Capillary rise between elastic sheets

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By Sung Hoon Kang


Title: Capillary rise between elastic sheets

Reference: Ho-Young Kim AND L. Mahadevan, J. Fluid Mech. 548, 141-150 (2006).

Soft matter keywords

capillary rise, surface tension, hydrophilic, three-phase junction, contact angle, Jurin’s law

Abstract from the original paper

When a paintbrush is dipped into a pot of paint and pulled out, surface tension forces cause the individual hairs in the brush to coalesce even as the brush becomes impregnated with paint. We study a simple model of this elastocapillary interaction in the context of the surface-tension-driven vertical rise of a liquid between two long flexible hydrophilic sheets that are held a small distance apart at one end. We provide an analytic theory for the static shapes of the sheets as well as the liquid rise height which is different from that of the classical law of Jurin, and show that our experiments are quantitatively consistent with the theory.

Soft matter example

(not done yet)

The hairs or bristles of a paint brush coalesce when taken out of a liquid because the surface tension at the air-water-hair interface wants to minimize the energy of the system. In this case, the total energy of the system is the sum of the elastic energy of the deformed hairs, gravity and the capillary energy of the liquid-vapor interface.

Fig. 1 Schematic and shape of the sheets when (a) the sheets are relatively stiff so that the ends are separate: coordinate system and experimental image of glass cover slips, 24mm long and initially 1mm apart, after they were slowly withdrawn out of water; (b) the sheets are relatively soft so that ends are in contact: coordinate system and experimental image of glass sheets, 42mm long and initially 0.6mm apart, slowly withdrawn out of water.

References

(not done yet)

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Hosoi, A. E. & Mahadevan, L. 2004 Phys. Rev. Lett. 93, 137802.

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Landau, L. D. & Lifshitz, E. M. 1986 Theory of Elasticity, 3rd Edn. Pergamon.

Senturia, S. D. 2001 Microsystem Design. Kluwer.