Continuous-flow microreactors are innovative systems extensively
utilized in various scientific and industrial fields. These systems are
designed to conduct chemical reactions by continuously transporting reagents
through specialized microchannels. This approach offers numerous advantages
compared to traditional batch reactors and has gained widespread adoption in
pharmaceuticals, organic synthesis, and other industries. Continuous-flow
microreactors make the technological process not only continuous but also
highly productive. The constant input of reagents and removal of reaction
products result in heightened efficiency and resource conservation.
Furthermore, these microreactors enable precise control of reaction conditions
through the reagent flow regulation and flexible temperature management. In
addition, their compact size allows for improved scalability and economic
efficiency [1, 2].
However, continuous-flow microreactors also present certain
drawbacks. Firstly, their small channel size predominantly results in laminar
flow, which restricts efficient mixing and makes the distribution of velocity
and concentration non-uniformly. This limitation hampers the potential use of
flow microchannels, especially in applications requiring a high level of flow uniformity.
Mutual diffusion of reagents in the transverse direction is the primary
mechanism of mass transfer, necessitating an increase in channel length to
achieve complete mixing. Researchers have proposed various strategies to
enhance liquid mixing in continuous-flow reactors [3-5]. One approach involves
enhancing the flow mixing by modifying the internal topology of the reactor [6,
7]. Another method employs external force fields, such as ultrasonic waves or
electromagnetic fields, to induce mass transfer within the channel [5, 8]. We
previously demonstrated that gravitational field can also serve the same
purpose by creating specific conditions that trigger hydrodynamic
instabilities. Notably, we illustrated that by exploiting the disparities in
density or diffusion coefficients of the pumped reagents, it is possible to
promote reagent mixing through gravity-dependent instability mechanisms [9].
The second challenge with microreactors is their small size, which complicates
and sometimes restricts the use of visualization and measurement techniques for
studying mass transfer processes. Currently, various visualization methods are
commonly employed. These include fluorescent markers that allow visualization
mixing and monitor flow characteristics, optical microscopy methods, and
techniques that rely on indicator reactions for qualitative and quantitative
assessment of mixing. The most accessible approach involves adding different
dyes (such as fluorescent, pH-sensitive, and food-grade dyes). However, previous
research has shown that dye addition can lead to erroneous results [10].
Dissolving a dye in the system is akin to adding a new component with its
density, diffusion coefficients, and surface tension, which can quantitatively
and even qualitatively change the nature of the mixing process.
Methods that visualize the refractive index field in solution
offer advantages over other techniques. They include shadowgraph and
interference methods. Shadowgraph techniques, such as synthetic schlieren [11],
are straightforward to implement and require basic instrumentation. However,
their main drawback is low sensitivity. In contrast, interference techniques
[12] exhibit much higher sensitivity. Experimental implementation of
interferometry is not significantly more complex but necessitates more
expensive equipment. The sensitivity of interference methods in hydrodynamic
problems relies on the dynamic range of the video camera used to record the
interferogram. A conventional industrial 8-bit video camera with a dynamic range
(DR) exceeding 50 dB enables the detection of optical path differences (OPD) as
small as 1/100 of a wavelength. The utilization of scientific-grade cameras
allows for achieving sensitivities of 1/1000 (DR > 70 dB) or even 1/10000 of
the wavelength (in case of expensive 16-bit cameras with DR > 90 dB).
Furthermore, employing multi-pass interferometric schemes, such as the
Fabry-Perot type, can enhance the sensitivity of interferometry, providing
almost unlimited potential. However, researchers commonly prefer using
double-pass schemes such as Michelson or Fizeau types because they are easier
to implement.
Interferometric technology has its drawbacks as well. Its high
sensitivity prevents the registration of significant refractive index gradients
beyond the resolution of the video camera. In simple continuous-flow reactors
(with Y or T-junction), high refractive index gradients occur near the merging
point of two incoming streams, where diffusion has not yet blurred the mixing
zone. In such cases, a shear interferometer can be used [13]. The shear
interferometer's optical scheme involves dividing the light beam into reference
and object beams after passing through the studied inhomogeneity. As a result,
the object wavefront interferes with its copy, shifted across the optical axis.
