Andreotti Bruno, Marchand Antonin, Das Siddhartha, Snoeijer Jacco H
Physique et Mécanique des Milieux Hétérogènes, UMR 7636 ESPCI -CNRS, Université Paris-Diderot, 10 rue Vauquelin, F-75005 Paris, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Dec;84(6 Pt 1):061601. doi: 10.1103/PhysRevE.84.061601. Epub 2011 Dec 1.
The elastocapillary instability of a flexible plate plunged in a liquid bath is analyzed theoretically. We show that the plate can bend due to two separate destabilizing mechanisms, when the liquid is partially wetting the solid. For contact angles θ(e) > π/2, the capillary forces acting tangential to the surface are compressing the plate and can induce a classical buckling instability. However, a second mechanism appears due to capillary forces normal to surface. These induce a destabilizing torque that tends to bend the plate for any value of the contact angle θ(e) > 0. We denote these mechanisms as "buckling" and "bending," respectively and identify the two corresponding dimensionless parameters that govern the elastocapillary stability. The onset of instability is determined analytically and the different bifurcation scenarios are worked out for experimentally relevant conditions.
对浸入液浴中的柔性板的弹性毛细管不稳定性进行了理论分析。我们表明，当液体部分润湿固体时，板可由于两种不同的失稳机制而发生弯曲。对于接触角θ(e) > π/2，作用于表面切向的毛细力会压缩板，并可引发经典的屈曲不稳定性。然而，由于垂直于表面的毛细力会出现第二种机制。对于任何接触角θ(e) > 0，这些力都会产生一个使板弯曲的失稳扭矩。我们分别将这些机制称为“屈曲”和“弯曲”，并确定了控制弹性毛细管稳定性的两个相应无量纲参数。通过解析确定了不稳定性的起始点，并针对实验相关条件计算出了不同的分岔情况。
