11
FIG. 7. (Color online) Acoustic energy
Eac(t)
/
Efd
ac(∞)
Eq. (13) (light green), streaming velocity
vstr(t)
/
vfd
str(∞)
Eq. (33) (medium purple), and streaming ratio (t) Eq. (34)
(dark brown, right ordinate axis). The gray background indicates
the time intervals where the actuation is turned off.
(a) Constant actuation for 0 < t < 3000 t0. (b) Actuation
on for 0 < t < 200 t0 followed by no actuation for
200 t0 < t < 1000 t0. (c) Actuation on for 0 < t < 30 t0
followed by no actuation for 30 t0 < t < 1000 t0.
radiation force-dominated motion of smaller particles,
we need to achieve a smaller value of . Obtaining a
value of = 0.8 at time tend, implies that the ratio of
the relative displacement due to the streaming-induced
drag force and the radiation force for the time interval
0 < t < tend is 20% lower than in the periodic state, corresponding
to a 20% reduction of the critical particle size
for acoustophoretic focusing, defined in Ref. 2, assuming
the particles can be focused during the time interval
0 < t < tend.
Figure 7(a) shows
Eac
,
vstr
and during the buildup
towards the periodic state. approaches unity slower
than
vstr
because is an integration of the streaming
and radiation contributions, whereas vstr probes the
instantaneous magnitude of the streaming flow. Figure
FIG. 8. (Color online) The same probes as in Fig. 7 but for
the following pulsed actuation schemes: (a) actuation is on
for 500 t0 followed by no actuation for 500 t0 repeatedly, (b)
actuation is on for 200 t0 followed by no actuation for 200 t0
repeatedly, and (c) actuation is on for 30 t0 followed by no
actuation for 210 t0 repeatedly.
7(b) and 7(c) show
Eac
,
vstr
, and when the actuation
is turned off at t = 200 t0 and t = 30 t0, respectively.
When the actuation is turned off,
Eac
decays faster
than
vstr
and thus begins to increase more rapidly,
reaching = 0.8 around t = 1000 t0 in both cases. From
the results shown in Fig. 7 it does not seem advantages to
turn off the actuation, as this only causes to increase
faster than for constant actuation. Figure 7(c) further
shows that when the actuation is turned off,
Eac
immediately
begins to decay, whereas
vstr
continues to
increase for some time, due to the present acoustic energy
in the system that still provides a driving force for
the streaming flow.