Manipulation of microparticles using phase-controllable ultrasonic standing waves

Forces acting on particles because of the scattering of ultrasonic waves^1,2 have proved effective in the manipulation of microparticles.³ This has led to substantial interest in the use of ultrasonic devices to manipulate biological cells,⁴ with applications including aggregation,⁵ separation⁶ and sensing.⁷ Many of these applications rely on the use of resonant standing waves and move the particles to positions determined primarily by the geometry of the device.^4–7 There has been recent interest in developing methods to trap and then move particles using the acoustic force: approaches include using focused transducers⁸ (in a manner analogous to optical tweezers) and mode switching between resonant states.^9–11 Here an alternative method of trapping and moving particles at arbitrary positions, which uses spatially controlled standing waves, is proposed and demonstrated by manipulating $5μm$-radius polystyrene spheres. This approach has significant advantages, in terms of the simplicity and flexibility of the device, over previous attempts to controllably manipulate particles using ultrasound. First, the monotonic relationship between a user-variable property of the input signals (the phase difference) and the particle position allows straightforward control of particle positions. This does not require detailed knowledge of system modes or calculations based thereon, as is the case for existing mode switching approaches and is not restricted to a limited set of nodal positions based on device geometry. Second, the device can be operated in a narrow frequency band that allows the transduction system to be optimized which, for example, allows the exploitation of the relatively high Q values of piezoceramics. Third, as the approach does not rely on establishing a standing wave throughout the device so it may be operated with pulsed excitation which leads to more rapid force variation, particularly where the chamber is many wavelengths across.

The principle of operation is to produce a standing wave in a liquid-filled cavity using counter-propagating traveling waves with a controllable phase difference between them. The traveling waves are generated by opposing piezoelectric transducers at either end of the cavity. The transducers are acoustically matched to the liquid to minimize resonances within the cavity. If the field amplitude generated by each transducer is the same then a standing wave pattern is generated with nodes positioned at half-wavelength separations. The acoustic radiation force exerted by the plane standing wave acts to move dense particles to the nodes of the pressure field.¹ Assuming that there is negligible reflection from the transducer faces, the position of the nodes changes linearly with the relative phase, $ΔΦ$⁠, between the excitation signals applied to the transducers.

Figure 1 shows a schematic diagram of a prototype device. The device can be divided into a levitation stage, which holds the particles against gravity in the $y$-direction, and a manipulation stage, which traps the particles in the $x$-direction and allows them to be moved in that direction. The levitation stage is a resonant system comprising a 5 mm-thick piezoceramic plate $(15mm×15mm)$ separated from a 1 mm-thick glass reflector by a 4 mm-thick water-filled cavity. The manipulation stage consists of two identical transducers placed facing each other. Each transducer comprises a $15mm×2mm$ section of 1.33 mm thick piezoceramic plate, with doped-epoxy matching and backing layers. A one-dimensional electro-acoustic transmission line model^12,13 was used to determine suitable thicknesses and acoustic properties for these layers, in particular the matching layer impedance, $Zm$⁠, would ideally be related to the impedances of the transducer $ZT$ and the water $Zw$ by the relationship $Zm=(ZwZT)1/2$⁠. The experimental results of Wang et al.¹⁴ were then used to select suitable epoxy dopant compositions to achieve the desired acoustic properties. The resultant $Zm$ is within 50% of this optimal value, however it still provides sufficient matching the present device to this work. The thicknesses (in the x-direction) and material properties of the components of the transducers are summarized in Table I.

A minimum in the reflection at the transducer faces occurs when the frequency is such that the thickness of the matching layer is equal to 3/4 of the wavelength within it. Theoretically this was expected to occur at 5 MHz for the current device, but in practise the best operation was found at 5.25 MHz. Each transducer was excited using a separate sine-wave generator and an amplifier to apply a sinusoidal voltage of $35Vp-p$⁠. The sine-wave generators were phase-locked to allow control of $ΔΦ$⁠. At this frequency a standing wave of wavelength $λ=0.28mm$ in the water was produced. The acoustic pressure field was imaged with a Schlieren imaging¹⁵ system in the absence of particles and with no excitation of the levitation stage, and was observed to form broadly uniform planes perpendicular to the $x$-axis. By varying $ΔΦ$ in the range $0≤ΔΦ≤2π$ it was possible to move the pressure field nodes one complete period in the x-direction (i.e., a distance of $λ/2=0.14mm$⁠). This behavior is shown in the Schlieren images in Fig. 2(a).

