Understanding contact angle hysteresis on an ambient solid surface

Abstract

We report a systematic study of contact angle hysteresis (CAH) with direct measurement of the capillary force acting on a contact line formed on the surface of a long glass fiber intersecting a liquid-air interface. The glass fiber of diameter 1-2μm and length 100-200μm is glued onto the front end of a rectangular cantilever beam, which is used for atomic force microscopy. From the measured hysteresis loop of the capillary force for 28 different liquids with varying surface tensions and contact angles, we find a universal behavior of the unbalanced capillary force in the advancing and receding directions and the spring constant of a stretched meniscus by the glass fiber. Measurements of the capillary force and its fluctuations suggest that CAH on an ambient solid surface is caused primarily by two types of coexisting and spatially intertwined defects with opposite natures. The contact line is primarily pinned by the relatively nonwetting (repulsive) defects in the advancing direction and by the relatively wetting (attractive) defects in the receding direction. Based on the experimental observations, we propose a "composite model" of CAH and relevant scaling laws, which explain the basic features of the measured hysteresis force loops.

Simultaneous observation of asymmetric speed-dependent capillary force hysteresis and slow relaxation of a suddenly stopped moving contact line

“…Details about the experimental apparatus and procedures as well as AFM operation have been described elsewhere [18,23], and here we mention only some key points.…”

“…The effect of fiber pulling at a constant speed u is to continuously stretch the liquid interface and thus produce a time-dependent elastic restoring force, δf = k s ut =ḟ t, acting on the CL. Herė f = k s u is the loading rate with k s being the spring constant of the liquid interface, which has been analytically calculated for a vertical thin fiber intersecting a liquid-air interface [18]. As the pulling force δf increases linearly with time t, the effective energy barrier E * b = E b (1 −ḟ t/f c ) 3/2 continuously decreases and the escape rate K(δf ) increases.…”

“…In a recent experiment [18], we used a newly developed hanging fiber probe [19] based on atomic force microscopy (AFM) to directly measure the capillary force acting on a CL. As shown in Fig.…”

“…Here i = a indicates the advancing direction and i = r indicates the receding direction. For a CL of length πd and contact angle θ i with a liquid-air interface of surface tension γ,f i (t) can be written as [18,[20][21][22], f i (t) = −πdγ cos θ i (t),…”

Capillary force on a tilted cylinder: Atomic Force Microscope (AFM) measurements

“…More recently, it has been transposed to Atomic Force Microscope (AFM) measurements, where the cylindrical probe is attached to the end of an AFM cantilever 8 . The very high force sensitivity of AFM cantilevers allows to perform capillary force and contact angle measurements on even smaller probes, with diameters ranging from a few micrometers down to about 10 nm [9][10][11][12] . It also allows to investigate the dynamical properties of liquid meniscii at thermal equilibrium and under a large variety of solicitations [13][14][15] .…”