Motile bacteria are equipped with flagella that are rotated by tiny, biological electrochemical engines which, in turn, propel the bacteria through a host liquid.
Consider a nominally spherical Escherichia coli bacterium that is of diameter D = 2µm. The bacterium is in a water-based solution at 3rC containing a nutrient which is characterized by a binary diffusion coefficient of DAB = 0.7 x 10-9 m2/s and a food energy value of N = 16,000 kJ/kg. There is a nutrient density difference between the fluid and the shell of the bacterium of ?pA = 860 x 10-12 kg/m3. Assuming a propulsion efficiency of ? = 0.5, determine the maximum speed of the E. coli. Report your answer in body diameters per second.