# Color-switching hydrogels as integrated microfluidic pressure sensors

Lucie Ducloué  Laboratoire de Physique et Mécanique des Milieux Hétérogènes,
UMR 7636, CNRS, ESPCI Paris, PSL Research University, Université Paris Cité,
Sorbonne Université, Paris, FR-75005, France  these authors contributed
equally to this work  Md. Anamul Haque  Laboratory of Soft & Wet Matter,
Faculty of Advanced Life Science, Hokkaido University, Sapporo, Hokkaido
001-0021, Japan  Department of Chemistry, University of Dhaka, Dhaka-1000,
Bangladesh  these authors contributed equally to this work  Martyna Goral
Laboratoire de Physique et Mécanique des Milieux Hétérogènes, UMR 7636, CNRS,
ESPCI Paris, PSL Research University, Université Paris Cité, Sorbonne
Université, Paris, FR-75005, France  Muhammad Ilyas  Laboratory of Soft & Wet
Matter, Faculty of Advanced Life Science, Hokkaido University, Sapporo,
Hokkaido 001-0021, Japan  Jian Ping Gong  Laboratory of Soft & Wet Matter,
Faculty of Advanced Life Science, Hokkaido University, Sapporo, Hokkaido
001-0021, Japan  Institute for Chemical Reaction Design and Discovery (WPI-
ICReDD), Hokkaido University, Sapporo 001-0021, Japan  Anke Lindner
Laboratoire de Physique et Mécanique des Milieux Hétérogènes, UMR 7636, CNRS,
ESPCI Paris, PSL Research University, Université Paris Cité, Sorbonne
Université, Paris, FR-75005, France<EMAIL_ADDRESS>
###### Abstract

Precisely measuring pressure in microfluidic flows is essential for flow
control, fluid characterization, and monitoring, but faces specific challenges
such as achieving sufficient resolution, non-invasiveness, or ease of use.
Here, we demonstrate a fully integrated multiplexed optofluidic pressure
sensor, entirely decoupled from the flow path, that enables local pressure
measurements along any microfluidic channel without altering its flow
geometry. The sensor itself relies on the compression of a soft mechano-
actuated hydrogel, changing color in response to a pressure change. The
hydrogel is separated from the fluid circulating in the channel by a thin
membrane, allowing for the unrestricted use of different types of fluids.
Imaging the gel through the transparent PDMS with a color camera provides a
direct, easy, and contact-free determination of the fluid pressure at the
sensing location for pressures as small as $20\text{\,}\mathrm{mbar}$ with a
resolution of around $10\text{\,}\mathrm{mbar}$. The sensitivity and
accessible pressure range can be tuned via the mechanical properties of the
sensing unit. The photonic gel can also be used to acquire 2D pressure or
deformation maps, taking advantage of the fast response time and fine spatial
resolution.

## Introduction

The widening applications of microfluidic devices in fields as different as
biomedicine, organ-on-chip, chemical analysis, material characterization or
water purification, have increased the need for reliable pressure-sensing in
those systems. pressure-sensing in such small fluidic circuits, however, faces
specific challenges stemming from the design of microfluidic chips. The lab-
on-a-chip layout requires that the sensor be fully integrable to the chip, and
so most commonly to PDMS architectures. The sensor sensitivity is challenging,
given that the pressure changes along short fluid sections can be minute. In
addition, the pressure sensor is required to be non-invasive and, as such, not
to modify the local flow geometry. The sensor is preferably easy to use and
read out.

Several methods have been proposed to overcome these difficulties, which rely
on soft-sensing elements that deform under pressure. This deformation is
usually measured via electric methods, which can be piezoelectric pillars [1],
conductive liquid circuits [2], conductive inflating membranes [3] or
capacitive sensors based on composite foam materials [4, 5]. Such methods
require that the microfluidic chip is wired to an external electrical
apparatus, which may not be convenient. Optical methods for the detection of
the deformation of sensing elements have been proposed, and overcome this
drawback. The deformation of an optical grating [6], interference patterns in
a deformed cavity [7], light focusing through an inflating membrane [8], color
intensity change in a concentric chamber [9], the displacement of a colored
liquid or a liquid-gas interface [10, 11] and very recently, nano-structured
photonic inflating membranes [12] have been used. All those methods enable
remote sensing of the fluid pressure, through precise calibration of the
optical detection of the small deformations involved. However, the pressure
measurements rely on the deformation of a sensing element and thus modify the
microfluidic flow geometry. The pressure drop in a flat channel scales with
the square of the channel height and such a deformation can thus have
important consequences on fluid flow and strongly modify the local pressure.
The work by Orth et al. [8] stands out as a realization in which the sensing
element is decoupled from the flow path of the fluid: therefore, the
deformation of the sensor does not modify the geometry of the channel in which
the fluid flows.

