Page 478 - Handbook of Biomechatronics

472 Ahmet Fatih Tabak

physical constraints allow, a Newtonian liquid will start exhibiting viscoelas-
tic behavior with the influence increasing actuation frequency, although this
is not expected under normal conditions.
As it should be obvious to the reader by now, the nondimensional anal-
ysis is meaningful if only the physical limits are observed properly. For
instance, increasing the actuation frequency while studying Re, Sp, Mn h ,
or De numbers of a magnetic micro-swimmer with an elastic flagellum does
not necessarily mean something impressive will happen as there are two pos-
sibilities at the extremum: either the elastic tail will lose structural integrity at
some point, or the deformation will go to zero as viscous friction will simply
overwhelm structural deformations. Furthermore, even before structural
failure occurs, the step-out problem comes to the attention. Step-out hap-
pens when the magnetic body cannot properly follow the magnetic field
(Tabak et al., 2011). The magnetic field might rotate sweeping all quadrants
or just oscillate, as depicted in Fig. 4, with a smaller reciprocating angle.
However, if that rotation or oscillation is very rapid than the magnetic body
will not be able to align itself properly, regardless of the angle swept by the
external magnetic field. In other words, if the viscous torque to overcome in
order to instantaneously align with the magnetic field is higher than the mag-
netic torque, desired wave propagation will not be achieved. Should this
condition arise, step-out phenomenon will be observed with elastic and
rigid tails alike.

Fig. 4 Depiction of an autonomous micro-swimmer with passively deforming elastic
tail, reacting to the oscillation of external magnetic field vector, B (T). The consecutive
realignment to the field-oscillation produces reciprocating elastic motion along the tail.
As a result, the time-irreversible planar wave propagation is induced pushing the head
in the opposite direction.