Humans cannot, under normal circumstances, either walk on water or climb up smooth vertical surfaces. But many animals, such as small lizards, snails, slugs and arthropods, easily clamber up walls or hang from the undersides of smooth leaves. A few, including fishing spiders and water striders, habitually walk on the surface of water.
Image: University of Nebraska-Lincoln
Small size unites these two capabilities. Small organisms have relatively large ratios of surface area to volume (S/V). The force that opposes both capabilities (gravity) acts on the mass of the animal, whereas the forces that support climbing (adhesion) and walking on water (surface tension and fluid drag) are related to the surface in contact with the substrate. A general consequence of the way the S/V ratio changes with size is that larger animals are more influenced by gravity and inertia, and smaller animals are more influenced by surface forces such as adhesion and fluid drag.
Apart from very small size being an advantage for both walking up walls and walking on water, the two phenomena are quite different. When a fly walks up a vertical piece of glass, adhesive forces between its tarsal pads and the glass are sufficient to resist both the tendency to slide downward and the tendency to fall away from the glass surface. If you were able to isometrically increase the size of the fly by a factor of 10, its volume and its weight would increase by a factor of about 103, whereas its surface in contact with the glass would increase by a factor of about 102. This creature would fall to the ground because the somewhat increased adhesive forces could no longer resist the greatly increased pull of gravity; moreover, its now too-small wings would not allow it to fly!
For the water strider or the fishing spider, adhesion is irrelevant; in fact, both animals' legs have a waxy, hydrophobic surface that repels water, so neither is wetted by the water it stands on. Because the legs are not wetted by the water, the animal does not become submerged until the downward pull of gravity (the animal's weight) exceeds the opposing vertical component of the water's surface tension. The opposing component of surface tension is proportional to the perimeter of the leg where it is in contact with the water.
Again, imagining an isometric increase in the animal's size is instructive; if you
were to increase a fishing spider's linear dimensions by a factor of 10, its weight would increase by a factor of about
103, whereas its perimeter in contact with the water would increase by a factor of only 101. The
spider might not sink to the bottom because it might not be denser than water, but it probably would become submerged.
Image: Robert B. Suter
Ironically, for both the fly and the fishing spider, the attributes that make support possible also inhibit locomotion. For the fly, the more tightly it adheres to the wall, the more energy it must expend in locomotion because at each step, the forces of adhesion must be overcome; yet another place where natural selection has fostered a compromise. For the fishing spider or water strider, the same hydrophobicity of the animal's surface that allows the water's surface tension to support the animal also makes terrestrial-style locomotion difficult on the water surface. The very small amount of interaction between water molecules and the waxy molecules of the animal's surface reduces friction to a small fraction of the amount that would anchor the animal's foot to a solid substrate.
Fortunately, the weight of the animal, when supported by the water's surface tension, pushes the points of contact downward, creating dimples in the water surface. When the legs are moved backward to thrust the body forward, it is the legs with their accompanying dimples that move backwards, and it is the drag of the water moving past this leg/dimple that gives the spider something to push against.
For more information, a book by Steven Vogel, Life's Devices: The Physical World of Animals and Plants, provides an excellent introduction to the kinds of phenomena discussed above. A detailed consideration of locomotion on the water can be found in a paper by me and Oren Rosenberg, Sandra Loeb, Horatio Wildman and John H. Long, Jr. titled "Locomotion on the water surface: Propulsive mechanisms of the fisher spider, Dolomedes triton" [Journal of Experimental Biology, 200, 2523-2538 (1997)].