Pressure sensing in liquids is important for engineering applications ranging from industrial processing to naval architecture. Here, we propose a pressure sensor based on highly compressible polydimethylsiloxane foam particles embedding fluorescent Nile Red molecules. The particles display pressure sensitivities as low as 0.0018 kPa–1, which are on the same order of magnitude of sensitivities reported in commercial pressure-sensitive paints for air flows. We envision the application of the proposed sensor in particle image velocimetry toward an improved understanding of flow kinetics in liquids.

The possibility of in situ measurement of pressure in a liquid flow, across a wide range of Reynolds numbers (0.1–106) and length scales (1–500 mm), is attractive for applications in industrial process engineering,1 naval engineering,2 and biomechanics.3,4 For example, the measurement of pressure in polymer flows may help improve manufacturing processes of composite and multi-material structures, where local fluctuations are a primary cause of defects in extrusion and molding processes.5,6 Detailed pressure measurements may inform the design of marine vessels, whereby knowledge of the hydrodynamic loading experienced by ship hulls during sailing and maneuvering is important for performance and safety.7 However, a sensor for in situ measurement of flow pressure in liquids is yet to be developed.

A critical research area entails the simultaneous measurement of pressure and velocity, toward an improved understanding of flow kinematics and kinetics. Particle image velocimetry (PIV) has been proposed as a powerful technique for non-invasive velocity measurement. PIV employs small particles as tracers to reconstruct the magnitude and direction of the velocity field. Small colorimetric sensors have been developed for simultaneous pressure and velocity measurements in microfluidic devices.8 These sensors are generated on a silicon substrate by controlled deposition of parylene polymers. Despite promising results, the limited scalability in the production of these sensors restrains their use in microengineering. Another technique for pressure sensing in PIV has been developed using air bubble generators.9 In this case, the diameter of suspended air bubbles is used to infer the local pressure, but scaling this technique to create a large number of bubbles presents technical difficulties.

In air flows, pressure sensitive paints (PSPs) constitute a viable solution for non-contact pressure measurements. The paint contains a chromophore designed to fluoresce at different intensities depending on the local oxygen concentration. PSPs have been used in the aerospace industry to monitor pressure on aerodynamic surfaces through commercial camera sensors.10,11 PSPs have also been integrated in polymer particles for fluorescence pressure measurement in PIV.12,13 In these experiments, single dye and multiple dye PSPs have been used to stain microparticles for detecting pressure jumps on the order of 80 kPa across a shockwave, although simultaneous PIV measurements are yet to be demonstrated.

In this letter, we propose particle sensors for in situ pressure measurements in liquids. The sensors are based on highly compressible foam particles embedding a fluorescent dye. By increasing the pressure of the liquid in which the particles are suspended, the fluorescence emission of the particles consistently decreases during their mechanical deformation, enabling the detection of pressure changes. Different from traditional pressure transducers,14 the fluorescent particles may enable in situ measurement of pressure in liquids without direct connection to the testing apparatus. The particles may be employed as flow tracers, toward simultaneous flow velocity and pressure measurements in PIV.

The fabrication of the particles is based on a single emulsion process using vegetable oil (corn oil) as the continuous phase. A schematic of the fabrication process is shown in Fig. 1(a). The particles are prepared from the polydimethylsiloxane (PDMS) elastomer (Sylgard 184) stained using Nile Red dye. PDMS is selected for its optical transparency, low modulus, and ability to undergo large reversible deformations.15,16 A large mass fraction (24%) of Expancel® 930 DU 120 microspheres is added to the PDMS and expanded during emulsion crosslinking to generate highly compressible foam particles. At room temperature, Expancel microspheres contain a hydrocarbon, which vaporizes at high temperature, thereby causing the capsules to expand to several times their original size. The expanded microsphere consists of a thin, highly compliant shell of approximately 0.1μm thickness, encapsulating an air void in a closed cell structure.

FIG. 1.

(a) Schematic of particle preparation. (b) Optical micrograph of the PDMS emulsion in vegetable oil.

FIG. 1.

(a) Schematic of particle preparation. (b) Optical micrograph of the PDMS emulsion in vegetable oil.

