SUBNANOWATT MICROBUBBLE PRESSURE TRANSDUCER
C. A. Gutierrez* and E. Meng
University of Southern California, Los Angeles, California, USA
Rayleigh-Plesset equation [4]:ABSTRACT
We present the first all-Parylene microbubble pressuretransducer (μBPT). The μBPT utilizes an electrolytically generated
microbubble (μB), trapped in a Parylene microchamber, forpressure sensing. Pressure-induced bubble size variation isdetected by electrochemical impedance measurement. Real-timehydrostatic pressure measurement with excellent sensitivity (-10.7
Ω/psi, ±0.1 psi) up to 1.8 psi and tracking of internal pumppressure in a MEMS-based implantable drug delivery system wereachieved. The transduction method and device format uniquely
leverage the surrounding liquid environment, obviating the needfor hermetic or special packaging techniques for sensing in wetenvironments. Arrayed μBPTs are biocompatible, fabricated on
flexible substrates, ultra-miniature (200 μm diameter, 10 μm
thick), and can be operated at very low power (≤ nW) making themespecially attractive for in vivo pressure measurement applications.

r&r& +

3 2 1⎛
2σ 4 μ ⎞−r& = ⎜ p g − p∞ −r& ⎟2ρ⎝rr ⎠(1)

where r is the bubble radius (dots denote time-derivative), pg andp∞ are the pressure in the gas at the bubble wall and ambientpressure far away from the bubble (infinite distance), σ is surface
tension, μ is fluid viscosity, and ρ is fluid density.

INTRODUCTION
It is known that gas bubbles respond to external pressure [1]but few efforts exploit this phenomena for sensing. At frequencies
below resonance (55 kHz for a bubble of 50 μm radius [2]),microbubbles respond instantaneously to pressure variations.
Using microelectromechanical systems (MEMS) technology,
miniature devices which can precisely produce, localize, andmeasure bubble response at very small scales can be fabricated.
Polymer-based MEMS fabrication technology in combination withmicrobubble dynamics are leveraged here to introduce a new classof pressure transducer with unique capabilities.
State-of-the-art ultra-miniature pressure sensing technologies
generally occupy 400-500 μm diameter footprints. Our uniqueelectrochemical-based pressure sensing technique does not utilize
conventional diaphragm-based pressure transduction, enabling
significant reductions in overall footprint, materials processing
costs, and power consumption. Electrochemical impedance-based
sensing can be accomplished at nanowatt power levels, making thisattractive for wireless and implantable applications. Previously,pressure measurements within a microfluidic channel weredemonstrated using μB-based transduction [3], however thisapproach utilized rigid substrate materials and thus was not
amenable to wide application (e.g. sensing small pressure
variations in vivo). Here, Parylene C is featured as both the flexible
substrate and structural material; this combination enables a novel
sensor configuration capable of controlling bubble generation,localization, and transduction in a completely released and portabledevice compatible with diverse liquid environments. In particular,
these features address the unmet need for robust in vivo pressure
sensors. Our μB pressure sensing approach eliminates the need forhermetic packaging (for operation in wet environments) and theexclusive use of polymer materials reduces cost, adds mechanicalflexibility, and facilities integration for medical applications.

Figure 1: (Left) Electrolytic generation and growth of a bubble
within a fluid-filled Parylene microchamber. (Right) Bubble size
instantaneously responds to variations in external pressure and istracked through measurement of solution impedance. Twoelectrodes are located at the periphery of the chamber and shownin black. Top row = top view, bottom row = cross-sections.
Under the condition that the pressure oscillation frequency ismuch smaller than the bubble resonant frequency and neglecting
any interfacial mass transfer effects, a simple assumption is thatthe gas follows a polytropic law of compression with a polytropic
exponent b ≈ 1 at low frequency [4]:⎛r ⎞p g = pi ⎜ 0 ⎟⎝r ⎠(2)

where r0 and pi are initial bubble radius and equilibrium gas
pressure inside the bubble, respectively. From Eq. 1, the followingpressure-radius relationship is obtained:

THEORYb⎛r ⎞2σ
p ∞ = pi ⎜⎜ 0 ⎟⎟ −rr⎝ ⎠Microbubble Dynamics
The response of suspended bubbles to changes in ambientpressure is well studied with regard to bubble dynamics and massdiffusion processes across the gas-liquid interface. The
fundamental dynamics of a suspended bubble fixed in an
unbounded incompressible viscous liquid are governed by the0-9640024-8-5/HH2010/$25©2010TRFb(3)The pressure-radius bubble response can therefore be
estimated by Eq. 3. which describes the balance of forces acting on
the bubble. For a given number of gas molecules produced by57

Solid-State Sensors, Actuators, and Microsystems Workshop
Hilton Head Island, South Carolina, June 6-10, 2010

electrolysis and a non-varying surface tension, bubble size is adirect and instantaneous measure of ambient pressure (Figure 1).
If one now considers the bubble behavior over larger timescales, the effects of mass transfer at the bubble liquid interface
become significant. The bubble will dissolve in the presence of anunder-saturated liquid as a consequence of diffusion across thebubble-liquid interface. Bubble dissolution rate in an undersaturated solution was derived by Epstein and Plesset [1]:⎞k (c s − c∞ ) ⎛⎜ 1
1dr⎟+=dt ρ ∞ + 2τ / 3r ⎜⎝ r (πkt )1 / 2 ⎟⎠electrolyte impedance (resistance), is a direct measure of externalpressure variations.

METHODS
Materials and Fabrication
The transducer features an all-Parylene construction (substrateand structural material) which provides flexibility andbiocompatibility for medical and in vivo applications. Electrodes
and traces are formed from thin film platinum. No further materials
were utilized nor were any hermetic sealing or encapsulation
techniques required. This “wet” sensor is open to and filled by thesurrounding aqueous liquid (via fluidic access ports) which serves
as the electrolyte (Figure 3). Isolation of the sensor from theenvironment is therefore not necessary. Added costs andcomplexities associated with hermetic packaging are avoided.

(4)

where k is the coefficient of diffusivity of the gas in the liquid, cs
and c∞ are the saturation concentrations of gas in the liquid at thebubble surface and in the bulk, ρ∞ the density of gas in the bubble
with a gas-liquid interface of zero curvature, and τ is the modified
surface tension. The mass-diffusion processes taking place acrossthe bubble-liquid interface play a significant role in the behavior ofgas bubbles because they may ultimately determine the presence orabsence of bubbles in a liquid. These processes are governed by
Henry's law, which establishes a connection between the partialpressure of a gas acting on a liquid surface, pg, and the equilibrium(or saturation) concentration of gas in the liquid:
cs = ap g(5)

a is a constant characteristic of the particular gas–liquidcombination and is a function of temperature. If the ambientpressure is fixed and equal to p∞, then it is clear that unless the gas
concentration c at the bubble surface satisfies Eq. 5, the bubble
will not be in equilibrium, and will either grow or shrink according
to whether c > cs or c < cs. Mass transfer driven bubble dissolution
is a slow process; typical values for bubbles of radius ~100 μm are
estimated to be on the order of ~0.1 μm/sec [4].

Figure 3: (Left) Model of pressure transducer. (Right) Optical
micrograph of actual device (200μm diameter) with a bubble.
Fabrication techniques were previously reported [7]. Briefly,platinum electrodes (2000 Å) were deposited and patterned on aParylene coated (10 μm thick) soda lime wafer (1 mm thick)followed by a 1 μm thick Parylene insulation layer. A 2 μm
sacrificial photoresist layer then formed the fluidic access ports
followed by a second Parylene deposition step (2 μm thick). A 1012 μm sacrificial photoresist layer was then spun-on and patterned
to establish the chamber height and diameter (200-300 μm). The
chamber structure was enclosed by a final of 4.2 μm Parylene
layer, followed by opening of access port vias by oxygen plasma.