By reducing the magnitude of the shift, we can decrease the interferometer
sensitivity, enabling the resolution of significant refractive index
inhomogeneities. The interference fringes on the interferogram correspond to
the refractive index gradient, similar to the shadowgraph method. Therefore,
this technique shares the same limitations as the shadowgraph method. To obtain
quantitative information about the refractive index distribution, one can
integrate a specific segment in the direction of the shift. The process of
integration introduces an additional variable error into the final result.
Note, that a complete reconstruction of the refractive index field requires a
minimum of two interferograms obtained with a shift in two perpendicular
directions unless the refractive index field exhibits axial or mirror symmetry
(a common situation in hydrodynamics). Hence, the shear interferometer proves
valuable for the qualitative analysis of convective structures characterized by
significant refractive index gradients. However, in other cases, it is
recommended to utilize interferometers assembled using a two-pass scheme that
enables the visualization of flow structure and facilitates precise
quantitative data acquisition regarding the refractive index field.
This article presents the visualization results obtained using a
shear interferometer and a Fizeau autocollimation interferometer. Both schemes
visualized the mixing process of two aqueous solutions within a continuous-flow
reactor under conditions of hydrodynamic instability formation. We investigate
two types of instability, gravity-dependent and gravity-independent. In the
case of gravity-dependent instability, we use the shear interferometer to
visualize the flow structure arising from the formation of double-diffusion
convection [14]. In the case of gravity-independent instability, we used the
Fizeau interferometer to visualize the development of Marangoni convection
[15]. Additionally, the Fizeau interferometer allows for the acquisition of
quantitative information regarding changes in the refractive index,
facilitating an evaluation of the effectiveness of the micro-mixer operating
based on the Marangoni effect.
We performed experiments in a continuous-flow microreactor with a
mixing zone in the form of a long rectilinear microchannel (Figure 1). The
microreactor's side walls were constructed from transparent plane-parallel
glass plates with a thickness of 2 mm. A chemically resistant spacer was
positioned between the plates to define the location of the supply channels and
the mixing zone. The microreactor's side walls have special holes. It allowed
for the supply and withdrawal of liquids via tubes connected to a syringe pump.
The design of the microreactor used offered flexibility in terms of adjustment,
as changing the shape and geometric dimensions of the mixing zone only required
replacing the spacer, thereby avoiding the complete reconstruction of the
microreactor.
The first set of experiments focused on visualizing and
investigating the mixing process of aqueous solutions induced by a
gravity-dependent type of instability, namely double-diffusion convection (DD).
This instability arises due to the difference in the molecular diffusion
coefficients between the components dissolved in the system. In the case of
initially stationary two-layer system formed by homogeneous solutions of two
different substances, instability develops in the form of finger-like
convective structures that symmetrically propagate in both directions from the
initial contact zone of the liquids [14]. To study the effect of this type of
convection on the mixing process, we used a Teflon spacer with a thickness of
1500 microns (Figure 1a). The contact of the initial solutions took place in
the Y-junction located at the base of the microchannel. The lower arm of the
Y-channel supplied a denser aqueous solution of faster diffusing potassium
chloride (KCl) with a mass concentration of 11.3%. Simultaneously, the upper
arm of the Y-channel delivered a less dense aqueous solution of slower
diffusing copper (II) chloride (CuCl2) with a mass concentration of
6.3%. The initially stable density stratification excluded the development of
Rayleigh-Taylor instability. The presence of a faster diffusing solute in the
lower layer was a prerequisite for the formation of double-diffusion convection
[14].