Here we propose a different sensing method, directly integrating a material
that changes color under applied pressure into a microchannel (see [13]). Such
mechano-chromic materials are for example pressure sensitive paint [14],
colorimetric films taking advantage of the photonic shift during the
disassembly of gold nanoparticle chains [15], nanostructured photonic
membranes [12] or the photonic hydrogel used here [16]. The use of these
materials remains scarce for optofluidic applications, with the exception of
the work mentioned above by Escudero  et al. [12] where a color shift is
elegantly used to detect membrane deflection or the integration of pressure-
sensitive paint, only suitable for gas flows and requiring observation in a
dark environment using UV light. Contrary to those applications, we directly
use the color change in visible light of a novel soft photonic hydrogel [16].
The gel is actuated under very small compressive stress and exhibits an
ultrafast response time and high spatial resolution
($0.1\text{\,}\mathrm{m}\mathrm{s}$ and $10\text{\,}\mathrm{\SIUnitSymbolMicro
m}$-$100\text{\,}\mathrm{\SIUnitSymbolMicro m}$ respectively) [16]. We built a
multilayered PDMS sensing unit composed of a pressure-sensing cavity separated
from the mechanochromic gel by a thin membrane. Such sensing units can be
fully integrated into microfluidic devices, by, for example, connecting them
at desired locations to microchannels, leading to a noninvasive multiplexed
pressure measurement. As the membrane separates the gel from the fluid
circulating in the microchip, the sensor can be used with all types of liquid
or air, while avoiding the presence of liquid/gas interfaces. We take
advantage of the softness of the gel to demonstrate pressure measurements at
very low pressures (from $20\text{\,}\mathrm{mbar}$ to
$140\text{\,}\mathrm{mbar}$) with high resolution of around
$10\text{\,}\mathrm{mbar}$. The combination between membrane bending
stiffness, cavity size, and theoretically gel properties (not systematically
varied in this work), allows for fine-tuning of the measurement range and in
particular the extension of the pressure range towards higher pressures.
Additionally, the gel can also be used to obtain 2D pressure maps and to
monitor spatial and temporal pressure differences or determine local
deformations.

## Results

### General design and operation principle

The pressure-sensing unit is designed as a multilayered PDMS system,
illustrated schematically in Fig. 1 (a,b). The sensor is made of two molded
PDMS layers, obtained by standard soft lithography techniques [17] and
separated by a thin PDMS membrane. The top layer contains a pressure-sensing
cavity that is filled with the pressurized fluid to be analyzed. The bottom
layer contains a chamber enclosing a slab of the photonic hydrogel. The
hydrogel being immersed in an aqueous buffer solution, the gel chamber has an
inlet and an outlet to refresh the buffer and is slightly larger than the gel
slab to enable its lateral expansion while being compressed. Details on the
assembly are given in the Materials and Methods section. Special care is taken
to match the height of the hydrogel slab and the chamber, to avoid pre-
compression of the gel or an offset in the pressure measurements. For
convenience the upper cavity has a disc-like shape but is not limited to this
choice. The pressure-sensing cavity fully covers the hydrogel slab as can be
seen in Fig. 1 (a,b). Under increasing pressure in the pressure-sensing
cavity, the membrane deforms, and the underlying gel is compressed,
subsequently changing color. In our setup, this color change is observed in
reflection from above via a camera. The quality of the color observation is
improved when the sensing unit is placed on a black background.

Figure 1: General design of the pressure-sensing unit Schematic of the cross-
sectional view (a) and the top view (b) of the assembled sensor (not scaled).
The dotted line indicates the position of the cross-sectional view. Color-
changing hydrogel (c) Color-response of a sample of a free-standing soft
photonic gel of $1\text{\,}\mathrm{cm}$ diameter under uniform applied
pressure between a glass slide and a substrate (see Supplementary Fig. 1). The
left row indicates the visual response of the gel with RGB color images and
the right row with hue value intensity images. (d) Maximum reflected
wavelength measured using a spectrometer as a function of applied pressure.
The line is a liner adjustment, $R^{2}=0.98$. Inset: hue value as a function
of the reflected wavelength. The line is a guide for the eye. Calibration of
the sensing unit. (e) Top view of a sensor (diameter $4\text{\,}\mathrm{mm}$,
gel layer thickness $140\text{\,}\mathrm{\SIUnitSymbolMicro m}$, PDMS membrane
thickness $100\text{\,}\mathrm{\SIUnitSymbolMicro m}$) connected to a pressure
controller to increase applied static pressure (from $0\text{\,}\mathrm{mbar}$
to $100\text{\,}\mathrm{mbar}$). (f) Average hue value profile across the
radius of the sensor, for pressures varying from $0\text{\,}\mathrm{mbar}$ to
$100\text{\,}\mathrm{mbar}$ with an increment of $5\text{\,}\mathrm{mbar}$.
(g) Calibration curve of several $4\text{\,}\mathrm{mm}$ diameter sensors
placed above the same gel slab: hue value as a function of applied pressure.

The soft photonic hydrogel has already been described before [16], and the
details of its fabrication and characterization can be found in the Materials
and Methods section. The layered gel has a lamellar structure formed by thin,
rigid, and light-reflecting bilayers embedded in a soft hydrogel matrix.
Typical interlayer distances are comparable to the wavelength of visible
light. As a consequence, the multilayer structure selectively diffracts
visible light, so that it appears colored under reflective white illumination.
Under compression, the layer spacing decreases leading to a color change of
the gel. The gel diffracts longer wavelengths in its undeformed state (orange
color), and shorter wavelengths when compressed (gradual shift to blue color).
Typical gel thicknesses are between $100\text{\,}\mathrm{\SIUnitSymbolMicro
m}$ and $1\text{\,}\mathrm{mm}$ with Young’s moduli between
$10\text{\,}\mathrm{kPa}$ and $100\text{\,}\mathrm{kPa}$ (see Supplemental
Fig. 2(b)). Thinner gels can be fabricated, but the quality of the color of
the reflected light is found to be reduced and in this work no gels below
$100\text{\,}\mathrm{\SIUnitSymbolMicro m}$ have been used. A color change
from orange (wavelength $\lambda\approx$ $600\text{\,}\mathrm{nm}$) to blue
(wavelength $\lambda\approx$ $450\text{\,}\mathrm{nm}$) corresponds to a
decrease in layer spacing and thus a compressive strain of the gel of
$\epsilon=\Delta\lambda_{max}/\lambda\approx 0.25$. For the thin gel this
corresponds to a decrease in height of about
$25\text{\,}\mathrm{\SIUnitSymbolMicro m}$ and for the thick gel of
$250\text{\,}\mathrm{\SIUnitSymbolMicro m}$. To be more compatible with the
dimensions of a microfluidic chip, we chose to mainly work with thin gels and
present the following results for a gel of thickness
$140\text{\,}\mathrm{\SIUnitSymbolMicro m}$, but successful tests with thick
gels have also been performed.

