Exp Fluids (2012) 53:777–782
DOI 10.1007/s00348-012-1321-5
RESEARCH ARTICLE
Imaging diffusion in a microfluidic device by third harmonic
microscopy
Uwe Petzold • Andreas Büchel • Steffen Hardt
Thomas Halfmann
•
Received: 23 December 2011 / Revised: 11 May 2012 / Accepted: 15 May 2012 / Published online: 6 June 2012
Ó Springer-Verlag 2012
Abstract We monitor and characterize near-surface diffusion of miscible, transparent liquids in a microfluidic
device by third harmonic microscopy. The technique
enables observations even of transparent or index-matched
media without perturbation of the sample. In particular, we
image concentrations of ethanol diffusing in water and
estimate the diffusion coefficient from the third harmonic
images. We obtain a diffusion coefficient D = (460 ± 30)
lm2/s, which is consistent with theoretical predictions. The
investigations clearly demonstrate the potential of harmonic microscopy also under the challenging conditions of
transparent fluids.
1 Introduction
In recent years, microfluidic devices have found a large
number of attractive applications, for example, in (bio)
analytical chemistry (Ohno et al. 2008), biotechnology
(Neethirajan et al. 2011), chemical synthesis (Abou-Hassan
et al. 2010; Hessel et al. 2008), and pharmacological
research (Dittrich and Manz 2006; Kang et al. 2008).
Corresponding devices enable processes such as separation, mixing, chemical reaction, and detection of minute
samples, often in a superior manner than on the macroscale. Microfluidic technologies permit implementation of
the ‘‘lab-on-a-chip’’ concept, that is, integration of sample
U. Petzold (&) A. Büchel T. Halfmann
Institut für Angewandte Physik, Technische Universität
Darmstadt, Hochschulstraße 6, 64289 Darmstadt, Germany
e-mail: uwe.petzold@physik.tu-darmstadt.de
S. Hardt
Center of Smart Interfaces, Technische Universität Darmstadt,
Petersenstraße 32, 64287 Darmstadt, Germany
preparation and analysis on a credit-card-sized device. The
latter offers the commercially attractive features of small
size and weight, scalability, easy handling, possible processing of small sample amounts, and the potential for
mass production at low costs for the single unit.
Mixing is a key step in many biochemical assays as well
as in micro-process technology. Typically, flows in microchannels exhibit very low Reynolds numbers—hence
permit operation in the regime of laminar flow only
(Squires and Quake 2005). In this regime, mixing of liquids
becomes a much more difficult task compared to turbulent
flows. Therefore, in the past decade, a substantial body of
research has been devoted to the development of efficient
micromixing schemes (Hessel et al. 2005; Nguyen and Wu
2005). Going along with such efforts, methods have been
developed for characterization and diagnostics of micromixing processes. In particular, a variety of spectroscopic
techniques offer potential to monitor mixing processes in
microfluidics. As examples, we note Raman spectroscopy
(Rinke et al. 2010), surface-enhanced Raman spectroscopy (SERS) (Strehle et al. 2007), infrared spectroscopy
(Hinsmann et al. 2001), online Fourier transform infrared
(FT IR) microscopy (Antes et al. 2003), attenuated total
reflection FT IR spectroscopy (Chan et al. 2009), or laserinduced fluorescence (LIF) (Hoffmann et al. 2006).
However, these methods exhibit specific limitations, for
example, some require tunable laser sources to address
resonances in the sample, some lead to perturbations in the
medium (e.g., by heating after resonant excitation or the
need of labeling with additional markers), some provide
only limited spatial selectivity to address a narrow fluid
layer directly at the surface of a microchannel, and many
techniques cannot image optically transparent media. We
also note, that due to the large surface-to-volume ratio of
microfluidic devices, it is especially interesting to measure
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species concentrations in the close vicinity of solid–liquid
interfaces. For such purposes, a number of experimental
techniques have been developed, most notably total internal reflection and surface plasmon resonance microscopy
(for an overview, see, e.g., (Kihm 2011)). In this context,
fluorophores are usually required to image the sample
concentration near channel walls. However, the application
of such additional chemical markers is a major disadvantage in a number of applications. As an example, fluorescence markers change some of the key properties of
biomolecules, for example, their ability to bind to specific
targets (Ray et al. 2010). Therefore, label-free methods for
concentration imaging close to solid–liquid interfaces in
microfluidics are highly desirable.
