Contact Angle Hysteresis and Interacting Surface Defects
Title: Contact Angle Hysteresis and Interacting Surface Defects
Author: J.M. di Meglio
Journal: "Europhysics Letters" 17 (7), (1992); 607-612
The focus of this paper is contact angle hysteresis, a process that sometimes occurs for non-wetting liquids. Contact angle hysteresis is when a liquid drop is moved on a solid and the contact angle ahead of the drop is larger than the contact angle at the rear and it is not a dynamical effect, i.e. it only occurs at very small velocities. Contact angle hysteresis is commonly attributed to surface defects in the solid (chemical heterogeneities or roughness). The paper focusses on the pinning of an advancing triple line on nondiluted defects (that have a long range of capillary interactions). The contact line has a long-range tail on each side of the defect and when the solid plane is vertical, the tail length is controlled by the capillary length. The capillary length is the length scale for a fluid that is under the competing forces of gravity and surface tension. This paper describes experiments to show the connection between defects and contact angle hysteresis.
The experiments involved overhead projector transparencies with defects represented as circular spots drawn using a plotter. Two sets of samples were made: one set with 1.5mm circular spots (type 1) patched randomly and with variable concentrations (Fig 2a below), the other with 0.5mm defects more uniformly distributed over the transparency (type 2) (Fig 2b below). The strength of the defects are changed by using different types of ink.
The large defect samples were wetted with hexadecane and the small-defect samples were wetted with heptane. The defects had a size comparable to the capillary length and both liquids exhibited contact angle hysteresis on the defects.
The samples were hung up to a force sensor which was connected to an amplifier and this was used to measure both the advancing and receding force exerted by the liquid. The liquids were displaced across the sample with velocities between 40 and 600 microns/second. The sample was dipped into the liquid at constant velocity to measure the advancing liquid force. The sample was then removed out of the liquid (at the same velocity) and the receding force was measured. The hysteresis was calculated as the difference between these two forces.
Figure 3 depicts the relative hysteresis (hysteresis on a patched area divided by the hysteresis on the defect-free area) along the sample as a function of the density of defects for type 1 samples. When the concentration of defects is really low (as in the lowest case with only four bumps), each bump corresponds to a peak on the hysteresis axis. When the concentration of defects is increased, there are 'avalanches' in the contact line - corresponding to pinning-depinning of the contact line on islands of defects. As the concentration of defects increases, so too do the 'large-scale events' on the hysteresis axis.
Figure 4 shows a plot of the increase in the mean hysteresis versus the density of defects (plotted on a log-log scale). On this plot, d* represents the critical density at which defects appear to interact with one another (i.e. above this density, the hysteresis is no longer increasing linearly). This critical density is around the square of the capillary length. The adjacent figure shows the root mean square amplitude of the noise (which increases with hysteresis). To gain a better understanding of the noise, the experimenters took another set of measurements with the type 2 samples which had a longer length of patched areas.
Six different velocities were measured and it was found that the hysteresis increases a little with velocity (shown in the figure below). Figure 6 shows the increase of the mean hysteresis (averaged over the six velocities) plotted against the density of defects. A nonlinear behavior is noticed here but - not the same nonlinear relationship as the one shown in the plot above. The author had no explanation for this difference.
The square of the spatial Fourier transform of the noise of the force in the region where defects were present was computed and plotted for the averaged hysteresis. This confirmed that the amplitude of the noise is important above the critical density (d*) and the noise follows a <math>1/f^2</math> behavior in the defect zone where the amplitude is most emphasized. This suggests that the pinning that occurred in this fall into a class of experiments of "avalanches of sandpiles or stick-and-slip related to self-organized criticality". (pg 610)
The author admits that the noise level without a sample was only 1 order of magnitude smaller than the hysteresis noise and therefore, it was hard to draw definitive conclusions from these experiments. The high level of noise prevalent in these experiments made it difficult to investigate the relationship between the velocity of the fluid and the hysteresis. Regardless of this fact, the experiments described in this paper provide a very interesting (and simple) way of changing the strength of the defects (concentration of pinning points) and to study the length (and velocity) scales over which contact angle hysteresis exists.