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 D_AB = 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 ∆p_A = 860 x 10^-12 kg/m³. Assuming a propulsion efficiency of η = 0.5, determine the maximum speed of the E. coli. Report your answer in body diameters per second.

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D= 2 um Water and nutrient Flagellum T= 37°C Electrochemical engine Escherichia coli