In the following, we will discuss the experimental
implementation of third harmonic generation (THG)
microscopy as a powerful alternative to monitor and
quantitively characterize diffusion processes in microfluidics. THG microscopy exhibits a specific example of
coherent nonlinear microscopy (see, e.g., (Aptel et al.
2010; Cheng and Xie 2004; Tzeng et al. 2011) and refs.
therein). The basic concept of coherent nonlinear microscopy is to drive frequency conversion processes in the
sample by tightly focussed laser beams. The generated
signal yields information on the material and geometric
structure in the focal volume. By scanning the laser focus
across the sample, we are able to obtain a three-dimensional image. We note that such nonlinear processes result
in effective excitation volumes smaller than the diffractionlimited volumes of the fundamental field—which enables a
larger resolution. In contrast to multi-photon fluorescence
microscopy, coherent nonlinear microscopy uses (coherent) frequency conversion processes rather than (incoherent) radiative decay. Coherent nonlinear microscopy
requires no staining, marking, or radiative quenching in the
sample. Examples for coherent nonlinear microscopy are
imaging techniques involving second harmonic generation
(SHG) (Hellwarth and Christensen 1975), third harmonic
generation (Barad et al. 1997), or coherent anti-Stokes
Raman scattering (CARS) (Duncan et al. 1982).
Schafer et al. (2009) already used CARS microscopy to
monitor the diffusion of ethanol in water. While CARS
microscopy requires tunable laser sources to drive vibronic
resonances in the sample, SHG and THG microscopy
typically are implemented as off-resonant frequency conversion processes, that is, without the need for tunable light
sources. As a significant advantage, off-resonant frequency
conversion does not deposit energy in the sample (Carriles
et al. 2009), which may otherwise lead to perturbations like
heating and degeneration of the medium. Moreover, offresonant SHG and THG are applicable to a larger variety of
media. In particular, we note that harmonic microscopy
yields a signal even in otherwise (i.e., in the sense of linear
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Exp Fluids (2012) 53:777–782
optics) fully transparent samples and mixtures. As another
interesting feature, in the case of strongly focussed laser
beams (which provide large signals and large resolution),
SHG and THG appear only at interfaces (Barad et al. 1997;
Squier et al. 1998). In the bulk medium, the harmonics
interfere destructively due to the Gouy phase shift (Boyd
2008). This makes harmonic microscopy a powerful tool to
monitor interfaces (or processes at interfaces). Finally, we
note that SHG and THG provide complementary information on samples composed of different types of media.
In contrast to THG, SHG is selective for non-centrosymmetric media (Carriles et al. 2009). Due to the cubic
intensity dependence, THG enables better intrinsic resolution compared to SHG at the same wavelength. Thus,
THG microscopy represents the appropriate technique to
monitor, image, and characterize microfluidic systems—
even if they involve transparent or index-matched flows
and mixtures.
Recently, we provided a first basic demonstration of
THG microscopy to image immiscible microfluids in specific geometries (Petzold et al. 2012). In the following
work, we will present the application of THG microscopy
to image and quantitatively characterize mixing (rp. diffusion) processes in microfluidic devices. In particular, we
investigate the mixing of ethanol in water near the surface
of a microfluidic channel. We note that these fluids are
transparent and exhibit almost equal indices of refraction
(nw = 1.329 and ne = 1.357). Nevertheless, from the THG
images, we directly deduce local ethanol concentration
gradients. This enables us to determine diffusion coefficients in the microfluidic device.
2 Experimental setup
Figure 1 depicts the schematic setup of our nonlinear
microscope. We apply an ultra-fast Titanium:Sapphire
laser oscillator (Spectra-Physics, Tsunami), pumped by a
continuous wave Nd:YVO4 laser (Coherent, Verdi G7).
