Identificación de amenazas

The simulation work described in this thesis has been carried out alongside the fabrication and test of an ultrasonic separator, guiding the work and providing essential experimental data. The ultrasonic separator device in question has been developed at the University of Southampton and takes advantage of the university micro-machining facilities to realise the device on a microfluidic scale, and therefore provide the potential for integration within microfluidic systems. The sepa- rator is designed to operate using a half-wavelength resonance and to separate particles held in a fluid suspension. Acoustic radiation forces drive particles to a plane within the processing cham- ber, and controlled extraction of various portions of the resulting flow aim to separate clear fluid from particle concentrated fluid. This section describes the fabrication and principle of operation, which is followed by a description of the acoustic modelling developed for use as a design tool and to understand the acoustic characteristics of such a resonator. A significant portion of this thesis is developed from this acoustic modelling and thereby builds a series of complimentary design tools.

2.5.1 Construction

The design and operation of the separator is related to the laminar flow separator device described by Hawkes et al. [4] in terms of the scale and operation of the device. The laminar flow separator was constructed from metal plates forming the reflector and acoustic matching layer, and encasing the fluid chamber. The operational frequency was approximately 3MHz and so to produce a half-

wavelength standing wave the fluid chamber had a depth of 250µm. The microfluidic separator

described here is on a similar scale, but uses materials such as silicon and Pyrex suitable for micro- machining processes and therefore results in different acoustic characteristics, although the fluid chamber was initially designed with the same fluid depth of 250µm.

The construction of the microfluidic separator is illustrated in figure 2.16 and shows the arrange- ment of the piezoelectric (PZT) transducer, silicon matching layer and the Pyrex reflector layer. The fluid chamber is created by isotropically etching into the Pyrex producing curved walls inside the chamber. This also means that the Pyrex wafer thickness used in the fabrication always equals the combined depth of the fluid and reflector layers. The Pyrex layer also allows observation of the particle suspension during operation and the condition of the fluid chamber. The silicon layer is etched to include three fluid ducts, with the characteristic angular geometry resulting from the anisotropic etch process clearly seen. Once etched, the Pyrex and silicon layers are bonded

Figure 2.16: Cross-section of the ultrasonic microfluidic separator (not to scale).

anodically.

Typical dimensions are indicated in figure 2.16 although the fluid chamber depth, and therefore the reflector layer depth, have changed during the study. Also note that the fluid chamber has a high length-to-height ratio typically greater than 50:1. The width of the chamber and ducts (not indicated in the diagram) are approximately 5mm, which results in a width-to-height ratio of at least 20:1.

2.5.2 Operation

The separator is a flow-through device within which a fluid sample can be continuously fed through the inlet duct. Figure 2.17 shows the flow path of the sample up through the inlet duct and into the main chamber of the device. Within this area the transducer is used to generate a half-wavelength standing wave across the chamber and perpendicular to the direction of flow. As particles move through this field they are deflected in they direction by the acoustic radiation forces acting on them and move towards the node of the standing wave positioned along the centre of the chamber. Simultaneously, the particles are subject to fluid drag forces which transport them along the cham- ber towards the outlets. For separation to be possible the particles must have formed into a narrow stream, as indicated in the diagram towards the end of the acoustic field (light grey shaded area). As the flow within the device is laminar this particle stream remains intact and can be extracted through either outlet. The diagram indicates the case when the flow rate through outlet 2 is greater than outlet 1 and therefore particles are extracted through outlet 2. Clarified fluid is extracted through the other outlet.

Figure 2.17: Operation of the ultrasonic microfluidic separator.

the particle stream is extracted must have a flow rate at least half that of the total, or inlet, flow rate. This means that the maximum concentration achievable is only a 2-fold increase, the device therefore acting more effectively as a clarifier.

Acoustic Simulation

To predict the nature of the acoustic field within the separator device an acoustic impedance trans- fer model is used. This model is described by Hill & Wood [3] and Hill et al. [2] and was origi- nally used to describe an h-shaped device. The approach considers the total acoustic impedance of the layered device which can then be related to the transducer using an equivalent electrical impedance.

Figure 2.18 illustrates a basic acoustic system and properties of the media. The input mechanical impedance of the acoustic system,Zm0, where a plane wave is propagating through a material with properties densityρ0, speed of soundc, areaS, and thicknessL, and with the cavity terminated with a material of impedanceZmL, is calculated as follows [133]:

Zm0=ρ0cS _Z mL+jρ0cStankL ρ0cS+jZmLtankL , (2.16)

wherekis the wave number.

When simulating the separator the impedance,Zm0, seen by the transducer is ultimately required and depends on the properties of the glue, silicon, fluid and reflector layers. Therefore, it is necessary to calculate the input impedance of each successive layer. For example, equation (2.16)

Figure 2.18: Acoustic Properties associated with a closed cavity.

Figure 2.19: Equivalent circuit of separator.

is first used to calculate the impedance from the reflector layer whereZmLis simply the impedance

of the surrounding air. The resulting value of Zm0 now describes the termination impedance,

ZmL, when looking through the fluid layer. This calculation is repeated until the transducer layer is reached.

The resulting value ofZm0 as seen from the transducer now describes the total mechanical im- pedance of the device and is represented by an equivalent electrical impedanceZ0. In order to model the resonant behaviour of the device and related electrical characteristics, an equivalent cir- cuit is considered as shown in figure 2.19 whereRerepresents the electrical losses,C0is the static capacitance of the transducer andCm,LmandRmare the equivalent mechanical capacitance, in- ductance and resistance, respectively. Further, to determine the nature of the acoustic field within the cell, the mechanical impedance is used to calculate the forces generated at layer boundaries, which in turn are used to describe the variation in the acoustic pressure and velocity fields. This transfer model is described in more detail by Hill et al. [2].

response. This can be compared to the measured frequency response of a device and used to fine- tune parameters. It can also be used in a predictive capacity to determine the resonant frequencies of the device.

To model the acoustic behaviour within the device, the force exerted by the transducer can be calculated and is proportional to the voltage applied across the transducer. As the wave propagates through the devices it in turn generates a force between each layer of the device. These forces can then be used to determine the acoustic pressurepand velocityu fields within each layer, as a function ofyin a direction perpendicular to the transducer and layer boundaries. Although the model does not simulate variations in the field along its length or across the width, it provides a 1-dimensional description of the most dominate component.

As can be seen from equation (2.11) the radiation force depends on the kinetic and potential energy. Kinsler et al. [133] give these energies as functions of the acoustic pressure and velocity and are time and position dependent. Here, the time averaged expressions are shown, whereρ0 is the undisturbed fluid density anduandpare time averaged acoustic velocity and pressure fields:

hE¯kin(y)i= 1 4ρ0u(y) 2_{, (2.17)} hEpot¯ (y)i= 1 4 p(y)2 ρ0c2 . (2.18)

MATLAB is again used to determine these values and by substituting them into equation (2.11) the radiation force as a function ofy can be calculated. The resulting data describes the spatial variation of radiation force, an example of which is shown schematically in figure 2.9.