Numerical Simulation of Cell Motility at Low Reynolds Number

As length scales decrease to microns, the mechanism for swimming becomes unfortunately counter-intuitive. In the macro-world, where human intuition has developed, we swim by accelerating the liquid around us. For microorganisms, which swim at Reynolds numbers much less than unity, Stokes law does not permit accelerations. As such, the fluid movement is governed entirely by the local boundaries of the microorganism and the fluid viscosity dampens velocity fluctuations rapidly as distance away from the swimmer increases. A well known byproduct of this, Purcell’s “Scallop Theorem”, forbids reciprocal motions to generate net forward movement [1]. To overcome this, flagella propagate waves down their length and cilia have asymmetric beats. This type of motility has been described as zero-thrust swimming since the net force on the organism-fluid system must be zero [2].