Three dimensional acoustic tweezers with acoustic vortex ...
Acoustic Tweezers: A further study
Transcript of Acoustic Tweezers: A further study
Outline
• Introduction about acoustic tweezers• Method of acoustic tweezers• Mechanism of acoustic tweezers
Introduction to acoustic tweezers
• Acoustic tweezers: Using acoustical method to trap small particles.
• Method: With an single transducer to generate pulse wave to capture particles.
transducer
Sound wave
Small particle
Transducerinput wave: continuous
Introduction to acoustic tweezers
wall or surrounding
black: transmitred: reflectstanding wave
standing wave is easily affected by surrounding
Method of acoustic tweezers
F V P=< ∇ >
First radiation force:
pF V P V Pt
∆= =< ∇ >= ∇ < >∆
For constant particle volume:
2
2[sin(2 2 ) sin(2 )sin 2
1 2 cos2i r i
g ir
T RF V P RR Rθ θ θθ
θ⎧ ⎫− +
= ∇ < > −⎨ ⎬+ +⎩ ⎭2
2[cos(2 2 ) cos(2 )1 cos2
1 2 cos2i r i
s ir
T RF V P RR Rθ θ θθ
θ⎧ ⎫− +
= ∇ < > + −⎨ ⎬+ +⎩ ⎭
Method of acoustic tweezersFlow chat
Simulate the time course of acoustic field :P
Calculate the gradient of the average P : ▽<P>
Calculate the force F
Use the iteration method to find the track of the particle
Mechanism of acoustic tweezers
Trapping model3. Wave leaves the particle, and acoustic field exerts no force on particle during PRI .
particle
wave Position A Position B
Mechanism of acoustic tweezers
Trapping model4. Viscosity will decrease the speed of particle
particle v
The force comes from viscosity
Mechanism of acoustic tweezers
Initial condition
ex: positiondensityvolume
Mechanism of acoustic tweezers
ex: wave formviscosityprfpressure..etc.
Particle track
Mechanism of acoustic tweezers
Pulse-Trapping system
Particle contacts with wave
Particle moves within PRI
second partfirst part
work time
second part (order): 104
first part (order): 1
Mechanism of acoustic tweezersFirst partWhen particle contacts with the sound wave
21( ) ( )( ) ( ) 2( ) ( ) ( )( ) ( ) ( ( ), ) ( ( ), )
v t t a t tx t t x tv t t v t a t ta t t a t A x t t t t A x t t
⎡ ⎤∆ + ∆⎢ ⎥+ ∆⎡ ⎤ ⎡ ⎤⎢ ⎥⎢ ⎥ ⎢ ⎥+ ∆ = + ∆⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥+ ∆ + ∆ + ∆ −⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎢ ⎥⎣ ⎦
A(x,t):=the acceleration at given time t and given position x
Mechanism of acoustic tweezersFirst part
acceleration caused by acoustic fieldacceleration caused by viscosity
When wave contacts with particle, viscosity can be ignored.
Mechanism of acoustic tweezersSecond part :During PRI
0 exp( )
dvm kvdt
dv k dtv m
kv v tm
= −
= −
−=
00
0
x1)tmkexp(v
km)t(x
)tmkexp(v
dtdxv
+⎥⎦⎤
⎢⎣⎡ −
−−=∴
−==
r6k πµ=
This imply: When PRI becomes longer, no significant change occurs.
μ : viscosity
r : particle radius
m : particle mass
Mechanism of acoustic tweezersWhen wave contacts with particle
Particle moves
Within PRI.
PRI:0.001 s
Phase plot
Mechanism of acoustic tweezersViscosity increase the chance of convergence
The velocity of the particle: -1*10-4 >2*10-5
Mechanism of acoustic tweezers
Without viscosity
Only three tracks converge
viscosity increases the converge range
Conclusion
• From the discussion above, viscosityplays an import role in the pulse trapping model.
• Although viscosity takes part of the trapping model, the sound wave still dominate the whole system.
• To obtain a better system stability, thewaveform should be smooth.
Future work
• To design a better waveform which mayincrease the stability
• Study all factors such as density,particle size and pressure etc.
• Study the stream flow which caused by acoustic pressure.