I know this is an old thread... Yesterday, I was curious so I bought a Santoku knife at Smart & Final. It has the grantons or kullens (scallops) cut out of the sides. (BTW if you want a great kitchen knife, buy the $10 or so carbon steel knives at Smart & Final or the ones made in China and Thailand (Kiwi). Then learn how to sharpen a knife--the hardest part is getting past all the hoodoo, cult of special stones, nonsense). I've got a $150 German knife in the drawer-it can't take a great edge. It's stainless steel - it's all looks.)

First I've learned that Santoku knives are 'more accurate' this is at the tip. That makes sense. It's a straight line. if the angle changes as you draw it (pull it towards you) the point and edge don't change position, a curved knife blade will. A common curved kitchen knife is I think, generally a lot more useful than a Santouku. You can't rocker cut with a straight blade.

Second the grantons and kullens are supposed to reduce friction. There are multiple forces going on between the side of a knife and what it's slicing through. It can all be called friction, because, well just about everything involves friction. The friction between the side of a knife and food usually involves moisture, moisture is sticky. (what's going to stick together better two slices of apple or two pieces of cardboard?) By reducing the overall surface area the resistance to the knife being pulled through is reduced, and the adhesion is repeatedly broken every time a granton passes a spot. (I'm yammering on a bit, but no one's going to read this anyway...)

There was a challenge a couple of years ago, Innovations or some similarly named site was looking for a solution to keeping foods like slices of potatoes from sticking together. I'm sure grantons came up long before they even put it out as a challenge. I had two immediate thoughts. pump some air into edge of the blade (or nitrogen) and whatever they were offering was far less than such an invention would really be worth.
I learned from this thread that grantons are on machine slicers. Be really interesting to know how they came up with the idea and what the tests were like. I do know from woodworking that you want the teeth of a blade to be wider than the rest of the saw. In manual saws, the teeth are bent outward a bit, for carbide tipped circular saw blades the carbide cutters are always wider than the circle. In fact if a saw blade sides get squeezed, even a little bit from a warped board, it can stop the blade. It's called binding.
So perhaps in the kitchen we might not notice the granton effect.
For the person who said oxygen. That's OK. Atmosphere has a lot less friction resistance than than water or apples. Now if a kitchen knife was like a saw blade, where the thickest part was right at the cutting edge... well the food would just bend in and rub up against any thickness of blade.