Study of "acoustic tweezer" chip for particles driving

: Surface Acoustic Wave (SAW) is one of the sound waves that travel parallel to the surface of an elastic material, and is capable of manipulating microparticles. This SAW device was named acoustic tweezers. Acoustic tweezers possess advantages of energy-efficiency, small size and easy-to-produce. Herein, we developed an acoustic tweezer chip to sort microparticles of different sizes. The chip consists of a pair of interdigital transducer (IDT) and a PDMS microfluidic channel. The IDTs generate the surface acoustic wave which acts on the particles in the microchannel. Finally the sorting of particles can be seen.


Introduction
Acoustic tweezers, the system which use sound as tweezers, are so small and can be placed on a chip to manipulating micron or nanometer sized particles [1,2] .
The energy consumption of acoustic tweezers is less than 500 thousand times [3] , which is much less than that of optical tweezers. Due to its small size, acoustic tweezers can be made by standard chip processing technology, so it has the possibility to be widely used.
Acoustic tweezers work through establishing a continuous surface acoustic wave. If the two sound sources are interrelated and each sound source produces the sound of same wavelength, then there will be a point which makes the related sounds cancel each other out, this point can be seen as the trough. Because sound waves have pressure, which can drive very small objects, so micro or nano particles move with the sound waves until the sound waves reach the trough, then the particles will fall to the trough and no longer move. If the sound comes from two parallel acoustic sources, the troughs will form a line or a series of lines. And if the sound source is perpendicular to each other, the troughs will form evenly spaced lines or columns like a chessboard. Also, these particles will also be pushed to places where the sound no longer moves.
Because of its versatility, low energy consumption, simple technology, miniaturization and so on, acoustic tweezers show obvious advantages. Acoustic tweezers will be used as a tool for (biological) tissue engineering, cell research, drug screening and so on.

Research on separation principle
The particles in the channel, as shown below, are affected by 4 forces, there are gravity, buoyancy, surface acoustic wave (SAW) and medium viscous force. In the vertical direction, gravity and buoyancy are balanced, so as to the motion of particles, we only need to consider the surface acoustic wave and viscous force in the horizontal direction. The acoustic radiation force comes from the interaction between particles and sound waves; the expression of the acoustic radiation force of particles by the acoustic surface standing wave produced by interdigital transducer is given below [4][5][6] : Equation (1) is the calculation of surface acoustic wave(F r ), therefore, without considering the environmental factors, the main factors affecting the surface acoustic wave(F r ) are wavelength(λ), particle volume(V p )， φfunction and sin(2kx). Obviously, the larger the wavelength(λ) is, the smaller the surface acoustic wave (F r ) is. When the wavelength(λ), particle and medium is constant, the surface acoustic wave depends on sin(2kx), k represents the wave vector, x is the distance between the particle and the node.
According to the picture above, when the particles are between the antinode and the node of the wave, the farther the particles are from the wave node, the larger the surface acoustic wave (F r ) is, so as the other way. So the particles will move towards the pressure node under the effect of surface acoustic wave (F r ), after reaching the pressure node, the force of the particles will disappear, and then stop at the node position.
To different particles in the same position，the surface acoustic wave (F r ) depends on the particle volume(V p ) and φfunction. Equation (2)  Equation (3) is the calculation of viscous force (F v ) [7] , so for particles of different sizes, viscous force (F v ) depends on the radius of the particle(r).
So when the particle size increases, the increase of surface acoustic wave (F r ) will be more than the increase of viscous force (F v ). In other words, the larger the particle, the larger the resultant force of F r and F v , and then particles move faster and more clearly. So the larger particles move faster than the smaller ones, which cause the separation of large and small particles.

The design of interdigital transducer
The chip includes interdigital transducer and PDMS microchannel, select the appropriate substrate, the PDMS microchannel is processed in the middle of the substrate and the interdigital transducers are processed on both sides.

Interdigital transducer(IDT)
In the whole system, interdigital transducers convert electrical energy into acoustic energy, and then acoustic energy is used to drive particles. In the design of interdigital transducers, we consider the following conditions. First of all, the interdigital transducers produce surface acoustic wave standing wave [8] , to achieve SAW with a high coupling coefficient, we choose Y+128°X-propagation lithium niobate (LiNbO 3 ) wafer (500 mm thick) as the substrate. For the design of interdigital transducers, acoustic wave length should be 300um, so the width and pitch of the IDTs were 75 mm and 150 mm [9] . The acoustic aperture is 16mm, there are 20 pairs of IDT, and the distance between one pair of IDTs is 8mm. As shown in the following picture: So our signal frequency is set at 12.6 MHz.

PDMS microchannel
In the design of microchannel, considering the particles move to the pressure node or antinode under the action of SAW, we set the width of the microchannel half a wavelength (150um), so we can guarantee the separation position. The model is as follows:

experiment of particle manipulation
In the experiment, we inject liquid by injection pump. As

Summary
Based on the unique advantages of acoustic tweezers, a particle sorting chip is designed in this paper. It produces surface acoustic wave by applying the pumping signal to