Flexibility, stroke, and dimensionless parameters: the importance of
telling the whole story for swimming micro-organisms in complex
fluids
Becca Thomases, UC Davis
Abstract:
Low Reynolds number swimming of microorganisms in Newtonian fluids
is an extensively studied classical problem, and the underlying
physics is well understood. However, many biological fluids such as
mucus are mixtures of water and polymers and are more appropriately
described as viscoelastic fluids. The question of how fluid
elasticity affects the swimming performance of micro-organisms is
complicated and has been the subject of many recent experimental and
theoretical studies. The Deborah number is typically used to
characterize the strength of the fluid elasticity in these studies,
and is expressed as the product of the elastic relaxation time and
the frequency of the swimmer stroke. In recent simulations of
undulatory flexible swimmers in an Oldroyd-B-type fluid, we find
that varying the frequency of the stroke OR varying the relaxation
time results in significantly different dependence of swimming speed
for the same range of Deborah number. Thus the elastic effects on
swimming cannot be characterized by a single dimensionless number.
The Weissenberg number is different dimensionless number used to
quantify fluid elasticity and it is defined as the product of
elastic relaxation time and characteristic strain rate. When the
swimmer is sufficiently flexible increasing the frequency of the
stroke will eventually result in a leveling off of the strain-rate
and it is in this regime where the Deborah number is no longer equal
to the Weissenberg number. This difference is due to the
introduction of another time-scale, the body elasticity time-scale.
We conjecture that the different swimming speeds for the same range
of Deborah number is a consequence of a "stroke-stabilizing" effect
that fluid elasticity has for flexible swimmers, in addition to a
Weissenberg-number transition in the fluid which depends on the
amplitude of the swimmer stroke.