**3.2 Microfluidic cavitation**

*Advances in Microfluidics and Nanofluids*

could be further lowered to about 80 nW.

discussed.

**3. Factors impacting the microfluidic flow sensing**

**3.1 Microfluidic channel and fluid interactions**

nanocomposite of permanent magnetic nanowire and PDMS mixture on the GMI layer. The formed flow sensor was placed inside the microfluidic channel. When the fluid flows through the pillars, the flow will force the pillars to bend, resulting in the change of the magnetic field sensed by the GMI layer and output the signals that can be correlated to the flowrate. The results showed a measurement of the water flow speed up to 7.8 mm/sec and a resolution of 15 μm/sec with a typical power of 31.6 μW. The study also indicated that by optimizing the parameters, the power

The flow metering at the microfluidic scale is quite different from those in a large pipeline. Many factors that may be trivial in the conventional fluidic dynamics become critical for microfluidic metrology. In this section, some critical factors are

In the classic fluidic dynamics, the Moody chart indicates that at laminar flow, the friction factor is inversely proportional to Reynolds number where only viscosity of the fluid plays the role and diffusion is normally not in consideration. In the dimension of a microfluidic channel, the surface area relative to the volume is dramatically larger than those in a large pipe. For the flow speed of interests, factors such as surface tension and diffusion are all having their critical contributions to the microfluidic flow metrology. The capillary number then would be much more important than the Reynolds number [80]. Besides, the majority of microfluidic processes are water-based. Water has a molecular size of about 0.27 nanometer, and it is dipolar in nature. Water interaction with the solid surface is inevitable, and such interaction will be pronounced as interaction will involve a significant portion of the total volume of the microfluidics. Most of the solid surfaces at the microscale would be imperfections that are full of defects with dimensions larger than the water molecule. Water viscosity is also very sensitive to temperature in the applicable ranges. These effects will be even more pronounced in the biological fluid case where the electrolyte is often present as the chemical state of the surface would be altered, either by ionization of covalently bound surface groups or by ion adsorption [81]. Hence, to ensure the accuracy in the flow measurement for microfluidics, the interactions between fluid and solid channel surface must be considered,

especially for the long term repeatability, reproducibility, or reliability.

The detailed studies on the fluidic handling and flowrates impacted by the fluid and microchannel interactions are not well documented. However, in a few reports on the long-term stability of the commercially available calorimetric flow sensors for microfluidics, it was reported that the measurement accuracy tended to have a time-dependence. The long-term *drift* was always towards negative directions with a more pronounced deviation at the full-scale flowrate. For example, one report [82] tested the reproducibility of several commercial calorimetric flow sensors of the identical model for the time dependence in water. It was found that although the sensor to sensor performance was inconsistent, the accuracies of all sensors *drifted* towards negative with time, with −25% deviations at the full-scale flowrate in about 5 months. Although the report did not speculate the reasons for the deviations, this phenomenon could be a direct reflection of the water interactions with the microfluidic channel walls. The sensor chip was fixed to a fine tube with a machined flat surface in the product package. It would difficult to guarantee the consistency

**68**

Cavitation is often known as a detrimental phenomenon in high-speed flows that leads to mechanical damages at the flow path. However, it can also be utilized for industrial processing in classic fluidic dynamics. In microfluidics, cavitation inception is via the diffusion of dissolved gas into the available nuclei. It can occur even at a pure Stokes flow, but the cavitating flow will not normally lead to mechanical defectiveness due to the relatively low energy release, but it can dramatically generate the local flow speed spike. Cavitation has become a growing research topic in microfluidics. It is not only because the cavitation flow is inevitable in many applicable microfluidic flow conditions, but it can also be employed as a tool for microfluidic manipulation such as pumping and mixing via the control of cavitation size alternation. The cavitation can harvest and release energy upon collapse in the microfluidic process. The removal of cavitation can be done with properly designed materials for the microfluidic channels [83–86].

The cavitation presence will greatly impact the measurement reproducibility or accuracy for any flow sensors regardless of the measurement principles. The calibration setup for a microfluidic meter normally requires a degassing device in serial to the calibration line, and degassing is always performed before the start of calibration [39]. The cavitating flow is in fact a two-phase flow. Therefore when a flow sensor calibrated at a cavitation-free condition is applied to measure a cavitating flow, the measurement deviations will be inevitable. The current tools of the cavitation studies are visualization approaches such as colorimetry or via high-speed camera for which a transparent flow channel will be required to collect the data. However, in practical applications, the channels are often opaque. Therefore, it is of interest to have additional measurement approaches that can alert *in situ* when the cavitation is present in microfluidics. In some applications such as drug delivery, the infusion with cavitating fluids into a human body will be very harmful, not just for the uncertainties in totalized delivered drugs. Of the flow sensing technologies discussed above, the thermal sensing approach could be a viable tool to detect cavitation while correcting the quantified microfluidic delivery. **Figure 3** shows the response of a thermal time-of-flight sensor used to detect the bubbles inside the microfluidic channel. (**Figure 3**, Left) The channel design can be found in a previous report [87]. As the two air bubbles (one big and one small) pass through the channel sequentially, the fluidic properties that the sensor senses will be drastically different from those of the pure liquid. In the case of water with air bubbles, the smaller thermal conductivity and substantially lower density for the mixture will prompt a faster heat transfer resulting in a recorded positive flowrate spike. With additional sensing elements to capture the flow speed of the fluid, the time of the burst spike can be used to estimate the sizes of the bubbles. Further, the gas properties inside the bubble might also be detected per the calibration of the sensing element thermal response to the fluid. While in another case, the sensor could also be applied to study the cavitation (**Figure 3**, right). The as-calibrated thermal time-of-flight sensor will normally have an accuracy within ±1%. After calibration in DI water and subsequent verification, the same sensor was kept at the same microfluidic channel at null flow

#### **Figure 3.**

*Left - Example of the response of a micromachined thermal time-of-flight sensor to air bubbles passing in a DI-water microfluidic channel; and right – shows the same sensor response at 20mL/min flow to the channel conditions: A – as calibrated DI water; B – tested after sensor powered on in a null flow DI water channel for 48 hours; C – After B test and degassing for 15 minutes; D – after C and full scale full (30mL/min) flow for 30 minutes; E – after D, the channel dried with N2 and re-test.*

condition with a 5 Vdc power applied for 48 hours. The sensor was then re-tested for the registered accuracies by referring to a high precision mechanical syringe pump in serial. One sees that a huge negative deviation of about −7% was recorded (Test B). This could be likely because the sensor's surface had been populated with small air bubbles due to the prolonged constant heat that promoted the bubble nuclei growth and air diffusion. When the flow was started, the drag force might force the collapse of these bubbles causing the cooling that led to the negative deviations. This was further supported by the fact that after degassing the flow microchannel for 15 minutes where the same sensor was installed. After the observed negative deviations, re-measurement of the flow accuracy with the identical procedure, the deviation was reduced (Test C). The deviation was further reduced by running the flow at the full scale for another 30 minutes (Test D). And finally, the sensor recovered to the original precision by dried the sensor surface with nitrogen and the re-test with the same procedure after degassing (Test E), which would effectively eliminate the cavitation by bubbles.
