If you look at your fingers, you’ll see that there are lots of little ridges. If you lick your finger, you create a little area of dampness on the tip of the finger. When you press it onto a surface, you squeeze water out in exactly the same way as if you were squeezing a sucker onto a pane of glass. You get this attraction of the water locking onto the molecules on the surface of the page and locking onto the ridges on your finger and it gives you a bit more grip.
However, when your hands have a huge puddle on it, what you end up with is a very thick layer of water. You have a layer of water coating your hands, a layer of water coating the other thing you are holding and a layer of water between the two. You end up with a layer of water sandwiched between two other layers of water and that it very slippery.
This is exactly the reason why tires on cars have tread. The tread means that your tire squashes the water out through the tread pattern and stops you getting this slippery sandwich and gives you a better grip on the road. Not enough tread and you slip because the pressure is all distributed evenly, a little water and you get a suction type effect, and too much water and the two objects aren’t actually touching each other and you hydroplane.
There are two forces at work here when it comes to wet grip: Surface tension and Friction.
Water molecules want to cling to things. When water is surrounded by water, it clings to the surrounding water. The surface of water, however, can’t cling as much to surrounding water and thus will cling to anything that touches it.
So, if you have a thin layer of water on your hands, the surface tension from the water will cling to things, which will feel a little grippy. But, if you add too much water, the water below the surfaces will cling to itself and become slick.
The stronger force from grip comes from friction. Friction comes from frictional coefficient and force. Water lowers the coefficient of friction, so water will always make grip from friction weaker.
So: Having slightly wet hands will provide grip to things that don’t require force (like opening a plastic bag, which is really pulling the two parts of the bag apart, not gripping them) The surface tension will provide some cling. Too much water, however, and surface tension is negated by the slickness of the water under the surface.
However, any wetness will reduce grip generated by friction, which is our main gripping ability, as we can control friction by pushing harder. So overall the grip “from a little wet” is only useful in certain circumstances, in almost every other case dry hands will aide grip more.
Edit: I missed one thing: skin (and some absorptive fabrics and materials) soften when wet. This leads to a higher coefficient of friction. However, most non absorptive materials, when wet, have a lower coefficient of friction. Additionally, as I stated, too much water acts as a lubricant and lowers friction on most materials. So… It really depends on the materials and how much water there is water will make two materials grippier or slipperier.
You know when your shoes get really really old and the rubber soles are hard like plastic? You try walking on the linoleum floors at school and slip if you’re not too careful? Or when your shoes are caked in mud, you run into the house, then slide on the wood floor and fall on your butt? That’s kind of what’s going on. Your fingers need a regular amount of moisture to work properly and grip stuff. Too much and you lose grip again.
This is a question of friction. There are two main types of forces contributing to friction.
First we have literal roughness/unevenness in the surface (termed [Asperity](https://en.wikipedia.org/wiki/Asperity_(materials_science))) which means two surfaces can hook into each other, sort of like velcro, and your hands has a lot of these (e.g. finger prints).
The second is a bit less intuitive and is called the Van der Waals force. This can cause friction between smooth surfaces because the force comes from the atoms and molecules themselves. This is the reason you get a better grip on your cellphone case that is made of soft rubber than you get from the glass and hard plastic of the phone itself.
Beyond this it can often be hard to specifically determine what forces will dominate for a given scenario.^([1]) Climbers generally want to chaulk their hands completely dry to get a better grip on the rough surfaces they climb on. If the surface is really smooth then you might want to rely on the Van der Waals force instead, for instance by using indoor running shoes with soft rubber soles when in a gym with equally soft rubber flooring. However, be careful of any lubricant that can come between the smooth surfaces, as this will remove the Van der Waals force completely and make it extremely slippery.
For your specific example I would conjecture that somewhat wet hands strikes a good balance between using the Van der Waals force and the roughness between surfaces to obtain relatively strong friction for a variety of scenarios. Too wet hands could for example act as lubricant on the Van der Waals force. (Dry hands I am less sure of but I have a feeling it could have something to do with reduced surface contact)
>[1] The relationship between frictional interactions and asperity geometry is complex and poorly understood. It has been reported that an increased roughness may under certain circumstances result in weaker frictional interactions while smoother surfaces may in fact exhibit high levels of friction owing to high levels of true contact.” [wikipedia.org/wiki/Asperity](https://en.wikipedia.org/wiki/Asperity_(materials_science))
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