Influence of Side-wall Material

The separator device relies on the etch depth of the Pyrex reflector layer to define the fluid layer thickness. However, the quarter-wavelength device used by Martin et al. [119] and discussed in section 6.3 uses a separate spacer to position the reflector layer relative to the matching layer. The spacer does not serve to seal the fluid chamber, therefore an elastomer seal is used, for example,

Sylgard 182 silicone elastomer which has propertiesρ = 1050kg/m3 andc = 1027m/s [135].

Striations are not readily observed in this device, the movement of particles suggesting that the axial acoustic field is dominant with only a smooth lateral variation reducing to a minimum near the fluid chamber walls. Hawkes et al. [118] use a similar construction and, although in this case there is clearly lateral movement of spores on reaching the nodal plane (reflector surface), the axial field still appears to dominate.

The presence of the acoustically damping seal may assist in the prevention of acoustic hot-spots and associated particle striations, therefore in the FEA model of the separator device, the Pyrex side-walls are replaced with a separate structure with Sylgard 182 properties to investigate the influence of the side-wall material on lateral variations in the acoustic field.

Figure 4.8 illustrates the mode shapes for the through-thickness resonant frequencies, but replacing the 0.9mm wide Pyrex side-walls in figure 4.6 with rectangular cross-section elastomer region. With mode 1 a significant difference between the fluid layer mode shapes of figures 4.6(a) and 4.8(a) can be seen. The latter, using the elastomer side-wall, does not predict the presence of acoustic hot spots across the width of the fluid layer and, although the contours suggest a small degree of variability in the acoustic field, it is significantly more uniform.

For mode 2, comparing figures 4.6(b) and 4.8(b) there is no significant difference between the acoustic field patterns within the fluid layers. In both figures the acoustic field varies across the width of the fluid showing periodic regions of high acoustic pressure (red contours), although the axialy field gradient still dominates the smaller lateral zgradient. Instead, the presence of the elastomer material has a greater influence on the reflector layer, reducing the magnitude of the acoustic pressure towards the right-hand edge of the Pyrex, above the elastomer seal and adjacent to the external pressure release boundary.

Mode 1∼3.4MHz (a)

Mode 2∼4.4MHz

(b)

Figure 4.8: Influence of silicone elastomer spacer side-wall on mode shape within separator for both modal frequencies.

It is also observed that for both modes shown in (a) and (b), the elastomer region appears to exhibit its own enclosure mode. For example, in (a) a quadrant pattern can be discerned, although the pressure amplitude is low compared to the field within the reflector and fluid region.

In general, it is shown that the use of alternative materials may aid in reducing lateral variations in the fluid layer acoustic field, in this case using an elastomer material to form the walls of the fluid layer. It is noted that the acoustic properties of the elastomer material are more closely matched to the fluid (in this case water) as compared with the Pyrex material of the reflector which sig- nificantly alters the impedance boundary conditions seen at the sides of the fluid layer. However, the materials are not matched such that all through-thickness modes will exhibit a more uniform acoustic field along the lateral direction, as demonstrated by mode 2 at∼4.4mHz, therefore the use of an alternative material does not present a universal solution to lateral modes.

4.4

Conclusions

In acoustic resonator devices used for the manipulation of particles, lateral variations in the acoustic field are known to exist and give rise to lateral acoustic radiation forces. Depending on the design of the device these lateral forces may be insignificant, although in the separator device investigated the forces are large enough to form striations as particles are drawn laterally towards positions of low acoustic pressure and potential energy. Although acoustic interference and structural modes can give rise to lateral variations, acoustic enclosure modes as a cause are instead investigated.

