed fiber may adopt several possible configurations inside the drop. We use the energy of the system to discriminate between the different configurations and find a intermittent regime between two-dimensional and three-dimensional solutions as more and more fiber is driven inside the drop.

Configurational forces and nonlinear structural dynamics

“…and for the part of rod outside the sliding sleeve Furthermore, as a complement to the differential systems (14) and (15), the minimization procedure also provides the boundary conditions at the two rod's ends…”

“…(A.4) Imposing the vanishing of this expression for every variation field x var (s, t), y var (s, t), θ var (s, t), and var (t) subject to the conditions (A.1) provides the systems of equations of motion (14) and (15), the boundary conditions (16) and the interfacial condition (17). It is remarked that, in addition to the curvature θ (s, t) and rotation velocityθ(s, t) fields, the internal forces N x (s, t) and N y (s, t) may also have a spatial discontinuity at the sliding sleeve exit s = l − (t), so that the symbol […”

Drop-on-coilable-fibre systems exhibit negative stiffness events and transitions in coiling morphology

“…Moreover they are structured with a period πD for the end-shortening ∆, each cycle corresponding to the addition of one coil inside the drop. Numerical computations 38 show that these cycles come from in-drop rearrangement of the coiling and that 3D and planar configurations alternate, depending on the value of the in-drop fibre length (see also supplementary video # 1). We indeed observe that the typical coiling morphology of a drop-on-coilable-fibre system oscillates between a fully ordered state and a fully disordered state, both extremes shown on fig.…”

Packing of elastic rings with friction

“…There have been many studies in recent years of the packing and crumpling of thin elastic sheets and rods under confinement, using theory [1][2][3][4][5][6][7][8][9], computations [10], and experiments [11,12]. Many studies have examined the basic physics and mechanics of the packing process [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29], and the geometry of the buckled and creased shapes [30][31][32][33][34][35][36][37][38][39][40][41][42].…”