After the development of elastomer microfluidics and the subsequent vigorous pursuit of its biological applications, it has become clear that the next generation of microfluidic devices would combine the fundamental technology with integrated electrical and optical systems for control and measurement. Such integration would offer new analytical and functional capabilities, as well as true overall device miniaturization.⁴ A few steps in this direction have already been taken, producing a capacitance cytometer,⁹ a thermal cycler,¹⁰ and a spectrophotometer.¹¹ Moreover, such devices can be arranged as independent but interconnected modules functioning within a single chip.¹²

As part of this emerging wave of devices, we present an electrical elastomeric pressure gauge. It utilizes the basic effect that an electrolyte-filled microchannel experiences a large increase in electrical resistance when it is completely pinched off by a microfluidic valve whose material is an electrical insulator. This effect establishes an electrical means of reporting valve status. On the other hand, each valve remains open up to some characteristic pressure determined by its dimensions.^13,14 Therefore, the status of a particular valve offers an inequality for the magnitude of the applied pressure—either larger or smaller than the characteristic closing pressure of the valve. Then, a heterogeneous valve array produces a system of such inequalities that limit the magnitude of the applied pressure to a particular interval of values. The overall system acts as a pressure gauge. Its compatibility with standard PDMS microfluidic technology and electrical measurement and control makes it ideally suitable for integration in the future PDMS microelectrome-chanical systems (MEMS).

The observed effect establishes a 1-1 correspondence between channel resistance (low/high) and valve status (open/closed). The mechanical properties of the valve establish another 1-1 correspondence, between the valve status (open/closed) and the applied pressure (insufficient/sufficient). The status of a single valve does not report the value of the applied pressure, but reports if the applied pressure is below or above the valve’s characteristic pressure. In essence, a single valve status produces a single inequality.

Valves of different dimensions have different characteristic pressures.¹⁴ Therefore a heterogeneous array of valves, acted upon by the same applied pressure, would report a set of inequalities, whose bounds are the different characteristic pressures. Thus the magnitude of the applied pressure would be limited to one of a set of intervals delineated by these bounds.

This analysis suggested the basic scheme described above. The scheme was implemented for applied pressures of 0.5 to 19 psi above atmospheric, in steps of 0.5 psi. The maximal value was set by the pressure at which all valves were closed. Further increase in the pressure would not change the result, while pressures in excess of 20 psi significantly increase the risk of layer delamination. Each flow-channel prong had low resistance (26–64 MΩ) when its valve was open, while the resistance increased beyond the dynamic range of the multimeter (2 GΩ) when the respective valve closed completely. Figure 2 shows the resistance pattern versus applied pressure. Since in certain cases multiple valves closed at the same pressure, their resistance patterns overlapped and are represented by the same color.

This system can be used as a pressure gauge. For example, if all valves up to and including “blue” in Fig. 2 are in “high resistance” state, while all valves above it (light green, red, black) are in “low resistance state,” then the applied pressure is between 10.5 and 11 psi.

The precision of the measurement is dependent on the spacing of curves in Fig. 2 and thus, on the spacing of characteristic pressures. In the demonstrated device, valve width, thickness, and material were kept constant, while valve length was varied between 55 and 200 µm. However, if that restriction is relaxed, many more values for characteristic pressure become available.¹⁴ Then the pressure spacing can be shrunk accordingly, thereby improving the precision of the measurement.

Meticulous mappings of the phase space of closing pressures versus valve dimensions¹⁴ showed that individual valve behavior is robust, reliable, and reproducible, thereby attesting to the robustness, reliability, and reproducibility of its derivative devices, such as the presented pressure gauge. Hence, the accuracy of the measurement is set by the accuracy of the digital gauge and the size of the pressure step used in calibration.

The response time of the overall system is governed by the mechanical actuation time of the valves and the time taken by the electrical measurements. Micropump characterization²⁴ sets the former at the scale of milliseconds, while the latter typically are orders of magnitude faster. Thus the overall sensor response time would be milliseconds. Such speeds are adequate both for isolated measurements and for continual monitoring in pressure regulation loops.

In the presented embodiment, the pressure gauge achieves large signal-to-noise in valve status measurements, through the use of a salty buffer. Hence, there are concerns that salt ions could diffuse through the elastomer, thereby adversely changing the ambient conditions in particular biochemical applications. However, biochemistry typically works with salinities at physiological level or above, which is essentially what we used here. Furthermore, in any particular case, the electrical measurement fluid can be set at the same salinity as the biochemical environment to prevent nonzero net ionic flux. Finally, potential losses of signal to noise in valve status measurements can be offset by optimizations of the geometry of the conducting channels.

Other pressure-sensing schemes and devices have been proposed and demonstrated. A microfluidic differential manometer has been used to study cells.¹⁵ However, it does not produce an absolute measurement of the pressure, while the readout is done visually and thus cannot be straightforwardly automated or miniaturized.

Piezodielectric¹⁶ and piezoelectric^17–20 sensors have convenient electrical readout and are miniaturizable. However, it may prove challenging to adapt these devices for inexpensive mass production, robust performance, and integration into particular systems, especially since many biological and biomedical applications already place tight constraints on the properties of the substrate, e.g., due to binding surface chemistries⁵ and/or cell toxicity. In addition, some of the devices^18,20 have inadequate dynamic ranges for typical elastomer microfluidics.

Vacuum-sealed silicon sensors²¹ utilize capacitance, piezoresistivity, or resonance measurements involving a silicon microdiaphragm. These sensors are compatible with mass production, are electrically readout, and are at the correct physical scale. However, the capacitance version requires voltages that are impractical for overall system miniaturization, the piezoresistive version is limited to silicon substrates, and the resonator versions are difficult to fabricate and are also limited to silicon substrates.

A pressure sensor,²² involving an interdigitated capacitor with metal oxide dielectrics, has high sensitivity but excessive physical size and insufficient dynamic range. An optical sensor²³ measures the deflection of a silicon membrane by the intensity of light reflected from it; however, a light source, waveguides, and a photodetector are necessary, and so, overall system miniaturization is problematic.