The laser setup provides a train of ultra-short pulses at
center wavelength of 810 nm, average output power of
1 W, pulse duration of 60 fs (FWHM of intensity), and
repetition rate of 82 MHz. The laser beam is focused by a
microscope objective (Zeiss, 46 04 08) with a numerical
aperture of 0.22 and a focal length of 16 mm into the
sample. The third harmonic (wavelength, 270 nm) generated in the sample at the laser focus is collimated by a
condenser (NA = 0.67), separated by dichroic mirrors
(DM) and an interference filter (IF), and finally detected on
a photo-multiplier tube (PMT). A lock-in amplifier (Scitec,
lock-in amplifier 450DV2 & Chopper 310CD at 75 kHz)
serves to amplify the PMT signal. We apply an external
chopper rather than the intrinsic laser modulation at
Exp Fluids (2012) 53:777–782
82 MHz to reduce signal fluctuations due to coherent
pickup. A galvano scanner enables two-dimensional scanning of the laser focus in the xy-plane of the sample (i.e.,
perpendicular to the optical axis of the laser beam). The
microscope objective is mounted on a translation stage,
which permits scanning of the laser focus in the z-direction
(i.e., parallel to the optical axis of the laser beam). Thus,
we are able to obtain point-by-point three-dimensional
images with a spatial resolution in the range of microns.
To investigate the mixing (rp. diffusion) process of two
miscible liquids, we use a fused silica microfluidic chip in
Y-channel geometry (Translume, Y-channel). The chip has
three inlets and one outlet (see inset of Fig. 1). Three
syringe pumps (New Era Pump Systems, NE-500) drive
water through two inlets (combined flow rate Qw = 1 ll/
min) and ethanol through the third inlet (flow rate
Qe = 1 ll/min). All channels possess a rectangular profile
with a width w = 300 lm and a height h = 100 lm.
Ethanol and water mix in the outlet channel. We performed
all experiments at room temperature (i.e., 25 °C) in an airconditioned and temperature-controlled laboratory.
3 THG images of diffusion in the microfluidic device
The laminar flow of ethanol and water in the mixing
channel permits us to determine the near-wall concentration profile resulting from the convection–diffusion
dynamics inside the channel. As THG microscopy is sensitive to interfaces, we record images with the laser focus
scanned at the interface between the fused silica base plate
of the microfluidic channels and the fluid layer directly
above the base plate.
We note that both ethanol and water generate a THG
signal in the laser focus. The THG signal from ethanol is
significantly stronger (i.e., by a factor of 2.5). To determine
779
the absolute THG yield from ethanol, we also record a
reference image with pure water all over the microfluidic
device. We subtract the water reference image from the
image of the ethanol/water mixture. Thus, the difference
image directly maps the ethanol concentration. By simple
calibration measurements (not shown here), we also confirmed that the THG difference signal from an ethanol/
water mixture is directly proportional to the ethanol concentration. Also, related experiments by Shcheslavskiy
et al. (2004) on methanol/water mixtures at the surface of a
fused silica substrate yielded a linear dependence of the
THG intensity versus methanol concentration.
Figure 2 shows an image of the ethanol concentration in
the microfluidic device, obtained by THG microscopy as
described above. Close to the inlet, the area of high ethanol
concentration is large (indicated by orange color). We see
only a rather narrow transition region (indicated by blue
color) toward the area with pure water (indicated by black
color)—as expected close to the inlet. When the flow
proceeds further along the outlet channel (i.e., in y-direction), the width of the area with high ethanol concentration
decreases, and the width of the transition region increases.
Thus, ethanol and water diffuse in each other and become
mixed.