Liquid Impedance-based TransductionThe underlying principle of impedance-based transduction is
the measurement of solution resistance. The electrode-electrolyte
interface has been well studied and characterized [5, 6] and issimply modeled as shown in Figure 2 below:

Figure 2: Electrical equivalent circuit for the electrode-electrolyte
interface (Randles model).
Figure 4: Fabrication process flow for a single transducer. Crosssection taken through electrodes.

where Cdl, Rct, and Rs are the double-layer capacitance, chargetransfer resistance, and solution resistance, respectively. By
applying a small alternating current at a sufficiently high frequency(typically >1 kHz), the parallel components are shorted throughCdl, and Rs dominates the measured impedance. The solution
resistance is a function of ionic concentration, distance between theelectrodes, and cross-sectional area of electrolyte between theelectrodes. A trapped μB acts as an insulating sphere in the
conductive incompressible electrolyte between the electrodes.
Therefore, monitoring μB size variations, through measurement of

Following removal of sacrificial photoresist by immersion in
acetone and isopropyl alcohol, chambers were simultaneously
filled at the wafer-level by passive soaking in a bath of the desired
electrolyte solution. The chamber design allows the ionic
conductive path to be constrained within in the chamber interior.
This enables the measurement solution resistance in a known
geometry and minimizes the potential for cross talk between
arrayed sensors. Test dies containing several μBPTs were58

fabricated. In addition, a μBPT array integrated at the tip offlexible Parylene cable was fabricated and completely released
from the substrate to form a pressure probe.

within the device while it is operated in a different medium [8].
This capability, combined with the small size and polymer
construction, makes this technology amenable to low power
applications such as implantable wireless pressure monitoring.

Experimental Setup
The devices were filled with deionized (DI) water or 1x
phosphate buffered saline (PBS) as the electrolyte. A microbubble
was electrolytically generated within the chamber by applying a
DC current pulse (typically 1 μA, 5 s for DI water). Device
impedance was monitored using a LabVIEW-interfaced Analog
Devices Impedance Converter (AD5933) calibrated using anAgilent Precision LCR meter (1 Vpp, 5 kHz). A calibrated pressuresource metered external hydrostatic pressure applied to μBPTs
housed in a testing jig. A series of pressure steps were applied up
to 1.8 psi while impedance was monitored.

RESULTS AND DISCUSSION
Hydrostatic Pressure Measurement
Measurement of hydrostatic pressure variations wasperformed. Impedance measurements exhibited excellent
resolution up to 1.8 psi (Figure 5).

Figure 6: Impedance-pressure plot generated from data in Fig. 5
Drug Delivery Pump Pressure Measurement
For practical applications, an array of μBPTs was fabricatedon the tip of a flexible Parylene cable. This allowed placement oftransducers in an environment of choice (Figure 7).

Figure 5: (Top) Profile of applied hydrostatic pressure fromcalibrated pressure source. (Bottom) The measured impedance
response (1x PBS) from the μBPT to the applied pressure profile.

Figure 7: (Left) Drawing of μBPT array positioned at the tip of aflexible Parylene cable. (Right) Optical micrograph of array.
Practical pressure sensor operation was demonstrated in thereal-time tracking of internal pressure in an electrolysis pumputilized in a MEMS drug delivery system [9]. Unlike conventionaltransducers, the small form factor and flexibility of the μBPT arraymade possible its integration within the polymer-based drugdelivery pump to assess internal pressurization conditions. The
μBPT array was placed in contact with fluid in the pump chamber.
(Figure 8). Pump ON/OFF states were clearly detected andcalibrated pressure measurements agree well with previously
reported data measured with a conventional silicon pressuretransducer [9] (Figure 9).

Measurements were obtained within 100 seconds of bubbleformation; minimal change in bubble volume occurred over thistime. Some measurement drift was observed at maximum pressure(1.8 psi) and was attributed to mass transport-driven bubble
dissolution at this elevated pressure. Stable measurements weremost easily obtained at pressures below 2 psi (13.9 kPa). A
calibrated sensor response of -10.7 Ω/psi was obtained by a best fit
linearization and clearly demonstrates pressure tracking capability(Figure 6). Pressure measurement resolution was estimated to be±0.1 psi (689.4 Pa). It was possible to detect pressure variations
with excitation amplitudes of only 100 mV, 10 nA (~1 nW);
detection at lower excitation amplitudes was also possible but not
characterized here. When DI water was used as the electrolyte, asolution resistance of several megaohms was typically observed
making it possible to realize sub-nanowatt device operation. The
bubble generation phase does require somewhat higher power
levels but these are typically in the microwatt range and only a few
seconds in duration. Although a device configuration open thesurrounding environment is desirable the integration of liquid
entrapment structures, such as a Parylene-based stiction valve, canprovide a means for the entrapment of a particular electrolyte

Figure 8: Experimental setup for monitoring intra-pump pressure
produced via electrolysis.