Snapshots of a free-standing gel sample (thickness
$140\text{\,}\mathrm{\SIUnitSymbolMicro m}$ at rest), not yet inserted into
the microfluidic pressure-sensing unit,are shown in Fig. 1 (c). Under the
application of increasing uniform pressure, the color change from
orange/yellow towards blue is visible on the left panel. The precise color
response is measured with a spectrometer for each pressure as the maximum of a
sharply-peaked distribution of the reflected wavelength [18]. Details about
the setup and the measured color spectra are given in the Materials and
Methods section and Supplemental Materials. The color response curve obtained
with the spectrometer is given in Fig. 1 (d) in terms of the maximum reflected
wavelength $\lambda_{max}$ as a function of the applied pressure $P$. The
decrease in wavelength (corresponding to a compression of the gel) [16, 18] is
observed to be linear for most of the range of pressures tested. A stiffening
of the gel for even larger deformations (toward a color response in violet)
has been observed, but this is not shown here. The Young’s modulus of the gel
sample tested has been determined to be approximately
$Y$=$90\text{\,}\mathrm{kPa}$ (Supplemental Fig. 2 (b)). Note that small
changes in the fabrication process and gel swelling can lead to variations in
the gel properties, such as initial layer spacing or gel modulus. For instance
for the gel shown in Fig. 1 (c) the color at rest was not perfectly orange,
but rather yellow preventing the full range of the visible light to be used.
We perform a calibration step for each realization of the pressure-sensing
unit to account for the precise properties of the gel sample used (see below).

For general pressure-sensing applications, using a spectrometer is not
necessarily convenient, and it can be useful to measure and quantify the color
switching of the gel with simpler equipment, such as a color camera or an
optical fiber. This can be done by transforming color pictures as those shown
in Fig. 1 (c) left row into a gray-scale intensity map of the hue value $H$
(Hue-Saturation-Value color model, obtained by image treatment) and shown in
the right row. The diffracted light being monochromatic, the $H$ value derived
from camera images is a good proxy for the wavelength. This is shown in the
inset of Fig. 1 (d), which compares the $H$ value calculated from images
acquired with a color camera and the maximum reflected wavelength measured
with a spectrometer. In the range between $480\text{\,}\mathrm{n}\mathrm{m}$
and $540\text{\,}\mathrm{n}\mathrm{m}$ $H$ decreases with $\lambda_{max}$, and
can thus be used to quantify the color response of the gel simply from color
images acquired with a camera, as done in this work. A saturation of the hue
value is observed for wavelengths below $480\text{\,}\mathrm{n}\mathrm{m}$.

### Calibration of the pressure-sensing unit

pressure-sensing units need to be calibrated to enable quantitative pressure
measurements. The calibration step is required to quantify slight changes in
the gel properties depending on the fabrication, hydrolyzation, and swelling
of the latter, but also to account for the possible coupling between the
membrane and the gel or the influence of the soft PDMS foundation on gel
deformation. All sensors used here have a cavity height of
$100\text{\,}\mathrm{\SIUnitSymbolMicro m}$, a PDMS membrane thickness of
$100\text{\,}\mathrm{\SIUnitSymbolMicro m}$, and a gel thickness of
$140\text{\,}\mathrm{\SIUnitSymbolMicro m}$. Two different sensing cavity
sizes were used, of diameter $4\text{\,}\mathrm{mm}$ and
$1\text{\,}\mathrm{mm}$ respectively, enabling different ranges of measured
pressure. In Fig. 1 (e) we show the calibration step for sensing units with
the large cavity diameter of $4\text{\,}\mathrm{mm}$, sensitive to smaller
pressures compared to the $1\text{\,}\mathrm{mm}$ diameter sensor (see
Supplemental Fig. 2 (c)). Several cavities have been placed on top of a long
slab of hydrogel and connected to a microchannel for simple pressure
application. The calibration step is performed by filling the sensing cavities
with water and applying static pressure with the help of a pressure controller
(Fluigent Lineup Flow EZ). One can rely either on the permeability of PDMS to
evacuate the air contained in the sensing cavities or connect the sensing
cavities to an outlet to directly evacuate the trapped air. The outlets are
closed during the calibration step so that the static pressure can be applied
to the system without flow. The pressure is increased stepwise and a color
image of each sensor is taken for each pressure value. Examples of pictures of
the color evolution during this procedure are given in Fig. 1 (e). At zero
applied pressure, the gel strip under the sensors is uniform orange in color.
When the pressure is increased, the sensing cavity bottom membrane presses on
the gel, making it locally compressed: circular spots appear on the gel strip,
which shift toward blue colors as the pressure is increased.

The color profile for each sensor is then analyzed in terms of the $H$ value.
Due to the circular shape of the sensors, this profile is axisymmetric. To get
optimal resolution, we detect the center of each sensor and average the $H$
value over the azimuthal direction. The resulting radial $H$ profile is
illustrated in Fig. 1 (f) for a given sensor. As the reflected wavelength
decreases linearly with the vertical compression of the gel, the profile of
the $H$ value is also a proxy for the deformation of the gel below the
membrane. For all $H$ value profiles one observes no deformation at the cavity
borders where the membrane is attached to the PDMS layer. The deformation
increases towards the middle of the cavity, where a plateau is reached for
smaller pressures ($20\text{\,}\mathrm{mbar}$-$40\text{\,}\mathrm{mbar}$) and
thus for small deformations. For larger deformations
($40\text{\,}\mathrm{mbar}$-$80\text{\,}\mathrm{mbar}$) more complex profiles
are observed, with a small dip in deformation in the middle of the cavity. For
the largest pressures used, above $80\text{\,}\mathrm{mbar}$, the sensor
saturates and the profile becomes completely flat. This saturation can result
from two origins, first the saturation of the hue value for small wavelengths
and second the stiffening of the thin gel layer under compression.