Close modal

In a typical preparation, 5 ml of Sylgard 184 part A is mixed with 0.5 ml of Sylgard 184 part B, 1.2 g of Expancel 930 DU 120 microspheres, and 100μl of the 40mg/ml solution of Nile Red (technical grade, Sigma Aldrich) in ethanol (absolute, 99.8%, Sigma Aldrich). First, the mixture is homogenized using a spatula. Then, with a syringe, 1 ml of the mixture is added drop-wise to 20 ml of vegetable oil and emulsified by stirring at 1200 RPM at the initial temperature of 80°C. The optical micrograph of the PDMS emulsion in vegetable oil is displayed in Fig. 1(b). We confirm the presence of polydisperse PDMS droplets, with each droplet containing a suspension of unexpanded Expancel microspheres. Experimental observations at room temperature show that this emulsion is stable after approximately 20 min, and coalescence is registered only for large droplets.

To rapidly crosslink the PDMS elastomer and expand the Expancel microspheres, the temperature of the emulsion is raised to 140°C in 5 min under continuous stirring and kept at 140°C for additional 4 min. The conversion of the initial elastomeric mixture into particles is almost complete, and the oil is clear at the end of the process. Particles floating on the oil surface are collected by filtration via Whatman paper and washed using a 10% solution of ethanol in de-ionized water (resistivity, 18.2 MΩ). The density of the particles, estimated through gravimetric analysis, is in the range of 0.25–0.29 g/ml. Particle diameters vary in a relatively wide range of 200 μm1 mm. The total volume of the particles produced in each batch is on the order of 17–20 ml (from the 5 ml initial solution).

The morphology of the particles is investigated through X-ray computed tomography (CT) and scanning electron micrography. The CT-scan of the particles is obtained via a Bruker Skyscan 1172 micro-CT scanner with a resolution of 1.09 μm/pixel. Scanning electron microscopy is conducted using a Hitachi S-3400N instrument. Figure 2(a) displays a cross-sectional image obtained from the CT-scan of one of the particles, and Fig. 2(b) shows the three-dimensional reconstruction of one eighth of a particle. Figures 2(c) and 2(d) display the scanning electron micrographs of a particle and a half-particle section, respectively.

FIG. 2.

(a) Tomographic section of a foam particle. (b) Three-dimensional reconstruction of one eighth of a particle from CT data. (c)–(d) Scanning electron micrographs of a particle and half particle section.

FIG. 2.

(a) Tomographic section of a foam particle. (b) Three-dimensional reconstruction of one eighth of a particle from CT data. (c)–(d) Scanning electron micrographs of a particle and half particle section.

Close modal

The microstructure of a particle is characterized by a large fraction of expanded Expancel microspheres. The microspheres are clearly visible on the surface of the particles, due to their relative large size, which generates a characteristic bumpy morphology (see Fig. 2(b)). From the cross-sectional images in Figs. 2(a), 2(b), and 2(d), we note that particles present a large central void surrounded by a foam wall comprising the expanded microspheres. The number of microspheres in the wall varies from 1 to 2 for particles with 500–600 μm diameter to 3–4 for particles with diameters on the order of 1 mm. Smaller particles (200–300 μm diameter) might not present the internal void such that porosity is only present within the microspheres. Images are analyzed via CTAn software (bruker-microct.com) to determine the porosity ϕ of the particles, defined as the initial volume fraction of the air voids in the particle. Air voids include both the central void and the air encapsulated in the expanded microspheres. By averaging data obtained from CT-scans of four particles, we estimate ϕ=0.793±0.009.

Compression tests are conducted on the material testing stage (MTS1) of the micro-CT scanner. To create an isobaric compression state, experiments are performed by adding a particle suspension in silicon oil (100 cst) to a 11 mm-long polycarbonate cylinder (Fig. 3(a)). A compressive force is applied to the suspension via a syringe plunger actuated by the testing stage. To monitor the geometry of the particles during compression, we use CT-scans with a resolution of 3.95 μm/pixel. Each scan has a duration of 2.5 h, during which the position of the plunger is controlled by the compression stage. In Fig. 3(b), we display the cross sectional images for one particle at increasing pressure levels and lateral views of the cylinder in the test chamber of the micro-CT scanner. The change in volume of five different particles is determined using a segmentation and masking procedure in MATLAB that isolates the volume occupied by a single particle. The experimental volume is computed using the function “convhull.” The effective radius of the particle is estimated as r=(3V)/(4π)3, where V is the volume of the particle. The pressure in the cylinder is estimated by tracking the volume of the air bubble at the top of the cylinder (see Figs. 3(a) and 3(b)).