The mode shapes within the fluid and reflector layers have been simulated using a FEA simulation, using modal analyses to identify the characteristics of the field at two through-thickness resonant frequencies. These simulations reveal lateral variations in the acoustic field within the fluid layer and acoustic hot spots of high acoustic pressure amplitude causing high lateral pressure field gra- dients in the fluid. Using the modal analyses it is possible to estimate the relative magnitudes of the axial and lateral radiation forces by measuring they andz components of the pressure field gradient. This demonstrates that when enclosure modes are excited, high lateral pressure gradients create lateral forces which are of the same order as the axial component of force, significantly in- fluencing particle trajectories. To validate the FEA simulation, the spacings of the experimentally observed particle striations are compared with that of the acoustic field variations predicted by the FEA simulation and show a reasonable level of consistency.

on the lateral field. It is shown that the width of the Pyrex etched side-wall significantly influences the occurrence of lateral modes, where reducing the width of the side-wall reduces the lateral variations in the field and therefore associated lateral acoustic radiation forces. The influence of the side-wall material is also investigated briefly and suggests that acoustically softer materials may introduce more favourable boundary conditions which discourage strong lateral modes.

Currently, these FEA simulations are simplified such that they simulate only two layers of the de- vices and therefore it is accepted that the solutions they present are approximations. Consequently, there is not yet enough confidence in the simulations in order to predict the magnitude of the lat- eral acoustic forces and particle trajectories. Also, it is known from experimental observation that forces exist in all 3 dimensions, demanding a more complex 3-d simulation to predict accurately the behaviour of a particle.

Even so, this study demonstrates that enclosure modes are a likely cause of the formation of particle striations in the separator device and that FEA is a useful tool to predict the presence of these modes and approximate the modal pattern. Further and more extensive experimental validation would be valuable to more fully understand the influence of the lateral geometry and materials used in the separator device construction and additional simulation work to predict more accurately the magnitude of lateral forces.

Simulation of Particle Motion

5.1

Introduction

As discussed previously, the combination of forces experienced by a particle determines whether it will move towards the acoustic nodal plane at a great enough rate for separation or capture to occur. Based on these forces, a simulation of particles as they pass through the acoustic and fluid fields, and the resulting trajectories, make it possible to predict the performance of an ultrasonic manipulator device and investigate the influence of a variety of parameters upon particle distrib- utions. In this chapter, such simulation methods are developed and are then used in a predictive capacity in chapter 6. Academic research into acoustic manipulation is occasionally accompanied by analytical or numerical simulations describing the particle trajectories in order to predict con- centration or separation efficiency as described more fully in section 2.4.3, although here more detailed numerical simulation of the device and acoustic field is used, thus making it possible to simulate the influence of a greater number of parameters upon particle movement, and adopting fewer assumptions.

A numerical model used to determine particle trajectories is described, where the approach in- volves considering forces exerted on a particle as it passes through the acoustic field. Solving these forces numerically gives a set of coordinate points describing the path taken by the particle in a given time interval. To calculate the acoustic radiation force, the simulation incorporates the acoustic transfer model introduced in section 2.5.2, and so is not limited to the simple case where the standing wave velocity nodes are positioned on the boundaries of the fluid cavity (equation (2.8)).

A visual inspection of particle trajectories can suggest whether complete clearance or capture has been achieved, but cannot give the degree achievable, e.g. the decrease in concentration or the percentage of particles captured on the chamber wall. More appropriately, by tracking multiple particles or considering the conservation of particles and treating them as a continuum, the concen- tration profile across the fluid channel can be calculated. The numerical approaches are described and simple cases are compared to analytical solutions. Concentration profiles are then used to determine predictions for outlet concentrations, the approach for which is described.

Although the latter numerical approaches to predict concentration profiles begin to resemble basic forms of numerical fluid simulation, it is considered unnecessary to combine particle simulations with computational fluid dynamics code when simulating the applications considered in chapter 6. As demonstrated in chapter 3, microfluidic flow is dominated by viscous forces, therefore, in a simple geometry typical of microfluidics a predictable laminar flow profile can be assumed to exist and does not require a computationally expensive solution. In the case of more complex flow, CFD data can be generated independently for low particle concentrations where the presence of particles has negligible influence on the fluid dynamics. The CFD data generated can be used in subsequent analyses such as that described in this chapter. A similar approach can also be considered to provide 2 or 3-dimensional data describing the acoustic field. However, the process of incorporating such data is time consuming and the work in chapters 3 and 4 has not aimed to provide accurate descriptions of the fluid and acoustic fields in 2 or 3 dimensions, therefore both the fluid and acoustic fields are here described in 1 dimension only (ydirection).