## Left, Right, Up, Down Contact Angles

Contact angles express the shape of a liquid against a solid or another liquid, which in turns tells us about the relative adhesion of the liquid compared to its own cohesion. This is their usefulness.

Contact angles can be measured in many different ways, so some precision is required in language to specify exactly what is being measured. The following list of terms may be useful:

Advancing angle. This is the contact angle that is most commonly measured. Lacking some other specification, it is what people mean when they simply say "contact angle." The advancing angle refers to a wetting process, where liquid is changing, or has changed, a dry solid surface into a wet one. More particularly, this means a solid-vapor surface has changed to a solid-liquid surface. In the rare case of liquid-liquid contact angles, this would be a liquid-vapor surface changing to a liquid-liquid surface. The word "advancing" comes from the requirement that the drop be just ready to spread further on the substrate surface. That is, if we added any more liquid to the drop, it would spread further. Thus the advancing contact angle is the largest possible angle with the drop still at steady state. If you carefully deposit a sessile [sitting] drop in an FTA system, the initial angle measured will be an advancing angle. Another way to make an advancing angle is to keep the needle captive in the sessile drop and slowly expand it by further pumping. Yet another way is the tilting plate technique where the sample is tilted until the drop runs down hill.

Receding angle. The receding angle is the opposite of the advancing angle. It is the de-wetting angle, and is the smallest steady state angle. With extreme care [see Contact Angle Measurements Using the Drop Shape Method] you can make a receding angle measurement with a captive needle by pumping in and removing liquid from the drop. The easier way is with a tilt table.

Equilibrium angle. This is ill-defined, but often used. It refers to a situation that is really not at thermal equilibrium, but comes to a steady state value after some time. Typically the drop starts out with a high contact angle and then the angle decreases as the drop spreads or absorbs into the sample. The equilibrium angle is the angle after it stops changing in time. It does not have any particular chemical meaning but is used as a comparative measurement, particularly in quality assurance situations.

Initial angle. This is also used in non-equilibrium conditions, where the measured angle changes in time, just as the preceding item. It refers to the first angle that can be measured after the liquid wets the surface. It therefore stands in contrast to the equilibrium angle which would be measured after a long time. The initial contact angle is a measure of adhesion, which is what is normally desired. However, it can be difficult to determine if the liquid quickly spreads or absorbs. Another measurement difficulty occurs when the test liquid has high viscosity, so its shape is initially determined by internal friction rather than by the chemical adhesion and cohesion forces that we desire.

Spherical fit. The liquid-vapor profile of the sessile drop can be measured in several ways, depending on the image analysis algorithm selected. In FTA software, this is done on the Contact Angle tab. There are pros and cons to each image "fit" type. A spherical fit assumes the liquid-vapor profile is part of a sphere. This is true if the drop is small enough that the pressure from gravity [i.e., the hydrostatic head] is small compared to the pressure from Laplace's rule. For water, this requires the height of the drop to be less than a millimeter. The advantage of the spherical fit is that it is very robust and it will successfully track as a drop absorbs into a specimen such as paper. When the drop is tall enough to be affected by gravity, then the spherical fit will read slightly low.

Non-spherical fit. Here the liquid-vapor fit is made with separate polynomials on each side, left and right. Therefore there is no presumption about the effect of gravity. This fit is less robust than the spherical fit because the profile is measured only near the three-phase line on each side, so far fewer edge points are used. You can choose to measure only the left or right sides of the drop should one side be defective. These choices are made on the Contact Angle tab. Unless you choose otherwise, the left and right sides are measured independently and the average of the available sides is reported as the "contact angle" in the Results window. Note the spherical fit reports only one angle since, by definition, the left angle will equal the right angle if the shape is truly part of a sphere.

Laplace-Young fit. The liquid-vapor profile is fit according to the Laplace-Young equation, the same equation used to measure interfacial tension on pendant [hanging] drops. It is useful for high contact angles measured on tall drops. Just as the spherical fit requires gravity to not be a factor in shaping the drop, the Laplace-Young method requires that it indeed be affected [distorted from a spherical shape] by gravity. The Laplace-Young method also requires that the drop be symmetric about its vertical central axis, so it is applicable only when the substrate is uniform so the drop is circular when viewed from above. The Laplace-Young method, because of this assumption of symmetry about the central axis, generates only a single contact angle: the left and right sides are presumed equal. The Laplace-Young method must be used on a level surface, so it can not be used in the tilting plate method.

Left and right angles. As discussed above, these exist separately only when the drop is not symmetric about its vertical central axis.

Sessile drop measurements. Sessile means "sitting." These are the most common measurements made with video instruments. The camera looks at the drop from its side and measures the liquid-vapor profile and the liquid-solid baseline and the software solves for the contact angle. This and the following three measurement types are selected on the Contact Angle tab of the Fta32 software.

Capillary rise measurements. Another way of making contact angle measurements is to measure the rise of a meniscus against the solid. This is a more difficult measurement than the sessile drop but is necessary for small, thin specimens such as hairs and fibers.

Protractor measurements. These are manual measurements made by fitting lines to the tangents of the surfaces. They are not highly accurate, as the eye has difficulty placing the lines, but are sometimes used for demonstration purposes.

Top View measurements. Here the viewing angle is down on the drop, from above. If the original volume is known, the contact angle can be deduced from the diameter of the top view profile. This is mainly used for very low angles and when the drop spreads unevenly on the substrate. Glass is a good example of a specimen analyzed by the top view method.

Inverted measurements. Think of an air bubble rising up against a horizontal surface immersed in water. This would be an inverted measurement, an upside down drop. Eyeglasses and contact lens are often measured this way. The air bubble appears as the dark "drop" in the image. Note that the contact angle is always measured within the liquid phase, so the apparent angle must be complemented to obtain the true contact angle.