Between the filaments, the space is divided by the thin secondary lamellae, creating tiny channels for the water. Each secondary lamellum contains a sheet of blood, one cell thick, flowing in the direction opposite to the water. Consider the medium. Water is 800 times as dense as air. Water, by contrast contains only about 10 ppm oxygen and under stagnant conditions this may drop much lower.
Fish have to be more efficient.
Surface tension of water clinging to the gill collapses the lamellae and the effective surface area is reduced to a tiny fraction of normal. Catfish survive better than most other fish because they have cartilage supports for the primary filaments and have the secondary lamellae thickened and separated more than usual. Hemoglobin in the blood will react with the oxygen to form oxyhemoglobin, keeping the DO low and high. As a result one ml of blood will carry as much oxygen as 15 - 25 ml of water. Hemoglobin exhibiting the Bohr effect will require a higher oxygen tension to fully load under conditions of low pH. Hemoglobin showing the Root effect can never be fully saturated with oxygen when pH is low.