Due to the complex shape of the $H$ value profile at larger pressures, we use
the value of $H$ at $R/2$, where $R$ is the radius of the sensors, to build
the calibration curves. Fig. 1 (g) shows such curves for the 6 tested pressure
sensors positioned above the same gel slab. For pressures below
$20\text{\,}\mathrm{mbar}$, no color change is observed. We suspect that this
is due to a small gap between the gel strip and the membrane, so the small
deformation of the membrane under low pressures is not sufficient to establish
contact with the gel. At the highest pressures tested, the sensors saturate.
For optimal precision, the exact shape of the curve is used for calibration
purposes for intermediate values. The calibration captures, as already pointed
out, any variations that might occur in gel properties from one batch to
another, the characteristics of the sensor geometry and the specific features
of the setup used, such as the illumination conditions. Within one
experimental realization, very good agreement between the curves is obtained (
Fig. 1 (f)) confirming the uniformity of the gel and the good repeatability
within one set of sensors.The working range of the sensors with diameter
$4\text{\,}\mathrm{mm}$ presented here is found to be from
$20\text{\,}\mathrm{mbar}$ to $80\text{\,}\mathrm{mbar}$, and for the
$1\text{\,}\mathrm{mm}$ diameter sensor (calibration Supplemental Fig. 2 (b))
from $60\text{\,}\mathrm{mbar}$ to $140\text{\,}\mathrm{mbar}$.

### Membrane-gel coupling and working range of pressure-sensing cavities

To better understand the mechanical coupling of the membrane with the color-
changing gel, we have modeled the sensing unit using a thin-plate
approximation for the membrane, described as a circular bending plate, clamped
at the edges and resting on an elastic foundation [19]. The coupled response
of the membrane and gel under varying pressure and sensor radius is presented
in the Supplementary Material. Qualitatively the shape of the predicted
deformation profiles is in very good agreement with the experimental
observations in Fig. 1 (f), including the small dip that develops in the
middle at strong compression.

The model also highlights how decreasing the radius of the cavity leads to
less deformation for identical applied pressures and thus to an effective
stiffening of the membrane/gel system. This principle can be used to extend
the accessible pressure range to higher pressures and explains that in our
system the smaller cavities react to a different pressure range as compared to
the larger cavities. For an increasingly large cavity radius, we expect the
role of the membrane to be less and less important and the deformation of the
gel to be only given by the gel Young’s modulus, defining in this way the
smallest pressures accessible.

Thus, the working range of the sensors can be tuned by playing with the
mechanical coupling of the membrane to the gel. For large sensors, the role of
the membrane can be neglected and the limiting factor is the gel Young’s
modulus itself. The smallest measurable pressure (as well as the resolution of
the pressure measurement) is given by the modulus of the gel and the accuracy
with which the color change can be detected. The calibration curves of the
large sensors shown in Fig. 1 (g) show hue values obtained at pressure
increments of $5\text{\,}\mathrm{mbar}$. taking also into account small
variations between the different sensors we estimate the resolution of our
sensors to be of $10\text{\,}\mathrm{mbar}$. Due to the imperfect alignment of
the membrane, the smallest value measured with our sensor is slightly larger
and corresponds to $20\text{\,}\mathrm{mbar}$. Higher pressures can be reached
when working with smaller cavities, where the membrane plays a stiffening
role. Tuning more precisely the parameters of the model presented in
Supplementary Materials could help the design of sensors with the desired
pressure range in the future.

## Validation of the sensor under flow

### Multiplexed integration into a microchannel

To measure the pressure inside microfluidic channels of variable design, the
sensing units can be directly integrated into microfluidic chips, and we
demonstrate here a realization using a straight square channel. In order to
avoid deformation of the flow channel geometry when the membrane deflects
under pressure, we take inspiration from the design introduced by Orth et al.
[8]. We decouple the sensing area by connecting the sensing units laterally to
the flow channel. The top view of our chip is shown in Fig. 2 (a): the main
flow channel is a straight channel of length $L=$$20\text{\,}\mathrm{mm}$ and
quasi square cross-section of width
$w=$$110\text{\,}\mathrm{\SIUnitSymbolMicro m}$ and height
$h=$$100\text{\,}\mathrm{\SIUnitSymbolMicro m}$. Equally spaced sensing units
are integrated into the chip and connected via narrow channels (width
$50\text{\,}\mathrm{\SIUnitSymbolMicro m}$) to the main channel. The sensing
cavities are embedded in the same PDMS layer as the flow channel and, as
previously separated from the hydrogel chamber in the second PDMS layer by a
thin membrane (see Fig. 1a,b). Each sensor is connected to an outlet opposite
to its side channel (see Materials and Methods). Two sets of sensors have been
placed in this chip, with 6 sensors on each side of the main flow channel.
Each series of sensors rests on a single photonic gel slab, which appears in
orange in the picture (Fig. 2b). Outlets (flow channel and sensors) are left
open during device filling and are closed for experiments of imposed static
pressure so that only the main flow channel remains connected to fluid sources
during normal operation of the device, thus avoiding flow in the lateral
channels and cavities. In the case of imposed flow in the channel, its outlet
is left open, while the sensor outlets remain closed.

