ELASTOMER MEMBRANE PRESSURE SENSORS FOR MICROFLUIDICSAntony Orth*, Ethan F. Schonbrun and Kenneth B. Crozier

School of Engineering and Applied Sciences, Harvard University,Cambridge, MA USA

ABSTRACTWe present a novel pressure sensor for microfluidics with optical readout. The multilayer soft lithographic design al-

lows high sensitivity pressure measurements in microchannels using only an optical microscope in transmission mode.We discuss their fabrication, operation and performance.

KEYWORDS: Pressure, Membrane, Microlens, Soft Lithography

INTRODUCTIONPressure measurement schemes for microfluidic devices are difficult to implement and often sacrifice important per-

formance metrics, such as response time or precision, in their basic design [1]. Ideally, one should be able to measurethe pressure over the entire extent of a microfluidic chip with a fast response time, high precision and without compli-cated equipment. In addition to enabling device characterization, such a pressure measurement technique would facilitatenovel microcirculation and multiphase flow experiments [1, 2]. Towards this end, we have developed a microfluidicpressure sensor, in which the deformation of a PDMS membrane is read out optically at various points in a microfluidicdevice. The deforming membrane acts as a microlens that focuses the illuminating light, allowing pressure measure-ments to be made over the entire field of view of the microscope.

FABRICATION AND EXPERIMENTALThe microfluidic device is fabricated in polydimethylsiloxane (PDMS) using multilayer soft lithography. Three lay-

ers are required: the first layer contains the desired microfluidic network with additional dead-end pressure taps protrud-ing from the main channel where the pressure is to be measured. A middle layer consisting of a thin PDMS membraneis sandwiched between the first layer and a third layer. The third layer consists of circular depressions that are aligned tothe pressure taps, as shown in Figure 1. The first and third layers are cast over an SU-8 on silicon master but are onlypartially cured. The membrane is fabricated by spin coating PDMS onto a bare, silane treated silicon wafer. Once par-tially cured, the membrane is transferred to the third layer by plasma oxidation. This composite layer is then aligned to,and fully cured against, the first layer, resulting in a single monolithic device. Once the device is filled with fluid, themembrane is free to deform in response to the fluid pressure. This deformation causes the membrane, along with thefluid below, to act as a microlens [3]. This microlens in-turn focuses the approximately collimated illumination into aspot, at a distance of a focal length from its back aperture.

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Figure 1: Left: Multilayered microfluidic device with pressure sensors. The PDMS membrane is free to deformunder pressure, as shown in a cross section to the right. Right: Experimental setup to determine pressure from pres-sure-deformed PDMS membrane.

The microfluidic device is viewed under a microscope whose focus is adjusted to make the imaging plane approxi-mately one focal length above the back aperture of the microlens at the maximum expected pressure. At this pressure,the focal spot observed in the microscope has peak intensity. At lower pressures, the focal length of the microlens in-creases, resulting in a decrease of the intensity of the spot in the imaging plane. By recording the intensity of the spotcreated by each of the microlenses at a series of known pressures, an intensity vs. pressure calibration can be effected.

For calibration, the chip is first filled with water and its inlet and outlet are then connected to a common source ofpressurized air. The air pressure is controlled with a precision air regulator from 0 to 15 PSI. During calibration, thereis no flow within the chip, so that the pressure everywhere along the microchannel is known. Figure 2 shows a typicalset of calibration data for nine pressure sensors within the field of view of the microscope. Each microlens region meas-ures 40 μm in diameter, with a PDMS membrane thickness of approximately 8 μm. The intensity value is the sum ofthe grey level of a fixed set of pixels in the microlens focus.

978-0-9798064-3-8/µTAS 2010/$20©2010 CBMS 1994 14th International Conference onMiniaturized Systems for Chemistry and Life Sciences

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Figure 2: Left: Typical calibration curves for a microfluidic device with pressure sensors. Right: Microfluidic devicewith pressure sensors circled in colors corresponding to the plot colors to the left. The bright sport in the middle ofeach colored circle is the focal spot of the microlens in the slightly defocused imaging plane.

