An in-depth Review on Flow Rate Sensing in Microfluidics

Flow rate measurement is used in several microfluidic applications, including microfluidic droplet generation, cell culture under flow, and organ-on-a-chip studies. Several technologies aim to provide accurate real-time flow measurement to meet this need. In this review, the different existing microfluidic flow sensing solutions for low-flow liquids are described.

The physical properties of the sample, including viscosity, density, conductivity, diffusion coefficient, solubility or phase equilibrium, and flow conditions, impact the measurement of the flow. The ideal flow sensor should provide accuracy and precision, function for a wide range of flow rates (from 1 nL/min to 10 mL/min for microfluidic applications), have a quick response time, and work with all types of liquid independently of the external conditions (temperature and humidity amongst others), all for a lower cost. We divided flow metering technologies into two main categories: active and passive flow sensors. Active sensors provide energy to the liquid and measure the changes they induce. They represent more than two-thirds of the flow sensors currently used in microfluidic applications. Passive sensors do not supply any energy to the fluid. Their principle is based on the evaluation of the disturbance the flow causes on the sensor. Each category can be divided into subcategories that are listed in the graph below.

Active Microfluidic Flow Sensing

Thermal Flow Meter

The most widespread flow sensors in microfluidics rely on heat transfer measurement. They have one heating element and one or several sensing elements. The flow rate Ql can be derived from the fluid velocity v understanding the tube section S. The fluid velocity is linked to the heat loss Qh in accordance with the following equation, where a and b are constants that depend on the channel and the fluid, which can be determined empirically:

The heat loss is proportional to the dissipated power P, known from the temperature T detected by the sensor, where I is the intensity of the current, and α is the resistivity:

Three different acquisition methods exist for this active microfluidic flow sensing subcategory.

• Firstly, the hot-film anemometer consists of only one element that heats and measures.
• Secondly, the calorimetric flow meter consists of one heating element supported by a constant current and surrounded by two sensing elements that measure the asymmetry of the temperature profile caused by the flowing liquid. Unlike the hot-film anemometer, it gives information on the flow direction and consumes less power.
• Lastly, the time-of-flight flow meter consists of one heating element, and a sensor that evaluates the flow rate based on the time needed by a heat pulse to travel a known distance. It is the lesser-developed thermal flow sensing method as temperature diffusion along the channel disturbs the heat pulse.

Advantages and limits

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Coriolis Flow Meter

An alternative to thermal microfluidic flow sensing is to use a Coriolis flowmeter. The flow rate measurement is based on the detection of the movement caused by the Coriolis force in a U-shaped conductive channel. Running an alternative current iact in the conductor submitted to a constant magnetic field B induces a periodical Lorentz force FL along the z axis that drives the channel with an angular velocity ωact. As fluid flows through the channel, a Coriolis force FC along the z axis that is proportional to the mass flow Φm and the angular velocity ωact is created:

This causes a second vibration mode with an angular velocity ωd. The flow rate Q is computed thanks to the optical measurement of the amplitude of both oscillations and several parameters linked to the microchannel, the operating modes and the detection-mode modal spring constant.

Advantages and limits

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Passive Microfluidic Flow Sensing

As of today, only active flowmeters are industrialized on a large scale. They are either adapted from other applications or inspired by natural phenomena. They aim to save power by taking advantage of the energy created by the fluid flowing. They have been tested for research purposes but are not commercialized for microfluidic applications yet.

Fluid/Structure Interaction Flow Meters

These flow sensors operate through the dissipated energy of the flowing liquid that leads to the motion or deformation of their body. Three technologies are featured below.

• Firstly, the differential pressure flowmeter computes the flow rate Q from the pressure difference Δp applied at the inlet and the outlet of the channel knowing its dimensions and the liquid viscosity, with the following formula, where Rh is the hydrodynamic resistance that can be obtained through a calibration step:
• Secondly, the cantilever-based flowmeter detects the distortion of a cantilever beam immersed perpendicularly to the flow. Its behavior mimics hair-cells or cilia.

This microfluidic flow sensing technology allows a better measurement dynamic range than differential pressure. Moreover, as they are made thanks to MEMS techniques, cantilever sensors can be compact and in the same price range than thermal flowmeters. Like them, they also need to be calibrated for each liquid. But the beam can wear out or break if the drag force is too strong, and be affected if covered by particles, cells, bubbles or proteins contained in the flow.

• Lastly, the particle seeding flowmeter measures the velocity of particles that were seeded into the flow thanks to particle image velocimetry or laser Doppler velocimetry, two optical detection methods.

Advantages and limits

These technologies are compatible with temperature sensitive samples, have low power consumption and have low effects on the flow conditioning, but they are based on prior knowledge of the liquid and are prone to contamination issues as the test bodies are in contact with the fluid. The concerns for their invasiveness, reliability, and repeatability prevent fluid/structure interaction sensors from being competitive with active flow sensors.

Non-invasive Flow Meters

Until this point, all the flow sensors reviewed had an impact on the liquid, whether through a contamination risk or a rise in temperature. Moreover, their price does not allow them to be considered as disposable products whereas biological applications often prefer Fluigent components that can be sterile or disposable. The following will focus on inconsequential microfluidic flow sensing methods.

Fluigent non-invasive flow sensing technology

Fluigent internally developed a unique flow sensing technology dedicated to pressure-based microfluidics. It is the first non-invasive and calibration-free flow sensing technology for microfluidic applications. The device is placed in the pneumatic path between the pressure controller and the fluidic reservoir. The liquid flow rate is derived from the gas flow rate in the pneumatic path thanks to calibrations and sensors, high-performance algorithms, and a zero-leakage system.

As it’s not positioned in the fluidic line, the device is able to tackle all contamination and clogging issues as well as time-consuming liquid calibration and cleaning steps. It shows high accuracy, and is liquid independent. They are thus adapted to perform experiments with a sterile environment for the fluid or to produce droplets using several different liquids.

However, the response time is < 10 s, making it incompatible if one needs to generate complex flow patterns during a specific timeline. In addition, gas flow calibration needs to be performed if one is not using air in the pneumatic path.

Learn more about this technology.

Three other technologies have been selected for this review. They are less developed than the others for now and still need improvement to be effective.

See our webpage.