### Flow measurements

Figure 2: Schematic of the channel design (a) top view and (b) picture of the
experimental realization, showing the orange color of the gel. The chip used
is the one calibrated in Fig. 1(g) and Supplementay Fig. 2(c). Response of the
pressure sensors (c) under steady water flow at
$50\text{\,}\mathrm{\SIUnitSymbolMicro}\mathrm{L}\mathrm{/}\min$ (blue
squares). Inset: top view of the sensors at a steady flow of
$50\text{\,}\mathrm{\SIUnitSymbolMicro}\mathrm{L}\mathrm{/}\min$. (d) Under
imposed pressure difference $\Delta P$ (bottom to top:
$50\text{\,}\mathrm{mbar}$, $100\text{\,}\mathrm{mbar}$,
$150\text{\,}\mathrm{mbar}$). The response is measured from the
$4\text{\,}\mathrm{mm}$ diameter sensors except for one data point (indicated
in the figure) which is from a $1\text{\,}\mathrm{mm}$ diameter sensor. The
pressure response as a function of distance is linear in all cases ($R^{2}$
values bottom to top: 0.86, 0.98, 0.98). Error bars are often smaller than the
symbol size and thus not visible on the figure. The error corresponds to the
standard deviation.

Once the device has been calibrated, according to the procedure described
above, it can be used for local pressure-sensing in flowing liquids. We first
tested our pressure sensor by imposing a steady flow of water (flow rate:
$50\text{\,}\mathrm{\SIUnitSymbolMicro}\mathrm{L}\mathrm{/}\min$) in the
straight channel and leaving the outlet open to the atmosphere while the
sensor outlets remained closed. The response of the large
$4\text{\,}\mathrm{mm}$ sensors to this flow is shown in the inset of Fig. 2
(c): a pressure gradient is visible along the channel. Note that the pressure
at the last sensing location is not large enough to activate the last sensor:
it is below $20\text{\,}\mathrm{mbar}$. Using the calibration curves of Fig. 1
(g), the pressure profile in the channel can be measured and is plotted with
blue squares in Fig. 2 (c). This profile is linear, as expected, and gives a
total pressure drop of about $25\text{\,}\mathrm{mbar}$ over
$15\text{\,}\mathrm{mm}$, which is within the uncertainties of the imposed
flow rate (estimated to be 10%) and the channel dimensions (estimated to be
5%) in reasonable agreement with the $30\pm 10\text{\,}\mathrm{mbar}$ drop
expected from the hydraulic resistance of the channel: $\Delta P=QR_{H}$ with
$R_{H}=\frac{12}{1-0.62(h/w)}\eta L\frac{1}{wh^{3}}$ with $\eta$ the viscosity
and $w,h$ the width and height of the channel, respectively [20]. Note that
the pressure at the channel outlet is not necessarily exactly zero even though
no tubing was connected at the outlet. This is due to the possibility of small
liquid droplets accumulating at the outlet and the small but finite height of
the water column in the outlet.

The linearity of the measured pressure gradient under steady flow has been
checked over a wider range by imposing a constant over-pressure at the inlet
(the outlet remaining at atmospheric pressure). Note that part of the applied
pressure drop occurs at the tubing connecting the channel to the fluid
reservoir, leading to a smaller pressure drop along the channel compared to
the imposed pressure difference. In addition, small changes in the tubing
might also slightly modify this pressure drop and thus lead to different
offsets at the in and outlet for different measurements. The measured pressure
response is shown in Fig. 2 (d) for 3 imposed pressure drops $\Delta P$. All
profiles are linear as expected and show an increasing slope with increasing
imposed pressure. At small pressure drops, the sensors closer to the channel
outlet cannot be used (lowest $\Delta P$) as the expected pressure is below
the minimal resolution of $20\text{\,}\mathrm{mbar}$. For very large pressure
drops, the large sensors saturate. The small sensors can however provide
complementary information and were used for the highest data point for the
pressure difference of $\Delta P=$ $150\text{\,}\mathrm{mbar}$ as indicated by
an arrow towards the data point of the figure. The calibration curve for the
$1\text{\,}\mathrm{m}\mathrm{m}$ sensor is provided in the Supplementary
Materials Fig. 2(c). This data set demonstrates that a larger pressure range
can be obtained by combining different cavity sizes of the sensing units.

In summary, the pressure-sensing unit integration into a microfluidic chip
demonstrates their potential for noninvasive pressure measurement of
hydrodynamic pressure underflow. All pressure profiles measured are linear as
expected and show an increasing slope with increasing applied pressure at the
channel inlet. For an imposed flow rate, the pressure drop measured over the
length of the channel is quantitatively correlated with the calculated
pressure drop. The pressure measurements obtained with sensors of different
diameters fall onto a single curve and expand the range of accessible
pressures.

### Spatially resolved pressure mapping

To demonstrate the good spatial resolution of our gel we have fabricated a
device where a flow channel is directly positioned above a slab of color-
changing gel, separated by the PDMS membrane. A schematic can be seen in Fig.
3 (a). The change in color under static pressure is first tested and shown in
Fig. 3 (c). The color change is smaller close to the channel walls where the
membrane is fixed to the channel and increases towards the middle of the
channel. Similarly to the pressure-sensing units (Fig. 1) a calibration step
is performed, this time using hue value profiles across the channel width
(Fig. 3 (b). The maximum value in the center of the channel is used for
calibration against the applied static pressure.