THEORYThe hydraulic capacitance of the PDMS membrane couples together the time response and the pressure resolution of

the pressure sensors. The hydraulic capacitance is the change in the volume of fluid stored under the membrane per unitchange in pressure exerted on the membrane. When the membrane deforms due to increased pressure, extra fluid isstored in the tap [4]. The flow that carries this extra volume of fluid is driven by the pressure differential between themembrane region and the foot of the tap. For laminar flows, the pressure differential P and volumetric flow rate Q arerelated by P=QR where R is a hydrodynamic resistance. In analogy to charging a capacitor in electronics, the timeconstant = RC (where C is a fluidic capacitance) gives the time taken to fill up the pressure tap with fluid and equili-brate the pressure gradient along the dead-end channel. A stiffer membrane decreases both the magnitude of deformationand the time needed for the deformation to equilibrate. That is, a stiffer membrane improves the time response and dy-namic range at the expense of pressure resolution and vice-versa. The other relevant parameter, the hydrodynamic resis-tance, is determined by the geometry of the channel and the viscosity of the fluid and has no effect on the absolute pres-sure resolution [4]. A dead end channel with a smaller cross section or of greater length will slow the time responsewhile the opposite is true for shorter, wider and deeper dead end channels leading to the membrane area.

RESULTS AND DISCUSSIONA convenient feature of the microlens pressure sensors employed here is that the intensity of the focal region is nearly

linear with pressure and as a result the sensitivity is practically constant throughout the dynamic range. We demonstrate thespatial resolution of pressure measurements in Figure 3 where the flow is driven via a syringe pump (Harvard Apparatus) at13 μL/hr. As expected, there is a clear linear increase in pressure along the channel in the flow direction.

Figure 3: Left: Pressure trace of nine pressure sensors placed along a microfluidic channel. The flow rate is main-tained at 13 ul/hr, causing a pressure drop along the direction of flow. The standard deviation of the pressure read-ings is ~100 Pa. Right: Pressure reading along microchannel. As expected, the pressure varies linearly.

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The noise level of the pressure sensors is dependent on both the sensitivity of the PDMS membrane and the video cam-era settings used. For a typical device, viewed at 232 frames per second (fps) and with a membrane thickness of 8 µm, thestandard deviation of the pressure sensors is approximately 100 Pa, as shown in Figure 3. Standard deviations of 20 Pahave been achieved with thinner membranes. Because the noise is Gaussian, averaging can further reduce the noise with asquare root dependence on the number of frames averaged over.

The time response of the pressure sensors has not yet been characterized experimentally. However, the expected time re-sponse can be estimated using standard approximations for both the hydrodynamic resistance and capacitance [4, 5]. Givena membrane diameter of 20 µm, thickness of 8 µm and a Young's modulus of 400kPa along with a pressure tap length,width and depth of 50 µm, 10 µm and 10 µm, respectively, the time constant of the sensor is approximately 0.3 ms.

CONCLUSIONWe have demonstrated a microfluidic pressure measurement system capable of resolving pressure changes smaller

than 100 Pa at multiple locations in microfluidic channels. The measurement system is implemented on-chip using aPDMS multilayered design, and requires only an optical microscope operating in transmission mode. We conservativelyestimate the time response of these sensors to be on the order of a millisecond; this will be studied in the near future.The time response, pressure resolution and spatial resolution are such that we expect these sensors to be useful for a vari-ety of applications from studying multiphase flow phenomena to microcirculatory experiments.

ACKNOWLEDGEMENTSThis work was funded by the Advanced Energy Consortium.

REFERENCES[1] M. Abkarian et al., High-speed microfluidic differential manometer for cellular-scale hydrodynamics, PNAS Vol.

103 no. 3 (2006).[2] M. Abkarian et al., Cellular-scale hydrodynamics, Biomed Mater. Vol. 3 034011 (2008)[3] L.P. Lee et al., Tunable liquid-filled microlens array integrated with microfluidic network, Opt. Exp. Vol. 11 no.

19 (2003).[4] B.J.Kirby, Micro- and Nanoscale Fluid Mechanics: Transport in Microfluidic Devices,

http://www.kirbyresearch.com/index.cfm/wrap/textbook/microfluidicsnanofluidics.html, Sept. 11 2009.[5] D. C. Leslie et al., Frequency-specific flow control in microfluidic circuits with passive elastomeric features, Nat.

Phys. Vol. 5 pp.231-235 (2009).

CONTACT*A. Orth, tel: +1-617-495-2560; aorth@fas.harvard.edu

1996