They reasoned that the water is bound to the dog by surface tension between the liquid and the hair. When the dog shakes, centripetal forces pull the water away. So for the water to be ejected from the fur, the centripetal force has to exceed the surface tension.
This model leads to an interesting prediction. If the animal has a radius R, the shaking frequency must scale with R^0.5. That makes sense, smaller animals will need to oscillate faster to generate forces large enough to dry themselves.
To find out whether that applies in nature, Dickerson and pals studied films of various animals of different sizes. They found that a mouse shakes at 27 Hz, a cat at about 6 Hz while a bear shakes at 4Hz. "Shake frequencies asymptotically approach 4Hz as animals grow in size," they conclude.
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