I don’t remember all of the details, but I thought it was essentially the water’s surface tension that foots the energy bill when climbing a paper towel or a capillary in a tree.
The surface of fluids like water are unhappy. Molecules on the surface would much rather be deep in the fluid because on the surface they have “dangling” Van der Waals & polar bonds to one side. You can calculate the potential energy of the surface due to all of those dangling weak bonds, & that’s the energy that is used to climb a capillary (the energy isn’t free).
I could be misremembering though, I admit. School was many years ago…
My favorite Halloween playlist. I return to it every year!