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9.3 Pressure Difference Flow Sensors                                          231

                                                                  Capacitive
                                Flow restriction                  pressure sensors
                         ++
                        p -silicon
                                           p 1
                                                                                   Pyrex
                                                                                   Silicon
                                        p 2                                    p 2
                                                                    p 1
                                              Glass                                Pyrex
                           p 1    p 2                            Input  Flow   Output
                         Inlet          Capacitor                flow  channel
                                Outlet                                         flow
                                     (a)                                 (b)


                                                                   Flow restriction
                            Sensor
                            diaphragm
                                   Flow
                                        Piezoresistor                 ZnO thin film ring
                                                         Polyimide
                              p 2
                                                         membrane  Sensor A  Sensor B
                               p 1
                                                                             Silicon
                             Orifice     Silicon
                                                               Inlet             Outlet
                                                                   Flow restriction
                                    (c)                                  (d)
                  Figure 9.22  (a, b) Schematic drawings of pressure difference flow sensors: (a) (After: [81].)
                  (b) (After: [82, 83].) The silicon membranes are 25 µm thick, 1.5 mm long, and 1.5 mm wide. The
                  flow restriction channel is between 200 and 570 µm wide, 2.9 mm long, and 21 µm deep. (c) The
                  orifice, acting as flow restriction, has a diameter of 100 to 400 µm in the middle of the membrane,
                  which is 20 µm thick. (After: [84].) (d) The membrane has a diameter of 1 mm, and a thickness of
                  25 µm. The thin-film sputtered ZnO is 1 µm thick. (After: [85].)



                      Richter et al. [84] uses a commercially available pressure sensor, drills a hole in
                  the middle, and uses it as a differential pressure flow meter [Figure 9.22(c)]. A
                  similar principle has been presented by Nishimoto [85] using a self-made pressure
                  sensor.
                      A polyimide membrane with thin-film sputtered ZnO piezoelectric sensors for
                  measuring liquid flow has been presented by Kuoni et al. [86]. Two round piezoelec-
                  tric sensors are placed before and after a flow restriction [Figure 9.22(d)]. The
                  restrictor has a hydraulic resistance of 60 mbar/(ml/h) with a channel length of 10
                  mm. The sensor has been tested in connection with a piezoelectric micropump, and
                  stroke volumes of 1 to 10 nl could be measured.
                      A flow velocity sensor based on the classical Prandtl tube was presented by Ber-
                  berig et al. [87]. It realizes flow velocity detection by measuring the pressure differ-
                  ence between the stagnant fluid pressure in front of the sensor chip and the static
                  pressure in the flow around the sensor chip. The pressure difference deflects a sili-
                  con diaphragm, which is the counter electrode of an integrated capacitor (see
                  Figure 9.23). Two fluid passages, which are on the side the sensor faces the flow,
                  connect the cavity with the ambient fluid. The purpose of the fluid passage is the
                  transmission of the stagnation pressure p into the sensor cavity, and in the case a
                                                       tot
                  liquid is used, the multiple passage allows for cavity priming. The outer side of the
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