*2.4.2 Differential pressure microfluidic flow sensing*

Measurement of flowrate with differential pressure is one of the oldest flow sensing technologies. Micromachined differential pressure sensors have been well established and are widely available on the market at a very low cost. Most sensors are made on a silicon nitride membrane or diaphragm with the piezoresistive sensing elements at the edges of the membrane or with a capacitance measuring principle for the low differential pressures [64, 65]. The advantages of a differential pressure sensor for flow measurement are lower power consumption and relatively easy installation with fewer effects on the flow conditioning. They are also independent of the fluidic properties. The microfluidic flow regime is purely laminar, and the pressure loss is linear with the flow velocity. However, limited by its sensitivity, the measurement dynamic range of a differential pressure sensor is normally small. In particular, for microfluidic applications, the pressure drop at a tiny distance may not even generate enough sensitivity for the measurement. The dependence of the microfluid's pressure loss on the dynamic viscosity also requires a temperature sensor at the proximity for the needed compensation. Other phenomena such as cavitation or multi-phase flow will have a big impact on the measurement of the pressure and hence the accuracy of the deduced flowrate.

Flow measurement with drag force is an alternative pressure-related flow sensing approach. Due to the size restriction, such a sensor does not favor being placed inside the microfluidic channel. However, in an ideally integrated microfluidic system, there will be valves and other actuators. The drag force-sensing approach could be combined with the actuation parts in the system. A typical drag force

sensor is to utilize a cantilever or a diaphragm [66]. The mechanical deflection can be read out with an optical microscope or photodiode. Another approach to measuring the deflection is to utilize the piezoresistive or piezoelectric elements embedded at the positions where maximal deformation could occur at the designed cantilever or diaphragm. To increase the measurement sensitivity, the Fabry Perot spectrum's fringe shift was used to measure the cantilever movement correlated flowrate, which, however, complicated the data acquisition and limited the package options [67]. The materials used to make the micro-cantilevers are silicon nitride, SU8, and polydimethylsiloxane (PDMS). An integrated micro-cantilever inside the microfluidic channel via the microfluidic favorable PDMS process achieved a capability of detecting 200 μL/min flowrate but only have a small 5:1 dynamic range [68]. Most of the micro-cantilevers measure microliter per minute flowrate, even though nanoliter per minutes sensitivity was reported, but the required optical readout often makes the fine readings and subsequent digitization a challenge [69]. While piezoresistive or piezoelectric configuration is more preferred as no optical assistance in readout will be needed. On the other hand, as the piezoelectric cannot detect a static flow, piezoresistive is considered a better choice. The cantilever sensors are more sensitive than diaphragm sensors, but there are still concerns for their reliability and repeatability per the moving cantilever. The sensitivity of these sensors also requires meaningful pressure or critical mass to activate the deformation of the cantilever or diaphragm. Such pressure is not necessarily existing in the microfluid subject to measurement.
