Question

1.

Swimming without inertia

For swimming microorganisms, only the linear drag will be considered, i.e.,~f=−b~v Imagine an extremely aggressive microbe is trying to escape this linear drag regime by giving itself a once-in-a-lifetime kick associated with an extraordinarily high initial velocity.

1. Considering the microbe is a sphere of diameter D , and the linear drag coefficient is thus b = 3πηD , where η is the dynamic viscosity, derive the natural time τ (tau) (the time scale characterizing the exponential decay of the speed) for this microbe.

2. The microbe starts off at v_x(t= 0) =v_x_0 = 1 cm/s (that is 10^4 body length in a second!). Use D = 1 μm, ρ = 1000 kg/m^3 ,and η = 10^( − 3) Pa · s to find how far the microbe can travel with this once-in-a-lifetime kick.

3. How high should the initial velocity be if the microbe needs to make a trip of 1 mm long? Was the linear drag still a good approximat

Answer 1