Comparison with Experimental Observations

The FEA model above is extended to describe the fluid and reflector layers in 2-d and uses the model structure represented in figure 4.2(b) with pressure constraints applied to the external sur- faces only. The simulation is based on the measured width of the Pyrex layer (external width) of 6.8mm and design width of the fluid of 5mm. The curved side walls created by the isotropic etch are also included in the model. This model can be compared to experimental observations such

Figure 4.5: Comparison between the acoustic pressure fields predicted by the FEA and MATLAB models for resonant frequencies of a) 3.37MHz and 3.46MHz for the respective models and b) 4.35MHz and 4.33MHz and based on an acoustic particle velocity of 0.002m/s at the fluid plane.

as that pictured in figure 4.1(a) and aims to validate the model and demonstrate the source of the striated patterns.

The two modes identified in the previous subsection are investigated as these are the modes used in operation of the separator. However, the resonant frequencies and behaviour of the 2-d modelled system are different to the 1-d system as additional boundary conditions and geometry are used in the simulations. As well as these two axial half-wavelength modes, the FEA model also identifies many other, predominantly lateral modes, although are not investigated here.

Figure 4.6 shows the results of a modal analysis of the reflector and fluid layers and describes the pressure field within the system. It can be seen that in (a) a standing wave of order approximately

m = 2andn = 1is present in the reflector layer, which is predominantly a through thickness

resonance resembling the pressure profile in figure 4.5(a). The field pattern within the fluid layer is much more complex and is highly non-uniform, showing acoustic ‘hot spots’ at regular positions across the channel width. These hot spots suggest that particles will move to a series of lateral positions across the fluid chamber with an approximate spacing of 0.25mm. The experimentally observed striations are spaced at approximately 0.21mm apart which is comparable to the modelled results, the discrepancy possibly due to inaccuracies in the fluid channel dimensions used in the simulation.

The higher frequency mode shown in figure 4.6(b) shows a more complex pattern than expected within the reflector layer which is likely to be caused by the axial resonance coinciding with a lat- eral resonance producing a 2-d pattern. However, the pattern within the fluid layer is more uniform and, although some lateral variation still exists at this frequency, the nodal plane (green contour) can be seen to run along the centre plane of the fluid layer as predicted by the 1-d simulations.

Lateral variations in the fluid layer acoustic field cause a variation in the axial strength of the radiation force and therefore obvious implications on the particle separation efficiency. Also the lateral variations themselves are accompanied by lateral radiation forces which may induce par- ticle agglomeration, allowing short range inter-particle forces to cause particles to cluster further. Although this may enhance particle separation as the radiation force is proportional to particle volume (equation (2.11)), sedimentation of particle clumps has been observed and is detrimental to successful separation.

By investigating the harmonic response of the fluid/Pyrex system to an applied pressure, it would be possible to extract acoustic pressure and velocity data used to determine the radiation force acting on a particle within the fluid layer. However, it is felt that a quantitative assessment of

(a)

(b)

Figure 4.6: 2-d mode shapes given by modal analysis of fluid and reflector layers for a) 3.40MHz and b) 4.36MHz.

the radiation force would be misleading as the simulation is highly sensitive to lateral dimensions (investigated further in the following section), and also the nature of the applied vibration is not accurately described without extending the model to include the silicon and transducer layers.

Instead, the modal analysis can provide a qualitative assessment of the significance of lateral modes and variations in the acoustic field. The radiation force acting on a particle held within the fluid layer is in part related to the gradient of the acoustic potential energy density (equation (2.11)), in turn related to the square of the acoustic pressure, and defines the magnitude and direc- tion of the force. Therefore, a particle will follow the route of maximum gradient and to regions of low pressure amplitude (green contours). Using the pressure data given in the modal analyses upon which figure 4.6 is based, the lateral gradient of potential energy density is up to approxi- mately 85% and 39% of the more dominant axial gradient for the 3.40MHz and 4.36MHz modes respectively, measured in the central region of the fluid layer near the plane of symmetry.

These values are significant regarding the movement of particles within the fluid and resulting separation and, although it is not intending to use these values in separation predictions, it does present a case for further investigation into lateral fields.