When applying flow to the channel, the change in color along it is visible in
the center of the channel (Fig. 3 (d)) and can be used to infer the local
pressure as a function of the position along the channel. Such spatially
resolved local pressure measurements could be very useful for applications in
more complex flow geometries such as branched channel networks, or channels
with varying cross sections. A drawback of this implementation is however
that, as discussed above, the compression of the gel leads to a significant
change in local channel height and thus a modification of the flow profile and
the hydrodynamic pressure. The pressure gradient in the straight channel shown
here is thus not expected to be constant.

Instead of using the gel as a local pressure sensor, it can also be used as a
local deformation sensor. As stated above, the color change of the gel
observed under application of pressure results from a decrease in layer
spacing of the lamellar gel and thus a change of the constructively reflected
wavelength. Therefore, a color change is directly proportional to a decrease
in layer spacing, and thus to an overall gel compression. The latter can be
quantified by evaluating the change in the hue value and linking it (see the
inset of Fig. 1 (d)) to the change of the wavelength of the reflected light.
From the change in wavelength, the change in layer spacing and thus the total
strain of the gel slab can be evaluated. Knowing the thickness of the gel
slab, we obtain the absolute local deformation. Fig. 3 (e) shows the local
deformation and therefore the local increase in channel height due to
compression of the underlying gel. The $z$\- axis has been multiplied by 100
to make the small deformations of at maximum slightly more than
$15\text{\,}\mathrm{\SIUnitSymbolMicro m}$ visible. The increase in
deformation is clearly seen when going from the channel wall toward the
channel center. Furthermore, the deformation at the center of the channel
decreases continuously when going from the channel inlet to the channel
outlet. Using the resolution of 3% with which the change in wavelength can be
measured, as estimated above, we expect to be able to resolve deformations
with a resolution of around $4\text{\,}\mathrm{\SIUnitSymbolMicro m}$. This is
in visual agreement with Fig. 3 (e) indicating the very good resolution of our
sensor. The spatial resolution in the $x$ and $y$ direction spanning the
bottom surface of the channel can be visually estimated from the noise in the
profiles of Fig. 3 (b) to be between $50\text{\,}\mathrm{\SIUnitSymbolMicro
m}$ and $100\text{\,}\mathrm{\SIUnitSymbolMicro m}$ in agreement with Yue et
al. [16]. Our results have not been optimized to improve the spatial
resolution and the values given can be considered as an upper bound.

Deformation of PDMS channels under applied pressure is a common problem in
these soft devices and is often difficult to quantify. However, their
influence on the local flow properties is large as flow velocities scale with
the square of the channel height. Embedding a color-changing gel into
microfluidic channels could help avoid these effects.

Figure 3:  2D pressure-sensing (a) Schematic of the chip for 2D pressure-
sensing. The line indicates the cross-section of hue value averaging. (b)
Average measured hue value profiles from images presented in Fig. (c). (c) Top
view of the chip: the rectangular flow channel has the same width and length
as the overlaid gel channel. The uniform pressure loading increases from top
to bottom. Non-uniform pressure as imposed by a steady flow of liquid : (d)
visual information and (e) reconstruction of the membrane deformation using
the calibration obtained from images shown in Fig. (b).

### Dynamic response

The dynamic response of the device under flow was tested by imposing an
oscillating pressure at the channel inlet for the chip shown in Fig. 2. The
imposed pressure profile and the response of the first large sensor (closest
to the inlet) are shown in the Supplementary Materials, together with the
experimental details. The sensor exhibits an oscillating response with a time
delay of about $1.3\text{\,}\mathrm{s}$ evaluated as the typical time scale
for the exponential increase in measured pressure after a step increase in
applied pressure. A time shiftof around 1s between the measured and applyed
pressure oscillations is observed and found to be of comparable order of
magnitude.. This response time is quite large, in particular compared to that
of the gel ($0.1\text{\,}\mathrm{ms}$[16]). We emphasize that this is not the
response time of the sensing element itself (which is difficult to access on
our device), but rather that of the whole chip. Thus, it is sensitive to all
compliant parts in the chip and is simply an upper bound for the response time
of the sensing element. This response time could be optimized by working with
stiffer materials or by minimizing the volume contained in the sensing
cavities. We observe that the shape of the oscillations is conserved,
indicating that there is no visible hysteresis in the sensor response for this
pressure range and experimental time scale.

## Discussion and conclusion

We have presented a novel type of pressure sensor, directly using the color
change in the visible spectra of a soft hydrogel. This gel can be integrated
into sensing units, where a pressure-sensing cavity is separated from the
hydrogel by a thin membrane. These multilayered sensing units can be fully
integrated into PDMS microchips and allow remote sensing of pressure at given
positions in a flow channel. Once calibrated, the read-out is very easy and
precise and can be done via a simple color camera. The hydrogel being very
soft, we have demonstrated the possibility of measuring pressure in the range
between $20\text{\,}\mathrm{mbar}$-$140\text{\,}\mathrm{mbar}$ with a
resolution of $10\text{\,}\mathrm{mbar}$ using two different sensor sizes. The
pressure range can be easily extended to larger pressures by playing with the
coupling between the bending stiffness of the membrane and the elastic gel.
For large cavity sizes the role of the membrane gets more and more negligible
and the gel deformation under pressure is solely given by the gel Young’s
modulus. Extending the range of pressures accessible to smaller pressures thus
either requires working with even softer gels or improving the resolution of
the color change readout. The use of a spectrometer might improve this
resolution and avoid the limitations resulting from the saturation of the hue
values occurring at strong gel compression and thus towards violet colors.

A more detailed modeling of the elastic coupling of the membrane gel system
for different sensor geometries might in the futur allow to achiev even more
precise control of the sensor resolution and working range. The full
understanding of the time response of the sensor requires additional
investigation addressing in particular the interaction between the elastic
chip/sensor system and the viscous fluid flow. Such an understanding is
required to work with non stationnary or turbulent flows, but is outside the
scope of the present work.