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[3]. Other electrolyte-gas combinations can be utilized, such as
ethylene glycol or alcohols, which may provide insoluble
conditions for entrapped gases for applications requiring long term
constant-volume μB transduction capability.

CONCLUSION
We have designed and fabricated a Parylene-based pressuretransducer utilizing a unique liquid-impedance transduction
technique. Response of a bubble to external pressure variations isharnessed to electrochemically monitor pressure. The sensor
operates in communication with the surrounding liquid
environment (either DI water or PBS), thereby eliminating theneed for hermetic packaging. Preliminary sensor characterization
indicates a sensing resolution of ±0.1 psi over a 0-2 psi range.

ACKNOWLEDGEMENTS
This work was funded in part by the Engineering ResearchCenters Program of the NSF under Award Number EEC-0310723,
an NSF CAREER Award (ECS-0547544), and the Bill andMelinda Gates Foundation (CG). The authors would like to thankDr. Donghai Zhu, Mr. Connor McCarty, Ms. Roya Sheybani andthe members of the USC Biomedical Microsystems Laboratory for
their assistance.

Figure 9: Impedance response to electrolysis pumpactivation/deactivation cycles (5mA pump current). Calibrated
measurement of pressure (-10.7 Ω/psi) are shown at two points.
Static Bubble Approximation
According to Faraday’s law, the number of gas molecules inan electrolytic gas bubble is determined by the total chargetransferred during electrolysis:

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[7] C. A. Gutierrez, C. McCarty, et al., "An Implantable AllParylene Liquid-Impedance based MEMS Force Sensor," inProc. IEEE MEMS 2010, Hong Kong, China, pp. 600-603.
[8] C. A. Gutierrez and E. Meng, "Improved Self-Sealing
Liquid Encapsulation in Parylene Structures by Integrated
Stackable Annular-Plate Stiction Valve," in Proc. IEEEMEMS 2010, Hong Kong, China, pp. 524-527.
[9]P.-Y. Li, R. Sheybani, et al., "A Parylene Bellows
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(6)

where z is the total charge associated with the formation of a single
gas molecule, F is the Faraday constant, and n is moles of gas
molecules. The electrochemical reaction of electrolytic bubble
generation was thoroughly studied in [10]. It was shown that H2and Cl2 gases are the main products of electrolysis of a NaClaqueous solution with negligible byproducts. In practice, the gas
composition of the bubble is nearly all hydrogen, due to the lower
standard potential required for hydrogen gas evolution.
Additionally, the solubility of hydrogen is about three orders ofmagnitude lower than for Cl2.
Once the bubble is formed, the slow diffusion-limited
dissolution process maintains an approximately constant bubble
size for a period of time (~20 min), and is dependent on thekinetics and solubility of the gas/liquid interface. There are several
factors enabling the use of a slowly shrinking bubble to measurepressure. Generally, smaller bubbles will have higher surface
tension and therefore higher internal pressures which serves tospeed up the dissolution according to Eq 1. The surface to volume
ratio also increases with decreasing bubble size. Finally, it isknown that platinum acts as a catalyst and can increase therecombination rate significantly.
In this device, the exposure of the platinum electrodes islimited to the periphery and there is essentially no contact between
the recombining gas and the electrodes, thereby minimizing any
catalytic effect. In addition, the bubble is compressed due to thefixed chamber height and is forced to expand only in lateral
directions. This effectively reduced the surface to volume ratio
over which bubble dissolution can occur by limiting mass transport
processes to the edges of the bubble. In other words, the top andbottom surfaces of the bubble, which are in contact with thechambers top and bottom surfaces, do not contribute significantly
to the mass transport process. These factors taken together giverise to longer bubble lifetimes allowing their use as quasi-constantpressure sensors over short to medium time scales (~15-20 min).
Over larger time scales, the measurement of pressure via bubble
dissolution rate is also possible and was previously demonstrated

CONTACT*C. A. Gutierrez., tel: (213) 821 3949; cagutier@usc.edu

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