The constant laminar flow of the fluids leads to stationary concentrations in the outlet channel. The concentration profile is the result of a quite complex convection–
diffusion process with significant concentration gradients
in x- and in z-direction. Due to the different flow velocities,
the largest concentration gradients in z-direction are in the
center plane of the channel (where the largest velocities
occur) and in a plane close to the channel wall (here, the
velocity is close to zero). At a fixed y-coordinate, differences in the flow velocity correspond to different times
available for diffusive mass transfer––leading to concentration gradients in z-direction. Only in the case of very
Fig. 1 Schematic setup of the
nonlinear microscope. The inset
shows an enlarged view of the
detected volume (i.e., the
microfluidic device) in the range
of the scanning laser focus. The
direction of the flow in the
outlet channel defines the y-axis
in our coordinate system
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Exp Fluids (2012) 53:777–782
Fig. 2 THG image of ethanol concentration in the microfluidic
device. The THG signal is directly proportional to the ethanol
concentration. The background THG signal from pure water is
subtracted in the image. The image exhibits an average over 3
experimental runs. Flows are directed from the three inlets on the left
to the outlet on the right. We added thin white lines to indicate the
channel geometry. The origin of the coordinate system is chosen at
the contact point of ethanol and water. The dashed, yellow line close
to the inlets indicates the position of a cut in x-direction, which we
show in Fig. 3. The image size is 4.1 mm 9 0.5 mm (2,050
pixels 9 250 pixels). The spatial resolution is 2 lm with a pixel
dwell time of 2 ms. The absolute position of the transition region
between pure ethanol and pure water fluctuates along the channel.
This is due to a jitter in the flow rate—which does not affect the
determination of the width of the transition region and diffusion
coefficient to any significant degree. The two dark spots in the last
section of the outlet channel are due to defects on the surface of the
fused silica plate. The bright line close to the end of the channel is due
to an air bubble in the flow. However, these small defects do not
disturb our analysis of the large image
shallow mixing channels, an analytical expression for the
concentration field is available (Wu et al. 2004). Though
mixing processes as discussed in our work are commonly
referred to as ‘‘diffusive’’, there is no fully accurate analytic treatment available to precisely determine the diffusion coefficient from a concentration profile in a xy-plane.
Nevertheless, determination of diffusion coefficients via
the (only available) simplified theoretical model of the
mixing process permits at least fine order-of-magnitude
estimations. This serves as a consistency check to prove the
validity of the image data taken by THG microscopy. A
certain position in y-direction measured with respect to the
channel crossing at y = 0 corresponds to an average
duration t = y/v of the diffusion process. The average
velocity of the liquids is given by the flow rates and
dimensions as v = (Qw ? Qe)/(hw) & 1.1 mm/s. The
width of the transition region at a position y (rp. a diffusion
time t = y/v) is a measure for the speed of the diffusion
process. For simplicity, we assume that the measured
concentration profile is the result of a one-dimensional
diffusion process, theoretically described by a simple error
function (Cleland 2003):
hx x i
c
cðxÞ ¼ c0 =2 1 þ Erf
ð1Þ
2b
Dy of one pixel, corresponding to 2 lm). In the averaging
procedure, we also ignore few single cuts with deviations
of more than 50 % from the average or with a relative
uncertainty of more than 50 %. We note that under optimal
conditions of observation, the symmetry center should
always be at xC = 0. Due to jitter in the flow, the symmetry
center xC slightly fluctuates (compare Fig. 2). However,
this does not affect the determination of the width b by the
fit procedure at all.
As an example, Fig. 3 shows the THG intensity in a cut in
x-direction of the image in Fig. 2 at position y = 738 lm
(see dashed yellow line in Fig. 2). Obviously, outside the
channel (i.e., in the fused silica bulk of the substrate), the
interface-sensitive THG signal vanishes. Inside the channel,
we obtain a plateau of large THG signal in the region of pure
ethanol and a plateau of low THG signal in the region of pure
water. As indicated above, we show differential THG signals
(i.e., calibrated with respect to the background THG signal
from pure water). Between the two plateaus, we observe the
transition region of the diffusion process, that is, a concentration gradient. By fitting Eq. (1) to the data points, we
determine the fit parameters, for example, the width b. From
b, we can obtain a rough estimate of the diffusion coefficient
pffiffiffiffiffiffiffiffiffi
D via the simple relation b ¼ D t (Cleland 2003), with the
diffusion time t = y/v. Such a procedure represents a consistency check for the experimental data rather than an
accurate determination of D.
If we now determine the widths b for all positions y in
our THG image (see Fig. 2), we obtain the dependence of b
with time. Figure 4 shows the variation of b with the difpffiffiffiffiffiffiffiffiffi
fusion time t. The fit with the function b ¼ D t (red line)
yields a diffusion coefficient for the ethanol/water sample
of D = (460 ± 30) lm2/s. This is consistent with recent
theoretical predictions of the diffusion coefficient for ethanol and water in the range between Dmin = 380 lm2/s and
Dmax = 840 lm2/s (Zhang et al. 2006). Figure 4 also
with the initial concentration of the pure liquid c0, the
position x (compare Fig. 2), the symmetry center xC of the
transition region, and the width b of the transition region.
