Consider a spherical colony of microorganisms having an effective diameter of 0.1 mm in stagnant water at 25°C that is neutrally buoyant, i.e., not floating up or down. Oxygen diffuses through water...

Consider a spherical colony of microorganisms having an effective diameter of 0.1 mm in stagnant water at 25°C that is neutrally buoyant, i.e., not floating up or down. Oxygen diffuses through water to the surface of the microorganisms where it is completely consumed, maintaining a zero concentration at the surface. Oxygen in the bulk water is in equilibrium with air (21 % oxygen). Henry's constant for oxygen and water is 4.4x 104atm/mole fraction at 25°C. Diffusivity of oxygen in water is 3.25x 10- 9 m2 / s and density of water is 1000 kg/m3• 1) Write the governing equation for oxygen diffusion in water at steady state, considering radial variation only. 2) Write the boundary conditions needed. 3) Solve for the oxygen concentration profile as a function of radius (leave in terms of symbols). 4) Calculate the oxygen concentration in bulk water in mol/ m3 assuming air and water are in equilibrium. 5) Calculate the rate of oxygen consumption by the microorganism colony in mol/ m2 -s.