Having demonstrated the ability to control the nodal positions of the acoustic pressure field, spherical polystyrene particles (radius, $5μm$⁠; density, $1050kgm−3$⁠; longitudinal bulk velocity, $2170ms−1$⁠) were added to the water. The piezoceramic plate in the levitation stage was excited with a sinusoidal signal at 5.00 MHz with an amplitude of $10Vp-p$⁠. The pressure field of the resulting resonant mode forced the polystyrene spheres to its nodal planes, forming bands perpendicular to the $y$-axis separated by 0.15 mm (half a wavelength at 5.00 MHz).

With the particles trapped relative to the $y$-axis, 5.25 MHz sinusoidal signals were again applied to the matched transducers and the particles moved to points separated by $λ/2=0.14mm$ in the $x$-direction. Thus a regular grid pattern, resulting from the actions of the levitation plate and the two side transducers, was formed. The concentration of particles was such that most of the traps contained multiple particles. This grid pattern can be seen in the top image of Fig. 2(b) and is similar to the pattern achieved by Shi et al.¹⁶ in the horizontal plane.

When $ΔΦ$ was increased from 0 to $2π$ the particles moved up to a maximum distance of $λ/2=0.14mm$ in the $x$-direction. Figure 2(b) shows images of the particles in a region of the test cell for five different values of $ΔΦ$⁠. When $ΔΦ$ reaches $2π$ the particles have been moved to the position of the adjacent trap in the original nodal pattern. The process can be repeated to move the particles over greater distances. A negative change in $ΔΦ$ produces movement in the opposite direction.

A similar, but more extensive, series of images was produced and used to measure the position of a specific group of particles as a function of $ΔΦ$⁠, relative to the initial position when $ΔΦ=0$⁠. The results are shown in Fig. 3. In addition to the experimental result, the position of the pressure field nodes predicted using the transmission line model is plotted. The behavior of the particles is in good agreement with the node positions predicted by the model; the small discrepancy is attributed to the sensitivity of the transducer matching layer performance to the matching layer thickness and material properties. The pressure amplitude of the standing wave generated is predicted by the model to be 300 kPa. Applying the analytical solution for a compressible sphere in a plane standing wave derived by Yosioka and Kawasima¹ to this pressure gives a peak force of 50 pN.

The deviation from linearity between position and $ΔΦ$⁠, seen in Fig. 3, is due to reflection at the transducers surfaces. The matched transducers have (according to the same transmission line model used to model particle position) a pressure reflection coefficient, $R=0.21$ (intensity reflection coefficient 0.04). The effect of nonzero reflection is to introduce a variation in the peak pressure amplitude as the phase is varied and an excursion from linearity of position with phase. If $P0$ is the maximum value of the pressure antinode amplitude for a given reflection coefficient then for $R=0$ the pressure antinode has the same amplitude, $P0$⁠, regardless of $ΔΦ$⁠, but for $R=0.21$ the pressure antinode amplitude varies, between $0.65P0$ and $P0$⁠, as $ΔΦ$ changes. For a hypothetical $R=0.42$ case, modeled by reducing the density used for the matching layer by 25%, but maintaining the same velocity, this variation is between $0.45P0$ and $P0$⁠. Figure 3 includes (in addition to the result of modeling the actual system used) the expected node positions for the ideal $R=0$ (which gives a linear relation) and for $R=0.42$⁠: an increase in the deviation from linearity with increased $R$ can be seen. While particle manipulation is, in principle, possible for large values of $R$ the amplitude variation and departure from linear control limit the effectiveness as $R$ increases.

The results reported here demonstrate that standing waves with nodal positions determined by the relative phase, $ΔΦ$⁠, between applied signals can be generated and used to control the position of microparticles in a liquid medium. It is anticipated that this will offer opportunities in biological research relating to the behavior of cells and in manoeuvring particles in microfluidic biosensors. In particular the response time of particles to changes in the nodal positions is a potential method to determine particle properties.