Page 198 - Bio Engineering Approaches to Cancer Diagnosis and Treatment

8.2 Approved modes for ultrasound therapy 197

Table 8.4 Types of acoustic streaming and specifications [9].
Streaming Assumptions Characteristics
Slow U << u Re << 1 U ∝ u U ∝u
0 19 0 1 U <<u19Re<<1
1
0
0
F (acoustic force) ∝ α u 2 1 F (acoustic force)∝αu12
u ( ⋅∇ u ) (Convective acceleration) 0 (u⋅∝)u (Convective acceleration)∝0
≈
Fast U ≥ u R ≥ 1 For coarse-grained streaming, U ≥u19Re≥1
2+
n
0
0 19 e U ∝ α u 1 , n is value for U ∝αu12+n
0
0
nonlinearity of the wave,
u Convective acceleration)
u ( ⋅∇ ) ( u⋅∝uConvective acceleration
Is significant.
Coarse-grained Traveling acoustic wave Streaming away from sound source
(multidimensional) from single source along into viscous fluid. The Reynolds
Eckart an axis number determines whether
L (characteristic length the streaming is fast or slow. *****
scale) >> λ L >>λ
Re = ρ U Re*****=ρfU *****µ
L f 0 µ 0
One-dimensional u ( ⋅∇ u ) = 0 Streaming away from sound
Eckart source into unbounded fluid. The u⋅∝u=0
Momentum equation is Reynolds number determines
linear. whether the streaming is fast or slow.
Traveling acoustic wave L
from single planner source Re L = ρ f U 0
with L >> λ µ Re*****=ρfU *****µ
*****>>λ
0
Medium-grained Acoustic wave bounded The Reynolds number determines
(Rayleigh) along sound propagation whether the streaming is fast or slow.
path: standing acoustic L
wave. Incompressible Re L = ρ f U 0
everywhere and inviscid in µ Re*****=ρfU *****µ
0
bulk of fluid Vortex flow; the scale of the vortices
is approximately the same as the λ.
Analysis valid only outside viscous
boundary layer.
Fine-grained Acoustic wave The Reynolds number determines
(Schlichting) bounded along sound whether the streaming is fast or slow.
propagation path: L
standing acoustic wave. Re L = ρ f U 0 µ Re*****=ρfU *****µ
Classical assumptions: 0
incompressible everywhere Bounded along sound propagation
and inviscid in bulk of fluid. path: standing wave. Vortex flow; the
scale of the vortices is approximately
the same as the λ.
U 0 , streaming velocity; u 1 , acoustic particle velocity.
of the sound flow for 80°C water to be increased by 50% between two rigid parallel
plates. For particles of the same density as the fluid, the effects of viscosity on the
ultrasound force are negligible, but as the density of particles increases, the viscosity
effects increase by up to 30%.