Our sensor distinguishes itself by its compatibility with diverse fluid types
(liquids and gases) as they do not enter into contact with the sensing gel.
The inherent design of the sensor ensures the absence of liquid/gas interfaces
that could induce measurement errors for small absolute pressures due to the
capillary pressure jump. The design is however not limited to the use of PDMS
as presented here, but could easily be fabricated using glass or another type
of polymeric materials. The membrane separating the sensing unit from the
hydrogel could also be replaced by a different material, even a thin metallic
sheet could be imagined as long as the pressure range to be evaluated is
sufficient to deform the coupled membrane and gel system. For non-transparent
membranes, the color-changing gel has to be observed from below the chamber
containing the gel and not as done here from above.

The use of our pressure sensor is not only limited to microfluidic
applications, but it can be plugged into any fluid circuit. For less precise
applications a read-out by eye can be imagined and could be useful for example
by giving a warning signal above a certain pressure threshold. The spatially
resolved pressure measurement opens numerous possibilities for fundamental or
industrial research as local pressure measurements in turbulent or complex
fluid flows, droplet generation, micro-reactors, cellular growth and
deformation, organ-on-chip technology, or medical applications, but also
validation of numerical models.

## Methods

### Preparation and characterization of the soft photonic gels

#### Gel preparation

The pressure-sensing gel is fabricated similarly to a previously reported
lamellar sheet hydrogel [18]. It consists of uniaxially aligned reflective
bilayers of PDGI (homo-polymerized poly(dodecyl glyceryl itaconate)) and a
chemically crosslinked elastic hydrogel matrix of PAAm (polyacrylamide). A
large sheet of soft PDGI/PAAm hydrogel with this lamellar bilayer structure
parallel to the sheet surface is fabricated by slightly modifying the
procedure described by Haque et al. [18]. Briefly, a polymerization chamber is
made of two parallel glass plates separated by $0.1\text{\,}\mathrm{mm}$ thick
silicone spacers. The reaction chamber possesses an inlet hole to be filled
with the precursor solution (aqueous mixture of
$0.1\text{\,}\mathrm{\textsc{m}}$ DGI, $0.0025\text{\,}\mathrm{m\textsc{m}}$
SDS, $2.0\text{\,}\mathrm{\textsc{m}}$ AAm, $2\text{\,}\mathrm{m\textsc{m}}$
crosslinker and $2\text{\,}\mathrm{m\textsc{m}}$ photo-initiator) and an
outlet hole connected to an automatic suction pump by a polyethylene tube.
Prior to the polymerization, the precursor solution is sucked out of the
chamber causing strong shear in the narrow gap between the two glass plates
and thousands of lamellar bilayers of self-assembled DGI are formed, perfectly
aligned in the direction parallel to the surface of the glass substrate. In
order to get stable PDGI bilayers in the hydrogel, this step is followed by
immediate polymerization by exposing the reaction chamber to UV light
($365\text{\,}\mathrm{nm}$) at $50\text{\,}\mathrm{\SIUnitSymbolCelsius}$ for
$8\text{\,}\mathrm{h}$ under an inert Ar atmosphere.
N,N-Methylenebis(acrylamide) (MBAA) was used as crosslinker and Irgacure as
initiator. After polymerization, PDGI bilayers are trapped inside the PAAm
matrix. The PDGI/PAAm gels synthesized in this way are then swollen in bi-
distilled water for one week with regular freshwater replacement to avoid
residuals. To further reduce the moduli of the equilibrium swollen PDGI/PAAm
in a second step, the parent PDGI/PAAm gels of
$100\text{\,}\mathrm{\SIUnitSymbolMicro m}$ thick were hydrolyzed using a
modified procedure that was described previously by Yue et al. [16]. The
parent gels were soaked in $1\text{\,}\mathrm{\textsc{m}}$ KOH(aq) aqueous
solution for $30\text{\,}\min$, followed by heating in an incubator at
$50\text{\,}\mathrm{\SIUnitSymbolCelsius}$ for $5\text{\,}\min$. The process
of hydrolysis partially changes the amide functional groups (PAAm) of the
parent PAAm hydrogel layers to sodium carboxylate groups (PAAc-Na). The
obtained hydrogel, which contains partially hydrolyzed PAAm (PAAcNa), was then
extensively washed several times with deionized water to achieve an
equilibrium swelling state. The strong swelling taking preferably place along
the direction of the layers splits the hard bilayers into smaller domains.
Subsequently, the rigid layers continue to reflect visible light, but play no
role in the gel deformation. The softness of this hydrolyzed PDGI/PAAm gel is
controlled by maintaining the pH of the water. To be used as microfluidic
pressure sensors the soft photonic hydrogel of thickness
$140\text{\,}\mathrm{\SIUnitSymbolMicro m}$ was maintained in a buffer
solution at pH $=6.92$ using $0.2\text{\,}\mathrm{\textsc{m}}$ KOH(aq) and
$0.2\text{\,}\mathrm{\textsc{m}}$ KH2PHO4(aq).

