*2.2.1 Calorimetric flow sensing*

The majority of the current micromachined commercial thermal flow sensors are utilizing the calorimetric principle. Most successful applications are for gaseous

**Figure 1.**

*Graphic illustration of the micromachined thermal flow sensors (on silicon) with the flow sensing principles: (a) calorimetry; (b) anemometry and (c) thermal time-of-flight.*

fluids, of which the automotive airflow sensors for fuel control are the dominant application. The structure showed in **Figure 1(a)** is a typical one for a micromachined calorimetric mass flow sensor on which a microheater is placed at the center of the membrane. Two temperature sensors are made symmetrically at the up and downstream of the microheater. These two temperature sensors can be simple resistors of identical resistance values or identical thermal-piles. There are a variety of approaches to realize data acquisition. The commonly used ones are either to keep the microheater at a constant heating power or to maintain a constant temperature from the up and downstream sensor and then measure the heat transfer or temperature differences between the measurements of the up and downstream sensors as the flowing fluid will take away the heat from the microheater resulting in a heat redistribution. By calibration, such heat transfer can be correlated to the mass flowrate of the fluids. In this approach, the measurement is susceptible to low flowrate. As its nomenclature indicates, the measurement is dependent on the fluidic thermal properties of thermal capacitance and thermal conductivity. The thermal sensing using the resistor-based microheater and resistor sensing has the intrinsic temperature effects associated with the environmental conditions, which need to be compensated for better accuracy. For this purpose, another sensor placed on the substrate (the yellow element shown in **Figure 1**) is used to gauge the environmental temperature and correct the resistance value due to environmental temperature variations. The detailed theoretical interpretation and governing physics can be found in the literature as well as the international standard [1, 46].

The major challenge of applying the micromachined thermal sensor to meter microfluidic is the package. For the gaseous sensors, the membrane often has openings that balance the surface's fluidic pressure against the membrane deformation. The change of the membrane position will greatly impact the measurement as the sensor position will be significantly altered with membrane flatness changes. However, for microfluidic measurement, the opening will be detrimental once the liquid-filled up the cavity underneath the membrane. Therefore, the commercially available approach [41] for the package is to have the sensor placed outside the channel with the sensor's surface close to the outer channel wall. Therefore, the channel will need to be thin enough and have good thermal conductivity for heat transfer effectiveness. One of the selections of the channel is a fused silica tube. As the membrane that supports the sensing element is typical with a thickness of 1 micrometer, attach the think tube to the sensor is a very tedious process with a high cost. In addition, compared to the applications for gaseous fluids, the thermal wall of the fused silica also reduces the sensitivity of the sensor, leading to a significantly smaller measurement dynamic range (<50: 1), which is certainly not desired for

**61**

*Microfluidic Flow Sensing Approaches*

*2.2.2 Anemometric flow sensing*

*DOI: http://dx.doi.org/10.5772/intechopen.96096*

more complicated than that for the calorimetry.

microfluidic applications. The commercially available calorimetric microfluidic sensors offer a typic <40:1 dynamic range with the lowest detection flowrate of 7.5 nL/min and the best accuracy of ±5% of reading at the full scale. There are also concerns about the constant thermal power at the channel's specific area during the

measurement in practical applications. This will be discussed later in detail.

One commercially available anemometric microfluidic flow sensor, per the structure described in the company's webpage, [43] also takes the package approach similar to the earlier mentioned one of the calorimetric microfluidic sensors. The sensor is placed at the outer wall of a thermally conductive fine quartz glass tube by machining the tube surface into a smooth flat. Instead of a single micromachined sensing chip, two chips are used. A special glue was applied to attach the chip to the quartz tube's flat surface, forming a close contact for the required heat transfer. The heater chip and temperature chip are separated at a certain distance forming the configuration of an anemometer. The heat transfer needed for the measurement provided by the sensor is achieved via thermal diffusion. These package approaches are also similar to the traditional capillary thermal mass flow sensors, where the hot wires are winded onto the surface of a special stainless tube. However, the micromachined sensor will have a much lower heating temperature than those by the capillary sensor. Because of the heat diffusion, control the heat for the low flowrate measurement would be very challenging, resulting in a small dynamic range and large measurement errors (full-scale error rate) towards the low detection limit. The current offered anemometric microfluidic flow meter has a guaranteed dynamic range of 50:1 with the lowest detectable

flowrate of 100 μL/min and the best accuracy of ±5% of reading.

Both the calorimetric and anemometric flow sensors require a calibration of the real fluid for the desired precision or metrological accuracy, as the fluidic properties will have a nonlinear response in the full dynamic range. The limited dynamic range and the accuracy would not be desirable for the precision requirements for many microfluidic applications such as drug infusion. Also, these flow sensing products

*2.2.3 Thermal time-of-flight flow sensing*

The first micromachined thermal flow sensor on silicon is made with the anemometric flow sensing principle [47]. Thermal anemometry is also known as energy dissipative sensing, and its measurement scheme is relatively simple, as shown in **Figure 1(b)**. Only one sensing element is placed downstream. Alternatively, the sensing element can also be placed upstream, as the measurement of the fluidic flowrate is only from the microheater (a sensing element). The temperature sensor is used as a fluid temperature reference. Therefore, instead of measuring the fluidic flow-induced changes of the temperature profile at the centralized microheater with calorimetry, the anemometry measures the heat loss due to the forced convection. In this case, with the supporting control circuitry, adjusting the microheater power will allow the measurement to be much easier for higher flowrates. Simultaneously, the sensitivity at low flow will be lower compared to the sensing principle of calorimetry. Another character of the anemometry is that its correlation with the fluidic thermal properties has a larger nonlinear effect resulting in the difficulties to apply a constant fluidic conversion factor for correction of the flowrate data when the measured fluid has different thermal properties from those of the calibration fluid. For the same reason, the temperature compensation scheme for the anemometry is
