acoustic tweezers: a further study

Acoustic Tweezers:A further study

9512535 丁孝鈞

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


-30 ns to foci

Gradient plot0 ns to foci

30 ns to foci

Method of acoustic tweezersThe net force of a particle

The force-axis diagram at given time T

Method of acoustic tweezersIteration method


Track of particle

Converge → S.H.M. → being captured


Unbound track

Track converge

Mechanism of acoustic tweezers

Trapping model2. Shake the particle1. Contact

particleparticle

wave


Trapping model3. Wave leaves the particle, and acoustic field exerts no force on particle during PRI .

particle

wave Position A Position B


Trapping model4. Viscosity will decrease the speed of particle

particle v

The force comes from viscosity


Initial condition

ex: positiondensityvolume


ex: wave formviscosityprfpressure..etc.

Particle track


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 tweezersA tool which may be able to help study the system

Phase plot

Mechanism of acoustic tweezersWhen wave contacts with particle

Particle moves

Within PRI.

PRI:0.001 s

Phase plot

Mechanism of acoustic tweezersConverge to the same point

Mechanism of acoustic tweezersBlack: without viscosity

Blue: with viscosity

Mechanism of acoustic tweezersViscosity increase the chance of convergence

The velocity of the particle: -1*10-4 >2*10-5

Mechanism of acoustic tweezerswith viscosity

all tracks converge to -25μm


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.

Thanks for your attention

acoustic tweezers: a further study

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