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9.5 Acoustophoretic motion of particles in a PDMS microchannel using SAW 241
0 (
ρ + ρ + ρ ∂ t )( v + v )
2
1
2
1
−
=−∇ p ( 0 + p + p ) ( ρ + ρ + ρ 2 v ( ) ( 1 + v )∇ v )( 1 + v ) + η∇ 2 v ( 1 + v ) (9.22)
1
2
0
1
2
2
2
∇
+ βη (∇ v ( 1 + v ) ) ρ +ρ +ρ ∂tv +v =−∇p +p +p −ρ +ρ +ρ v +v ∇v +v +η∇ v +v +
2
2
0 1 2 1 2 0 1 2 0 1 2 1 2 1 2 1 2
βη∇∇v +v
ρ ∂ t v = −∇ p +∇ 2 v + βη∇ (∇ v ) ρ ∂ t 1 ρ 0 v ( ∇ v ) 1 (9.23) ρ ∂tv =−∇p +η∇ v +βη∇(∇v )−ρ ∂tv 1 2
v −
η
−
1
2
2
2
1
2
0
1
2
2
1
2
0
2
2
−ρ (v ∇)v
It is obvious that the time averaging of the second-order fields will generally be 0 1 1
nonzero, and during the time averaging, the first-order product term will come as the
source term on the right of the governing equation.
The nonzero velocity v is called the acoustic flow, where the bulk fluid moves v
2
due to the viscous stresses produced in the fluid near the wall, when the acoustic 2
wave oscillation velocity has to be zero due to the nonslip condition. The nonzero
pressure p , increases the acoustic propagation force due to the scattering of the p 2
2
acoustic wave on the particle and causes acoustophoretic motion of the particle.
9.5 Acoustophoretic motion of particles in a PDMS
microchannel using SAW
The importance of particle manipulation methods is well known in the last decade.
Different methods including passive and active methods were applied so as to
improve the manipulation of cells. Precise handling of particles both in active and
passive methods depends on the efficient design and correct analyis of fluid-par-
ticle interaction and imposed external field in microchannel. SAW as a label-free
approach, brings this opportunity to separate biocells efficiently without any dam-
ages to cells. Clear surface of PDMS lets exact monitor of cells by microscope and
since the acoustic pressure field shape well and efficient in a microchannel with
PDMS wall, it made as a popular method to separate or sort biocells.
Numerical investigation of particle motion in a microchannel is studied. In this case,
the perpendicular section to fluid flow is considered and acoustofluidic motion is dis-
cussed. A rectangular section has 600 µm width and 125 µm height. The working fre-
quency is 6.65 MHz and the wavelength is 600 µm which fits in the channel width.
Particle materials are polystyrene and fluid is water. The acoustic contrast factor of poly-
−1
styrene in the water is positive. Polystyrene diameter is 10 µm with 249 Pa compress-
−1
3
3
ibility and 1050 kg/m [79]. Water density is 997 kg/m and its compressibility is 448 Pa
[79]. The section of this channel is illustrated in Fig. 9.10. The effect of the PDMS wall
and Lithium Niobate is considered as a boundary condition on the fluid domain.
The primary radiation force imposed on spherical particles to separate cell in the
standing ultrasonic field is:
π PV β 4π x
2
F =− 0 p f ( φβρ )sin (9.24)
R 2λ λ FR=−πP02Vpβf2λφ(βρ)sin4πxλ
5ρ − ρ β
( φ βρ = p f − p (9.25)
)
2ρ + ρ f β f φ(βρ)=5ρp−ρf2ρp+ρf−βpβf
p