Specifically, we apply Boyle's law such that the pressure is given by p=p0(V0/V), where p0=101kPa is the atmospheric pressure and V0 the original air bubble volume. In Fig. 3(c), we report the normal stretch of the particles measured during the compression tests. The normal stretch is defined as r/r0, where r0 is the radius of the particle in the original configuration at p = p0. To demonstrate the large compressibility of the proposed foam particles, we compare the particle's normal stretch with the stretch that would be induced in an air void of the same dimension as the particle. The experimental results demonstrate that the particle is only moderately stiffer than an air void, with differences increasing as the applied pressure is increased. Specifically, the average normal stretch of the particles is r/r0=0.88 at p=165kPa (absolute), while the normal stretch for an air void is r/r0=0.85. As the pressure increases to p=363kPa (absolute), the difference is more appreciable, wherein we register r/r0=0.75 for the particles and r/r0=0.65 for an air void.

FIG. 3.

(a) Cylinder used for compression tests. (b) Deformation of a foam particle at increasing pressure is displayed in the first row. Images in the second row are side views of the cylinder during CT-scans, where the dashed red box identifies the region including the air bubble. (c) Experimental normal stretch of a particle as a function of pressure (dashed black lines); error bars are standard deviations for the five particles. In (c), theoretical normal stretch for an air void (red line) and a prediction from the composite model in Eq. (3) (blue line) are also reported.

FIG. 3.

(a) Cylinder used for compression tests. (b) Deformation of a foam particle at increasing pressure is displayed in the first row. Images in the second row are side views of the cylinder during CT-scans, where the dashed red box identifies the region including the air bubble. (c) Experimental normal stretch of a particle as a function of pressure (dashed black lines); error bars are standard deviations for the five particles. In (c), theoretical normal stretch for an air void (red line) and a prediction from the composite model in Eq. (3) (blue line) are also reported.

Close modal

The larger stiffness with respect to an air void is likely related to the microstructure of the particle foam rather than the stiffness of the PDMS structure and the shells of the expanded microspheres. This proposal rests on a simple composite model for the particle, in which we account for the microstructure of the air voids and hypothesize that the overall particle deformation is the result of the isobaric compression of the air voids. Under this assumption, the normal stretch of a particle due to the change in volume of its constituent air voids is

rr0=1+i=1N(ρi3ρ0i3)r033,
(1)

where N is the total number of air voids in the particle and ρi and ρ0i are the deformed and undeformed radii of air void i.

By using Boyle's law for the total volume of air contained in the particle, we find

p0p=i=1Nρi3i=1Nρ0i3.
(2)

Finally, by substituting Eq. (2) in Eq. (1), we obtain the following constitutive response

rr0=1+ϕ(p0p1)3,
(3)

where ϕ=(i=1Nρ0i3)/r03 is the porosity of the particle. In Fig. 3(c), we display the normal stretch of the particle predicted using Eq. (3) and the average value ϕ=0.793. The shaded area represents the uncertainty in the prediction of r/r0 associated with the uncertainty in the estimation of ϕ. The close agreement between Eq. (3) and experimental observations supports the possibility that the compressibility of the particle is controlled by its porosity, which is, in turn, related to the air voids encapsulated by the expanded microspheres and the larger internal void. In agreement with data from the manufacturer,17 it is tenable to hypothesize that the microspheres buckle under a small applied pressure, thereby causing the compliant shells to play a secondary role in the particle deformation. Similarly, it is possible that the PDMS structure undergoes a similar elastic failure under isobaric compression such that only air porosity contributes to the mechanical stiffness of the particle.