This form roughly approximates the concentration profile
for the case of equal volume flows of water and ethanol. To
reduce statistical fluctuations in the image data, we apply a
straightforward averaging procedure: We take cuts in xdirection (columns) at each position y in the THG image.
Afterwards, we fit function (1) to the measured concentrations and obtain the width b as a fit parameter in each
column. Finally, we average the resulting fit parameters
b over 300 adjacent columns (each with a column width
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Exp Fluids (2012) 53:777–782
Fig. 3 THG intensity in a cut in x-direction at position y = 738 lm
in the image according to Fig. 2. The THG signal is directly
proportional to the ethanol concentration. The dashed lines indicate
the boundaries of the outlet channel. Blue dots depict experimental
data points. The red line depicts a fit with Eq. (1). The shaded area
indicates the width b, as determined from the fit
781
general concentration-dependent. The theoretically expected maximal diffusion coefficient is valid in the dilute limit,
that is, small quantities of a specific component diffusing in
a background fluid. On the other hand, the theoretically
expected minimal diffusion coefficient is based on the
assumption of an almost 50:50 initial mixture of water and
ethanol. In the experiment and the specific regime of flow
rates, diffusion occurs mainly in the transition region
between the fluids. This area is characterized by similar
concentrations of water and ethanol (even at early times).
Thus, the experimentally diffusion coefficient is closer to
minimal theoretical value. Finally, we note that we confirmed the derived value of the diffusion coefficient also by
systematically varying the velocity v at a fixed location
y (rather than varying the position y at fixed velocity v,
as applied to determine the data in Fig. 4). This alternative procedure yielded the same value for the diffusion
coefficient.
4 Conclusion
Fig. 4 Variation of the width of the transition region with the
diffusion time. Blue dots depict experimental data points. The error
bars indicate the standard deviation after averaging 300 adjacent cuts
in x-direction (columns). The red line depicts a fit with the
pffiffiffiffiffiffiffiffiffi
function D t. The shaded area indicates the range between the
theoretical predictions with calculated minimal and maximal diffusion coefficient (Zhang et al. 2006)
depicts the full possible range for the time dependence of
the width b, as determined by the theoretically predicted
limits Dmin and Dmax. The experimentally determined
dependence (based on the simplified model) is inside this
range. Our result is also consistent with an early (macroscopic) experiment to determine the diffusion coefficient of
ethanol in water (Tyn and Calus 1975).
We also note that our experimentally determined value
of the diffusion coefficient is closer to the lower limit of the
theoretical prediction. As our model to determine the diffusion coefficient from the experimental data is very much
simplified, we must be careful when interpreting this evidence. Indeed, the convection–diffusion process is already
quite complex. Moreover, the diffusion coefficient is in
We applied third harmonic microscopy to image and characterize the near-surface diffusion of two miscible, transparent (or even index-matched) fluids, that is, ethanol and
water in a Y-channel microfluidic device. No labeling,
staining, or resonant excitation is required to obtain highresolution images by harmonic microscopy. After subtracting
the background harmonic signal generated by water, the third
harmonic yield is directly proportional to the ethanol concentration in the sample. Thus, the technique enables direct
mapping of ethanol concentrations in microflows near a
surface with a spatial resolution in the range of micrometers.
From the images, we also get information on the speed of the
mixing process, being related to the value of the diffusion
coefficient. In particular, from the third harmonic images, we
obtain an estimate of D for ethanol/water samples. We find a
value of D = (460 ± 30) lm2/s, which is consistent with
recent theoretical predictions as well as previously measured
values. The investigations clearly demonstrate the potential
of harmonic microscopy also under the difficult conditions of
transparent fluids and similar refractive indices. This serves,
for example, to obtain information on diffusion/mixing processes, temperature gradients, or reaction dynamics in
microfluidic devices—at high spatial and temporal resolution
and without perturbation of the samples.
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