"My brother is too kind. He was eminent when my eminence was only imminent." -Niles Crane
Question #91747 posted on 10/18/2018 9:36 a.m.
Q:

Dear 100 Hour Board,

Does water have enough surface tension that an ant (maybe your average small, black kitchen ant) could walk across it? Conversely, how much surface tension would a liquid have to have for a human to walk across it? Is such a liquid possible?

-the mad hatter

A:

mad hatter,

Beautiful question. Just beautiful. 

Short answers:

  • no
  • 587170 mN/m
  • depends on your definition of "possible", "liquid", and how exclusively it needs to be caused by surface tension.

Explanation:

I'm not a physicist or an entomologist. If a professional were to proof this, they would likely find many errors. But I probably know more about it than you do because now I've been reading about it for like six hours. 

The potential in your first question r e a l l y depends on the ant, and I wouldn't call it "walking." Ants have a lot of different sizes and a lot of different instincts. Black kitchen ants in the western US are much smaller than the mammoths back home in Maryland.  But there aren't any species I know of that can really "walk" on water. Even bugs who are designed to travel on the surface aren't so much picking up their legs and walking, as they are pushing through the surface layer.

Maintaining surface tension is not strictly about mass. It's about weight distribution and the pressure placed on individual bonds between water molecules. Think of a needle laying on top of fabric vs the needle being stabbed through the fabric. Singular ants are often small enough not to break the surface tension of water. Their exoskeletons are hydrophobic which helps a lot. But after a few minutes the ant will sink. Their tiny legs break the surface tension because of the pressure applied at the point of the leg without being distributed. Water skeeters (or the Gerridae family) on the other hand, distribute that pressure with tiny hairs all along their legs that allow them to push through the surface layer of the water without breaking it. 

Red ants (Solenopsis invicta) have a rafting instinct to save the colony in the event of flooding. They lock their mandibles together, forming tight pockets of air between them. The air bubbles help distribute the weight to prevent the specified pressure on the water bonds. The colony can float for weeks while they wait for floodwaters to subside. So, yeah they can sit atop the surface layer but that's about it. Too much motion or release of the air pockets could penetrate the surface tension and, depending on the density of the ant, it would sink or at least get waterlogged. 

Technically, maintaining surface tension is a different phenomenon than floatation.  Floatation is a relationship between density, buoyancy, and maybe viscosity. You can get wet with water and still float. But if you get wet you've broken the surface tension. 

Basically, water skeeting(riding the surface tension) requires a certain relationship between the weight, the perimeter(or area) of the contact point, and the angle of the contact point. Human feet have many angles and contact points so it would require a liquid with enough surface tension (exerted force when stretched) to constantly out compete your weight/foot area/contact angles relationships. 

Surface tension is the force F per unit length L exerted by a stretched liquid membrane. Think of stretching a rubberband and how much force is waiting to be released. It's like that, only recognizing that such force is already being applied on your finger, and can be measured in terms of F over L. So how much force is being exerted by water when it gets stretched? Usually about 73 millinewtons (mN) per meter (m). 

Mercury has the highest surface tension relationships of any known element usually at around 485 mN/m. Converting that to pound-force you get .11 lbs/m. So mercury can support .11 pounds for every meter of contact. So a 132 pound human (such as myself) would require 1200 meters (3937 feet) of contact to maintain surface tension on a pool of mercury. I would basically need to be flattened into a very thin sheet of mass. Without being flattened out like that I would sink and bob until I reached equilibrium. That would probably submerge me partially and then flip me to have the most surface area distribution a.k.a laying flat. 

The average adult foot is about 1 meter. For simplification we won't talk about contact points and angles of that foot, or those of a foot in motion. But since walking requires one foot at a time and it is a very convenient conversion factor, we're going to use it. You need a liquid that can support 132 pounds over only 1 meter. The force of that liquid would have to be 132 pounds. Or, for the sake of comparison with mercury's 485 mN/m, it would have surface tension of 587170 mN/m. That is a very active amount of energy stored in the surface of a liquid. Like a swimming pool that is also a trampoline that also isn't defined by viscosity.

That brings me to non-Newtonian fluids. If you don't know what those are you should check out this video. Non-Newtonian fluids are about non-static viscosity. Not surface tension. These things can behave as both a liquid and a solid depending on the force applied to them. So they get the "walking on liquid" job done quite nicely. Whereas a liquid with high surface tension holds things up by applying force, non-Newtonian fluids hold things up by having force applied and becoming more solid. If you could have a liquid that was both non-Newtonian and had a high enough surface tension, the force would be applied to itself and it would act as a solid. Which actually turns out to be pretty boring because now it's just a solid. So I guess that's how we get trampolines. 

There you have it! Bonus analysis: If Jesus altered surface tension to walk on water he would have had to make up for pretty much his entire body weight in exerted force on a 1 meter foot. Scholars estimate that he was probably about 5'1 and weighed about 110 pounds. He was probably pretty muscular based on his profession, maybe with some atrophy at the time of the miracle. So he might have weighed a little more. So we're looking at maybe like a spiritual pound-force of 120?

Some other videos for your imagination:

Mercury + non-Newtonian fluid

Non-Newtonian fluid + hydraulic press

 

Babalugats