The fluorescence response of the particles is studied using the setup in Fig. 4(a). To minimize interactions between particles during the fluorescence measurements, approximately 100–150 particles are distributed in a thin layer (one particle thick) in the test chamber. A photographic image of the particles layer in the test chamber is displayed in Fig. 4(b). During the test, the chamber is filled with water and sealed using a transparent cap. Fluid pressure is controlled through a syringe and monitored via a Festo SDE1-D10-G2-R18-C-PU-M8 piezoelectric pressure sensor. Particle fluorescence is excited using a LZ4-40B208 light emitting diode (LED) with emission centered at 460 nm. Emission is measured via an Ocean Optics USB2000+ spectrometer. To filter out the excitation source from the spectrum, a 475 nm longpass filter is used. The data reported in this work are obtained for five separate experiments. In Fig. 4(c), we compare the fluorescence emission as a function of the pressure, with the reference emission of the LED used for the excitation. As expected, we register a reduction in the particle emission with the increasing pressure up to 220 kPa (absolute), while LED emission remains constant. The reduction in fluorescence emission should be associated with the deformation of the particles, which results in a reduction of the outer surface, responsible for absorption and emission.18 

FIG. 4.

(a) Testing setup for fluorescence characterization of the particles. Blue and red colors indicate LED and particles' emission, respectively. (b) Fluorescence image of the particle layer prepared in the test chamber. (c) Fluorescence emission of the particles and LED at increasing pressures p = 0, 60, and 120 kPa; the values are normalized with respect to the peak value at 0 kPa. (d) Emission intensities of the particles (circles) and LED (squares) as a function of pressure; error bars are standard deviations obtained for the five experiments. In (d), theoretical emission computed using Eq. (4) is also reported.

FIG. 4.

(a) Testing setup for fluorescence characterization of the particles. Blue and red colors indicate LED and particles' emission, respectively. (b) Fluorescence image of the particle layer prepared in the test chamber. (c) Fluorescence emission of the particles and LED at increasing pressures p = 0, 60, and 120 kPa; the values are normalized with respect to the peak value at 0 kPa. (d) Emission intensities of the particles (circles) and LED (squares) as a function of pressure; error bars are standard deviations obtained for the five experiments. In (d), theoretical emission computed using Eq. (4) is also reported.

Close modal

To investigate the dependence of the emission on the deformation, we propose a linear relation between the change in emission and the variation in the surface area of the particle

II0I0=α((rr0)21),
(4)

where I0 is the emission intensity of the undeformed particles, I is the emission intensity of the compressed particles, and α is a fitting parameter. By substituting Eq. (3) in Eq. (4), we obtain the emission of the particles as a function of the external pressure. In Fig. 4(d), we compare the emission predicted from Eq. (4) using α=0.44 with experimental data. The close agreement between the theoretical prediction and experiments suggests that the reduction of the outer surface is the primary cause for the decrease in emission.18 

The repeatability of the pressure measurement is assessed via cyclic loading. During a cycle, a layer of 100–150 particles is pressurized to approximately 220 kPa (absolute) for 30 s. The pressure is then decreased to the atmospheric value for 30 s before the loading is applied again. The fluorescence emission of the particles during 10 successive loading cycles is displayed in Fig. 5(a). During these experiments, the emission of the particles is simultaneously recorded using a FLEA FL3-U3-13E4C-C camera (1.3 megapixels), mounting a Nikon AF Micro-Nikkor 60 mm f/2.8D lens and a bandpass filter with a center wavelength of 570 nm. The emission intensity computed from the images through an averaging procedure19 is also displayed in Fig. 5(a). Figure 5(b) shows a close-up view of one of the particles in the test chamber during compression.

FIG. 5.

(a) Normalized emission intensity of the particles during repeated loading measured using the spectrometer (red line) and camera (black line). A linear detrending in MATLAB is used to eliminate the effect of a slow emission intensity drift that we primarily attribute to the LED used for excitation. (b) Compression of one particle recorded during a cyclic loading experiment.

FIG. 5.

(a) Normalized emission intensity of the particles during repeated loading measured using the spectrometer (red line) and camera (black line). A linear detrending in MATLAB is used to eliminate the effect of a slow emission intensity drift that we primarily attribute to the LED used for excitation. (b) Compression of one particle recorded during a cyclic loading experiment.

