Flexural Plate Waves

In another approach, ultrasonic acoustic flexural plate waves (or Lamb waves) were used to generate fluid mixing motion of microspheres in water in a Si device. A 10-pm-thick piezoelectric ZnO film was deposited on the back side of a Si wafer (see Figure 3.48). This thickness is an odd-multiple of the acoustic half-... 

Figure 1.2 Schematic sketches of the four types of acoustic sensors discussed in detail in this book (a) Resonant quartz crystal like that used in electronic communications systems (after Lu [6]) (b) Suiface-acoustic-wave delay line with selective absorptive coating (after Wohltjen and Dessy [3]) (c) Acoustic-plate-mode delay line made from quartz crystal (after Ricco and Martin [7]) (d) Thin-membrane flexural-plate-wave delay line made by microfabrication techniques from a silicon wafer.

Devices based on piezoelectric crystals, which allow transduction between electrical and acoustic energies, have been constructed in a number of conrigurations for sensor applications and materials characterization. This cluqtter examines those devices most commonly utilized for sensing a( licatithickness-shear mode (TSM) resonator, the surface acoustic wave (SAW) device, the acoustic plate mode (APM) device, and the flexural plate wave (FPW) device. Each of these devices, shown schematically in Figure 3.1, uses a unique acoustic mode. 

Figure 3.1 Schematic sketches of the four types of acoustic sensors, (a) Thickness-Shear Mode (TSM) resonator (b) Surface-Acoustic-Wave (SAW) sensor, (c) Shear-Horizontal Acoustic-Plate-Mode (SH APM) sensor, and (d) Flexural-Plate-Wave (FPW) sensor.

In a flexural plate wave (FPW) device, an acoustic wave is excited in a thinned membrane. Figure 3.38 (page 112). As with the other acoustic sensors discussed — the TSM, SAW and APM devices — the flexural-plate-wave (FPW) device can sense quantities that cause its phase velocity, Vp, to change. A unique... 

Figure 3.38 Schematic diagram of a flexural-plate wave (FPW) device.

The characteristics of flexural plate waves are found by a process similar to that used for surface acoustic waves ... 

Figure 3.40 Calculated phase velocity of flexural plate waves vs ratio of plate thickness, d, to wavelength. A, for silicon nitride. Material is assumed to have the elastic properties of Si3N4 and no residual tension. The mode shapes ate illustrated at the right with a greatly enlarged vertical scale for clarity. Ellipses at left show the retrograde elliptical particle motions of the lowest S3rmmetric and antisymmetric modes for d/A = 0.03. (Reprinted with pemtission. See Ref. (621.)...

Just as flexural waves can propagate at low speeds in a plate whose thickness is much less than the wavelength, a low-speed flexural wave can propagate in a cylindrical rod whose diameter is much smaller than the wavelength [87]. Because of the low wave speed, operation as a gravimetric sensor in liquids is possible, as with the flexural plate-wave sensor. The gravimetric sensitivity for this sensor is typically S = — l/(2p ), where a is the radius of the rod. 

An example of a two-port device is the surface acoustic-wave (SAW) delay line shown in Figure 6.3. Acoustic plate mode (APM) devices utilize a two-port configuration that is conceptually identical to that of the SAW for the flexural plate wave (FPW), there is typically a third connection to its ground plane (see Section 6.2.3). In principle, the ground plane connection is unnecessary, but in practice more stable operation results when this connection is made. Notice that there... 

The excitation and detection of surface acoustic waves, flexural plate waves, and other plate waves on piezoelectric substrates is most readily accomplished by use of an interdigital transducer (IDT) first reported by White and Voltmer [6]. The comb-like structure of the IDT, illustrated in Figure 6.4, is typically made from a lithographically patterned thin film that has been deposited onto the surface of a piezoelectric substrate or thin film. The metal film used to make the IDT must be thick enough to offer low electrical resistance and thin enough so that it does not present an excessive mechanical load to the AW. Typical IDTs are made... 

Microcantilever sensors offer many orders of magnitude better sensitivity compared to other sensors such as quartz crystal microbalances (QCM), flexural plate wave oscillators (FPW), and surface acoustic wave devices (SAW). There are several distinct advantages of the microcantilever sensors compared to the above mentioned and other MEMS sensors ... 

Functional polymers may be used for dihierent types of chemical sensors, including acoustic wave sensors (bulk acoustic wave, surface acoustic wave, and flexural plate wave sensors), electronic conductance sensors (semiconducting and capacitance sensors), and calorimetric sensors. ... 

In this article, we will describe in some detail the fundamentals of the three types of streaming flows associated with the microfluidic applications. First, the quartz wind which corresponds to the one-dimensional compressible flow will be introduced. Second, the Eulerian streaming flow in two-dimensional space will be considered. Kundt s dust phenomenon will also be explained. Finally, we will address the flexural plate wave and its net effect, i.e., the Stokes drift flow. 

Usually, by acoustic streaming we mean Eulerian streaming. However, the recent application of the flexural plate wave in microfluidics implies that the Stokes drift flow should also be considered as a type of steady streaming flow, because the net effect in the fluid transport is not discemable... 

Fig. 5 Microfluidic device utilizing the flexural plate wave, (a) Fabricated device (b) shape of the flexural plate and the coordinates for analysis [2]...

Acoustic Streaming, Fig. 6 Distributions of the Stokes drift velocity across the fluid layer for three channel depths given by the flexural plate wave... 

Acoustic Streaming, Fig. 7 Effect of the channel depth on the flow rate at three Reynolds numbers for the flexural-plate-wave pumping. Dashed line corresponds to Re = oo... 

We also need to analyze the case for the flexural-plate-wave flow in more detail and to simultaneously perform numerical simulations of the resultant flows. The results of the full numerical simulation may be used to prove that the steady flow components are generated by the mechanism known as the Stokes drift flow. 

Nguyen NT, Meng AH, Black J, White RM (2000) Integrated flow sensor for in situ measurement and control of acoustic streaming in flexural plate wave micropumps. Sens Actuators A 79 115-121... 

---