#### Gel characterization

At rest, the swollen hydrolyzed gels have an orange color. Under compression,
the distance between the light-reflecting bilayers is reduced leading to a
change in color from orange to blue, covering the whole range of visible
light. The relation between the applied pressure and the consequent color
change, as well as the moduli of the fabricated gels, were characterized using
a custom-made setup combing commercial mechanical testing equipment (Tensilon
RTC-1310A, Orientec Co.) together with movable angle reflection measurement
optics (Hamamatsu Photonics KK, C10027A10687) coupled to a photonic
multichannel analyzer (Hamamatsu Photonics KK, C10027) (see Supplementary Fig.
1 (a)). Disc-shaped samples of diameter $10\text{\,}\mathrm{mm}$ were cut out
using a gel cutter (model JIS-K6251-7). Samples were placed on a black
substrate and compressive loading was applied using the tensile machine. White
light was used to illuminate the gel throughout the experiments. The
reflection spectrum under compressive loading was acquired by keeping both the
angles of incident and reflection at
$20\text{\,}\mathrm{\SIUnitSymbolDegree}$. The wavelength at maximum
reflection intensity was obtained from the reflection spectrum (see
Supplementary Fig. 1 (b) for an example). The applied compression force, $F$
was registered for each step, together with the real area $A$ of the
compressed disc, allowing to calculate the applied pressure $P=F/A$. In this
way, the color change as a function of applied pressure was obtained (see Fig.
1 and Supplementary Fig. 2(a)). During compression, the change in thickness of
the gel was also registered from the tensile machine. Note that the thickness
change can also be deduced from the color change, corresponding to a well-
defined change in spacing between the reflecting bilayers. Both methods lead
to similar values for the gel compression [16, 18]. From these stress versus
strain curves the Young’s moduli can be measured and have been found to range
between $10\text{\,}\mathrm{kPa}$ and $100\text{\,}\mathrm{kPa}$ (see
Supplemantary Fig. 2 (b)). These values are slightly higher compared to the
$3.2\text{\,}\mathrm{kPa}$ given in [16] and result from slight changes in the
hydrolysis time, swelling and buffer conditions. Gels with slightly higher
moduli were more suited to be used in the microfluidic application as they
were easier to handle during chip assembly.

#### Device fabrication

The device is composed of two main PDMS parts: the top part corresponding to
the fluid channel and cavities and the bottom part to the gel chamber. Both
are obtained by pouring a Sylgard 184 PDMS mixture on silicon wafers using
photolithography and pre-designed molds following the standard procedure. The
lithography parameters are adjusted to the desired final height and later
confirmed through profilometer measurements. The error in the gel thickness as
well as the wafer fabrication have to be taken into account and adjusted in a
way that the PDMS gel chamber height remains minimum equal to or slightly
higher than the gel thickness to prevent pre-compression. A higher chamber
leads to an offset of the pressure. The poured PDMS is vacuumed to remove
bubbles and cured at $70\text{\,}\mathrm{\SIUnitSymbolCelsius}$ for
$2\text{\,}\mathrm{h}$. The two parts are separated by a commercially
available thin PDMS film (Silicon Sheet, GFSC 6000-100 µ -300Q) purchased from
“TOMITA MATEQS, Japan”.

To assemble the device, we first put the top PDMS part containing the cavities
and a thin PDMS membrane of $100\text{\,}\mathrm{\SIUnitSymbolMicro m}$, in
the oxygen plasma cleaner for $5\text{\,}\min$, at
$0.2\text{\,}\mathrm{mbar}$, $20\text{\,}\mathrm{W}$ and
$50\text{\,}\mathrm{kHz}$. The pieces are assembled together and cured at
$90\text{\,}\mathrm{\SIUnitSymbolCelsius}$ for $5\text{\,}\min$. This
operation is repeated with the assembled top cavities/thin membrane and bottom
PDMS part containing the gel chambers. When removed from the plasma cleaner,
just before assembling, the pieces of gel are cut with a blade and put in the
gel chamber. At last, the final parts are aligned, assembled, and cured at
$90\text{\,}\mathrm{\SIUnitSymbolCelsius}$ for $5\text{\,}\min$. Finally we
add buffer in the gel chamber to make sure it is well hydrated and we clog the
holes to avoid evaporation. The gel chamber was always kept filled with a
buffer with closed outlets and refilled if the buffer partially evaporated.

#### Microfluidic setup

The pressure-sensing unit was combined with microfluidic devices. It was
observed under a binocular microscope with a white light source oriented
perpendicularly toward the gel sample. The observation was made from "above"
through the pressure-sensing unit. A black background was insured with black
isolation tape at the bottom of the device (below the gel chamber) so that the
reflected light gave a better color contrast. The images were acquired using a
reflex Nikon camera, mounted on the binocular microscope. A pressure
controller (Fluigent Lineup Flow EZ) was used to impose controlled static
pressure for the sensor calibration, in a range from $0\text{\,}\mathrm{mbar}$
up to $140\text{\,}\mathrm{mbar}$. For flow experiments, a steady flow was
imposed inside the microfluidic channel with a syringe pump (Cetoni) at a
controlled flow rate.

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## Acknowledgements

We thank Benoit Roman for the useful discussions. This work was supported by
Global Station for Soft Matter, Global Institution for Collaborative Research
and Education (GSS, GI-CoRE) Hokkaido University, and JSPS KAKENHI (Grant no.
22H04968, 22K21342). We acknowledge support from the ERC Consolidator Grant
PaDyFlow under grant agreement 682367. We thank Institut Pierre-Gilles de
Gennes (Investissements d’avenir ANR-10-EQPX-34) and AAP Carnot 2021 et PSL
Valorisation - Qlife 2022. This research was partially supported by the UGC
Research Grant (2023-2024), University of Dhaka, Dhaka-1000, Bangladesh.

## Author contributions statement

AH, LD, JPG, and AL designed the study. AH and MI fabricated the color-
changing gel. AH, LD, and MG performed experiments and analyzed the results.
LD, AH, MG, and AL wrote the manuscript. All authors reviewed the manuscript.

## Additional information

The authors declare no competing interests.

## Data availability

All data generated or analyzed during this study are included in the
supplementary information files.