Close modal

The results of the cyclic loading demonstrate the stability of the particles' fluorescence, whereby we observe (i) a consistent decrease in emission during each loading step, with an average decrease of 0.152 ± 0.007 in emission intensity when the pressure in the test chamber reaches 220 kPa (absolute); and (ii) a limited drift of the emission intensity when particles are under pressure, which amounts to approximately 4% of the total emission decrease measured by the camera. We do not observe an effect of Nile Red photobleaching during the measurement, likely due to the high photochemical stability of this dye.20 However, we cannot dismiss the possibility that high energy excitation sources may induce a reduction of emission intensity over time.18 We also remark that a reduction of the particles' functionality is expected over prolonged use, due to progressive degradation of their structure and washout of the dye.

To explore the possibility of utilizing the foam particles as pressure sensors, we define the pressure sensitivity as K=(ΔI/I0)/Δp. The value of K is estimated by evaluating the initial slope of the curve in Fig. 4(c), whereby we obtain ΔI/I0=0.055±0.021,Δp=30kPa, and K= 0.0018 ± 0.0007 kPa1. This value is on the same order of magnitude of sensitivities obtained through PSPs,21,22 where the value of K is approximately 0.008 kPa−1. Similar sensitivities could be achieved with particles fabricated using mechanochemical and mechanochromic polymers, assuming the possibility of activating their response during compression. For the deformations measured in this work, the pressure sensitivity of spiropyran-based mechanochemical polymers23 would be K=0.0008kPa1. Similarly, pressure sensitivities that could be achieved through mechanochromic networks24–26 would be K=0.00080.0023kPa1 (supplementary material).

In this letter, we presented the development and characterization of highly compressible fluorescent elastomeric foam particles for pressure sensing experiments in liquids. The particles can be easily synthesized in-house using a single emulsion process, which allows the preparation of large volumes of particles in a limited time (approximately 10 min) and at low cost (approximately 0.3 $/g). Particles display pressure sensitivity on the order of 0.0018 kPa−1, which is comparable to other methodologies for in situ pressure sensing, such as PSPs. These sensors may find application in medium-to-large scale PIV experiments in liquids, whereby existing in situ pressure-sensing systems can hardly be utilized due to limited stability9 and the difficulty of producing large sensor batches.8 Future work will focus on improving particle sensitivity, by combining their compressible structure with pressure sensitive dyes and reducing their size to study high velocity flow regimes at smaller length scales.

See supplementary material for the infrared absorption spectrum of the particles, additional analysis of the mechanical properties of a bulk foam, and a discussion of spatial resolution in camera-based pressure sensing and flow tracing.

This research was supported by the National Science Foundation through Grant No. CBET-1332204. The authors also acknowledge the support of the Office of Naval Research through Grant No. N00014-10-1-0988 that has allowed the acquisition of equipment used in this study. Finally, the authors would like to express their gratitude to Dr. Avi Ulman and the Institute for Engineered Interfaces (IEI) at New York University, for granting access to the laboratories, and to Steven E. Zeltmann, for his help during CT experiments.

