Fick’s Law states that the net diffusion rate of a gas across a fluid membrane is proportional to the difference in partial pressure and the area of the membrane, and inversely proportional to the thickness of the membrane.
How could Fick’s Law affect Harrison Odjegba Okene’s survival after a boating accident?
Harrison Okene’s story of survival began in the early hours of May 26, 2013 when a rogue wave capsized a tugboat off the coast of Nigeria. Okene, the ship’s cook, had awakened early and was in the bathroom when the boat began to sink.
According to Okene, the remaining eleven crewmembers were all locked in their cabins as a safety precaution against pirates who regularly robbed and abducted vessels in the area. Unfortunately, this safety measure apparently doomed the sleeping crewmembers.
Okene’s story is that he eventually made his way to the engineer’s office, where he found a small pocket of air. By this time, the boat had come to rest upside down 30 meters (100 feet) underwater on the sea floor. Almost naked, and with nothing but a bottle of Coke, Okene appeared doomed to die a slow death. Alone and terrified, Okene said he could hear what he believed were the sounds of sharks devouring the bodies of his crewmates.
Divers from a neighboring oil-rig were sent to the scene. This was not a rescue operation, and four bodies had already been pulled out of the wreck. Miraculously, however, they found Okene alive. In the YouTube video showing his rescue, one of the divers sees and reaches for the hand of what he believes is a body floating in the cold murky water. To his shock, almost as out of a horror movie, the hand moves and grabs him. Shock and fear eventually give way to joy as the diver says, “He’s alive!” How did Okene survive trapped in a cramped room underwater for sixty hours? Can science explain his miraculous survival or is there more to this story?
Okene’s Survival as a Science Problem
Air is made of mostly nitrogen (78.084%) and oxygen (20.946%) with trace amounts of carbon dioxide (0.0314%). As a person exhales, this percentage changes; oxygen falls between 16-17% and while carbon dioxide rises somewhere between 4-5%.
As a result, a person trapped in an enclosed room faces a major problem. From the first breath, the concentration of carbon dioxide will quickly rise and become toxic. Depending on the size of the room, a person could asphyxiate in a matter of hours. Remarkably, Okene managed to survive in a small room for over two days. How exactly did he do this?
As the boat sank and turned over, the trapped air pocket acted as a diving bell; a type of chamber that is open at the bottom where the pressure of the water keeps air trapped inside the bell. This air bubble could have played a role in Okene’s survival. To understand how this took place, we must understand the master of this device, the diving bell spider.
Diving Bells as Breathing Gills
The diving bell spider (Argyroneta aquatic) constructs a ‘diving bell’ out of silk, which it attaches to an underwater plant. This underwater bubble can exchange gases with the water. Very little was known about the conditions inside the bell, or how much gas exchange occurred across the membrane, until a 2011 paper by Roger Seymour, PhD, a University of Aselaide biologist.
To measure the oxygen in these tiny bells, biologists use optodes, oxygen-sensitive fiber optics that can continuously measure oxygen levels. Ole Pedersen, a biologist who studies physical gills at the University of Copenhagen, tells Decoded Science, “the ability of an oxygen optode is based on the quenching of a lumiphore.” A lumiphore is the part of a molecule that is responsible for light emission. Quenching, in physics terms, means this luminescence is either stopped or diminished.
In an interview with Decoded Science, Pedersen explained that they send blue light through an optical fiber where the tip of the fiber is coated with the lumiphore. When there is no oxygen present, the lumiphore becomes excited and emits light of a different wavelength; a process known as Stokes shifting. The researchers measure the intensity of this light. However, molecular oxygen quenches or diminishes the light produced, this allows them to determine oxygen concentration.
Researchers can measure without disturbing the animal, as these gas sensors are tiny, and Seymour observed that spiders ignore the optical probe when the scientists place it inside the spider’s bubbles. By measuring the gas changes of bubbles, both with and without spiders, scientists can measure how much oxygen the spider consumes – and determine gas exchange across the bubble’s surface.
As the spider consumes oxygen and breathes out carbon dioxide, the partial pressures of these three gases change as described by Dalton’s Law—the total pressure of a gas is the sum of all the partial pressures of the gases inside. This creates a pressure imbalance between the various gases in the bubble and the dissolved gases in the water. The oxygen partial pressure decreases while carbon dioxide partial pressure increases.
Gases diffuse across the bubble’s surface as they move from areas of high pressure to low pressure; oxygen dissolved in the water passes through the bubble’s surface and into the bubble while carbon dioxide inside the bubble dissolves into the water. The rate at which gases diffuse across a fluid membrane or in this case, the bubble interface, is determined by Fick’s Law. This law, derived by German physiologist, Adolf Fick, in 1855 explains how your lungs are able to transport and exchange oxygen across the membranes of the small balloon-like structures called aveoli.
If there were enough dissolved oxygen in the water, a bubble could supply all a spider’s breathing needs, provided the bubble does not collapse in on itself. The pressure inside a bubble depends on two things—how deep underwater the bubble is, or the hydrostatic pressure, and the curvature of the bubble, or the Laplace pressure.
In his 2011 paper, Seymour noted for an empty diving bell, the internal pressure of the gases will always be greater than the dissolved gases in the water and its volume decrease. This very slow process can take 21 days to reach half the original volume. As the bubble shrinks, the Laplace pressure increases, hastening the bubble’s demise.
With a spider present, a bubble takes 37 hours to reach half its original volume. Despite uptake of oxygen from the water, the bell collapses because nitrogen is continually lost to the water due to an increase in the nitrogen partial pressure. The diving bell spider must frequently go to the surface to trap air between its hind legs and abdomen to fill its air bubble. If it did not, the bubble would eventually collapse and drown the spider.
A Human Breathing Gill
Dr. Neil Shirtcliffe of Nottingham Trent University is a member of the McHale/Newton Research Group, and studies the physics of water-repelling surfaces. He and his team have calculated that a bubble with surface area 90m2 – or diameter of 2.8 meters- is enough to provide enough oxygen for a human being.
This bubble is different from the diving bell the diving bell spider uses; Shirtcliffe’s bubble is based on a special non-collapsible bubble known as a plastron. These bubbles are permanent, with stiff supports or hydrophobic hairs, such as those along the abdomen and legs of the diving bell spider, to hold the air/water interface steady. MIT mathematician, Dr. M. Flynn described this “hair pile” design in a 2008 paper by MIT mathematician, Dr. M. Flynn.
Shirtcliffe tells Decoded Science, “As the bubble dissolves into the water, the air/water interface takes on a shape like a U between each support. If they are close together, the curvature of the interface can then allow for a much lower pressure inside the bubble than outside.” So although it is possible for a bubble to provide enough oxygen for a person to breathe, the bubble in which Mr Okene was sitting is not likely to be this type. His bubble will eventually collapse but this doesn’t mean that it will do so quickly. Some insects use simple collapsible bubbles that can last a surprising amount of time.