Nonlinear effects of line tension in adhesion of small droplets

Abstract

Three-phase line tensions may become crucial in the adhesion of micro-nano or small droplets on solid planes. In this paper we study for the first time the nonlinear effects in adhesion spanning the full range of physically possible parameters of surface tension, line tension, and droplet size. It is shown that the nonlinear adhesion solution spaces can be characterized into four regions. Within each region the adhesion behaves essentially the same. Especially, inside the characteristic regions with violent nonlinearities, the co-existence of multiple adhesion states for given materials is disclosed. Besides, two common fixed points in the solution space are revealed. These new results are consistent with numerical analysis and experimental observations reported in the literatures.

Contact Angle of Glycerol Nanodroplets Under van der Waals Force

“…Barberis and Capurro studied the equilibrium shape of nanodroplets by experiments and developed a continuum mechanics model, indicating contact angle depending on the drop size . LV et al showed theoretically that nonlinear effects of line tension lead to multiple equilibrium shapes of nanodroplets …”

“…11 LV et al showed theoretically that nonlinear effects of line tension lead to multiple equilibrium shapes of nanodroplets. 12 As the thickness of the liquid film reduces to nanometers, the van der Waals (vdW) force produces a pressure in the film, or so-called disjoining pressure, 2,13 which is a key factor in the mechanical equilibrium of the film. 2 Analogous to thin film, as the height of the droplet further decreases to nanometers, the vdW force also plays an important role in the force balance.…”

Magnetically Actuated Superhydrophilic Robot Sphere Fabricated by a Femtosecond Laser for Droplet Steering

“…As the droplet passes through the narrower channel, the wall pressure on the droplet increases significantly, as does the resistance. Eventually, the droplet fails to pass through the channel because the adhesion to the MSR is not strong enough to balance the resistance in the opposite direction. − The curves shown in Figure f were fitted by repeated experiments of the MSR carrying droplets of different sizes through channels with different widths. As we can see from the diagram, the volume of droplets that can pass through the silt changes rapidly when the width of the channel increased from 3.8 to 4.4 mm.…”