1.
Y.
Jaluria
,
J. Fluids Eng.
123
,
173
(
2000
).
2.
B.
Volker
,
Practical Ship Hydrodynamics
(
Elsevier
,
2012
).
3.
S. E.
Jahren
,
G.
Ochsner
,
F.
Shu
,
R.
Amacher
,
J. F.
Antaki
, and
S.
Vandenberghe
,
Artif. Organs
38
,
316
(
2014
).
4.
S. A.
Mirbagheri
,
E.
Ceniceros
,
M.
Jabbarzadeh
,
Z.
McCormick
, and
H. C.
Fu
,
Exp. Mech.
55
,
427
(
2015
).
5.
R.
Valette
,
P.
Laure
,
Y.
Demayb
, and
J.-F.
Agassant
,
J. Non-Newtonian Fluid Mech.
121
,
41
(
2004
).
6.
T.
Centea
,
L.
Grunenfelder
, and
S.
Nutt
,
Composites, Part A
70
,
132
(
2015
).
7.
M.
Porfiri
and
A.
Shams
, “Pressure reconstruction during water impact through particle image velocimetry: Methodology overview and applications to lightweight structures,” in
Dynamic Response and Failure of Composite Materials and Structures
(
Elsevier
,
2017
), pp.
395
416
.
8.
N.
Banerjee
and
C. H.
Mastrangelo
,
Analyst
141
,
1413
(
2016
).
9.
A.
Akonur
and
A.
Prasad
,
Meas. Sci. Technol.
11
,
398
(
2000
).
10.
B. G.
McLachlan
and
J. H.
Bell
,
Exp. Therm. Fluid Sci.
10
,
470
(
1995
).
11.
J. W.
Gregory
,
K.
Asai
,
M.
Kameda
,
T.
Liu
, and
J. P.
Sullivan
,
Proc. Inst. Mech. Eng., Part G
222
,
249
(
2008
).
12.
F.
Kimura
,
M.
Rodriguez
,
J.
McCann
,
B.
Carlson
,
D.
Dabiri
,
G. E.
Khalil
,
J. B.
Callis
,
Y.
Xia
, and
M.
Gouterman
,
Rev. Sci. Instrum.
79
,
074102
(
2008
).
13.
D.
Lacroix
,
G.
Viraye-Chevalier
,
T.
Seiter
,
J.
Howard
,
D.
Dabiri
,
Y.
Khalil
,
G. E.
Xia
, and
C.
Zhu
,
Rev. Sci. Instrum.
84
,
115107
(
2013
).
14.
D.
Van Nuffel
,
K.
Vepa
,
I.
De Baere
,
P.
Lava
,
M.
Kersemans
,
J.
Degrieck
,
J.
De Rouck
, and
W.
Van Paepegem
,
Ocean Eng.
77
,
42
(
2014
).
15.
S.
Krishnan
,
H.
Van der Walt
,
V.
Venkatesh
, and
V. B.
Sundaresan
, “
Dynamic characterization of elastico-mechanoluminescence towards structural health monitoring
,”
J. Intell. Mater. Syst. Struct.
(published online).
16.
T.
Ioppolo
and
M.
Manzo
,
Appl. Opt.
53
,
5065
(
2014
).
17.
AkzoNobel
. “
Expancel microspheres and elasticity
,” Technical Information TI.PRP04.EN/01-01-2014,
2014
.
18.
J. R.
Lakowicz
,
Principles of Fluorescence Spectroscopy
(
Springer Science & Business Media
,
2013
).
19.
F.
Cellini
,
S. J.
Osma
,
S. D.
Peterson
, and
M.
Porfiri
,
IEEE/ASME Trans. Mechatronics
21
,
2989
(
2016
).
20.
D.
Basting
,
D.
Ouw
, and
F.
Schafer
,
Opt. Commun.
18
,
260
(
1976
).
21.
H.
Sakaue
,
T.
Kakisako
, and
H.
Ishikawa
,
Sensors
11
,
6967
6977
(
2011
).
22.
G. E.
Khalil
,
C.
Costin
,
J.
Crafton
,
G.
Jones
,
S.
Grenoble
,
M.
Gouterman
,
J. B.
Callis
, and
L. R.
Dalton
,
Sens. Actuators, B
97
,
13
(
2004
).
23.
H.
Zhang
,
Y.
Chen
,
Y.
Lin
,
X.
Fang
,
Y.
Xu
,
Y.
Ruan
, and
W.
Weng
,
Macromolecules
47
,
6783
(
2014
).
24.
B. R.
Crenshaw
and
C.
Weder
,
Macromolecules
39
,
9581
(
2006
).
25.
F.
Cellini
,
L.
Zhou
,
S.
Khapli
,
S. D.
Peterson
, and
M.
Porfiri
,
Mech. Mater.
93
,
145
(
2016
).
26.
F.
Cellini
,
L.
Block
,
J.
Li
,
S.
Khapli
,
S.
Peterson
, and
M.
Porfiri
,
Sens. Actuators, B
234
,
510
(
2016
).

Supplementary Material