Adhesion and Capillary Action

Adhesion and Capillary Action

Why is it that water beads up on a waxed car but does not on bare paint? The answer is that the adhesive forces between water and wax are much smaller than those between water and paint. Competition between the forces of adhesion and cohesion are important in the macroscopic behavior of liquids. An important factor in studying the roles of these two forces is the angle \(\theta \) between the tangent to the liquid surface and the surface. (See the figure below.) The contact angle\(\theta \) is directly related to the relative strength of the cohesive and adhesive forces. The larger the strength of the cohesive force relative to the adhesive force, the larger \(\theta \) is, and the more the liquid tends to form a droplet. The smaller \(\theta \) is, the smaller the relative strength, so that the adhesive force is able to flatten the drop. The table below lists contact angles for several combinations of liquids and solids.

In the photograph, water beads on the waxed car paint and flattens on the unwaxed paint. (a) Water forms beads on the waxed surface because the cohesive forces responsible for surface tension are larger than the adhesive forces, which tend to flatten the drop. (b) Water beads on bare paint are flattened considerably because the adhesive forces between water and paint are strong, overcoming surface tension. The contact angle \(\theta \) is directly related to the relative strengths of the cohesive and adhesive forces. The larger \(\theta \) is, the larger the ratio of cohesive to adhesive forces. (credit: P. P. Urone)

One important phenomenon related to the relative strength of cohesive and adhesive forces is capillary action—the tendency of a fluid to be raised or suppressed in a narrow tube, or capillary tube. This action causes blood to be drawn into a small-diameter tube when the tube touches a drop.

If a capillary tube is placed vertically into a liquid, as shown in the figure below, capillary action will raise or suppress the liquid inside the tube depending on the combination of substances. The actual effect depends on the relative strength of the cohesive and adhesive forces and, thus, the contact angle \(\theta \) given in the table. If \(\theta \) is less than \(90º\), then the fluid will be raised; if \(\theta \) is greater than \(90º\), it will be suppressed. Mercury, for example, has a very large surface tension and a large contact angle with glass. When placed in a tube, the surface of a column of mercury curves downward, somewhat like a drop. The curved surface of a fluid in a tube is called a meniscus. The tendency of surface tension is always to reduce the surface area. Surface tension thus flattens the curved liquid surface in a capillary tube. This results in a downward force in mercury and an upward force in water, as seen in the figure below.

(a) Mercury is suppressed in a glass tube because its contact angle is greater than \(90º\). Surface tension exerts a downward force as it flattens the mercury, suppressing it in the tube. The dashed line shows the shape the mercury surface would have without the flattening effect of surface tension. (b) Water is raised in a glass tube because its contact angle is nearly \(0º\). Surface tension therefore exerts an upward force when it flattens the surface to reduce its area.

Contact Angles of Some Substances

Capillary action can move liquids horizontally over very large distances, but the height to which it can raise or suppress a liquid in a tube is limited by its weight. It can be shown that this height \(h\) is given by

\(h=\cfrac{2\gamma \phantom{\rule{0.25em}{0ex}}\text{cos}\phantom{\rule{0.25em}{0ex}}\theta }{\rho \text{gr}}.\)

If we look at the different factors in this expression, we might see how it makes good sense. The height is directly proportional to the surface tension \(\gamma \), which is its direct cause. Furthermore, the height is inversely proportional to tube radius—the smaller the radius \(r\), the higher the fluid can be raised, since a smaller tube holds less mass. The height is also inversely proportional to fluid density \(\rho \), since a larger density means a greater mass in the same volume. (See the figure below.)

(a) Capillary action depends on the radius of a tube. The smaller the tube, the greater the height reached. The height is negligible for large-radius tubes. (b) A denser fluid in the same tube rises to a smaller height, all other factors being the same.

How does sap get to the tops of tall trees? (Recall that a column of water can only rise to a height of 10 m when there is a vacuum at the top—see this example.) The question has not been completely resolved, but it appears that it is pulled up like a chain held together by cohesive forces. As each molecule of sap enters a leaf and evaporates (a process called transpiration), the entire chain is pulled up a notch. So a negative pressure created by water evaporation must be present to pull the sap up through the xylem vessels. In most situations, fluids can push but can exert only negligible pull, because the cohesive forces seem to be too small to hold the molecules tightly together. But in this case, the cohesive force of water molecules provides a very strong pull. The figure below shows one device for studying negative pressure. Some experiments have demonstrated that negative pressures sufficient to pull sap to the tops of the tallest trees can be achieved.

(a) When the piston is raised, it stretches the liquid slightly, putting it under tension and creating a negative absolute pressure \(P=-F/A\). (b) The liquid eventually separates, giving an experimental limit to negative pressure in this liquid.