In the second series of experiments, our objective was to study
the impact of soluto-capillary Marangoni convection, a gravity-independent
hydrodynamic instability, on the mixing process of initial solutions. This
instability arises in the presence of a liquid-liquid or liquid-gas interface,
along which a surface tension gradient is created due to a concentration gradient
of surfactant located at the interface [15]. In these experiments, we utilized
a silicone spacer with a thickness of 200 microns (Figure 1b). The contact of
the initial solutions took place at the T-junction located at the base of the
microchannel. In these experiments, the lower arm of the T-channel supplied the
denser pure water. The upper arm of the T-channel delivered a less dense
aqueous solution of isopropyl alcohol with a mass concentration of 9.6%. An
additional inlet tube located at the upper boundary of the microchannel
provided an air supply to create a gas bubble inside the microreactor. It
formed a liquid-gas interface inside the microchannel, adjacent to the
diffusion zone between the pumped solutions.
In both sets of experiments, the microchannel had a length of
L
=7
cm and a height of
h
=0.2 cm. The flow rate ranged from
Q
= 0.001
to 0.02 ml/min, corresponding to a flow velocity range of
v
=0.033 to
0.066 cm/s. When operating within this flow range, we tightly clamped the
silicone spacer between the side glass plates to ensure leak-free conditions.
This becomes possible because silicone has high adhesion to glass, unlike other
materials, and securely "sticks" without the need for gluing.
However, for the Teflon spacer, we sealed the perimeter of the microreactor
with glue. All experiments were performed at an ambient temperature of 22 ± 1
°C.
Figure 1. The diagram of the
microreactor: 1 – side glass walls of the microreactor, 2 – the spacer defining
the geometry of the microreactor. Large arrows indicate the position of the
inlets and outlet channels. A small arrow demonstrates the air supply inlet
used to create a liquid-gas interface inside the microreactor during the study
of Marangoni convection.
We used a laser interferometer to visualize the flow structure and
study the mixing process. We applied two different optical schemes, depending
on the type of hydrodynamic instability. In the first case, we investigated the
development of double-diffusion convection. The instability occurs directly at
the junction point of the flows. Convection induces significant concentration
variations, leading to the formation of regions characterized by large
refractive index gradients. To visualize these phenomena, we employed a shearing
interferometer. Figure 2 depicts the optical scheme of the interferometer and
an example of the flow structure visualization in the case of the development
of the double-diffusion convection. Also, in Figure 2, for comparison, the
visualization of the flow in the non-convective case, when mixing solutions in
the transverse flow direction occurs solely due to diffusion, is given. In this
optical scheme, two glass plane-parallel plates of interference quality 2,
located parallel to one another at a small distance
(see Fig. 2),
are used to split the wavefront passed through the inhomogeneity. The wavefront
is incident on the plates at an angle of 45° and reflected mainly from the back
plane of the first plate and front plane of the second plate, which have a
semitransparent coating. As a result, two identical reflected wavefronts
laterally sheared relative to each other by an amount of d
are projected on the camera matrix 4. The
d
value is
modified using a special adjustment screw that enables fine-tuning the
wavefront shearing and, therefore, an interferometer sensitivity.
Figure 2. Scheme of the
optical setup: 1 - He-Ne laser, 2 - the element responsible for implementing
the shift, 3 - microreactor; 4 - CCD camera. The
d
value is 0.1 mm. The
vertical size of each interferogram is 25 mm.
In contrast to a stationary liquid condition (Q=0 ml/min),
where the instability leads to the symmetric spreading of a finger-like
convective structure in both directions from the initial contact zone, the
presence of liquid pumping (Q
> 0) significantly alters the flow
structure. At the beginning of the channel, the original layers remain unmixed,
and a thin diffusion mixing zone forms between them, characterized by a large
concentration gradient. Moving away from the Y-junction, DD-convection gives
rise to a convective structure around the diffusion zone. The continuous flow
of liquids along the microchannel carries developing "fingers" from
the point of their origin, causing them to elongate and leading to a more
intricate structure (Fig. 2, top interferogram). An interferogram demonstrating
the mixing of liquids in the absence of convection, solely reliant on
diffusion, is provided for comparison in the same figure. A comparison of the
interferograms highlights that the development of DD convection leads to flow
splitting, folding, and recombination, similar to how it happens in
microreactors with complex geometries. It is known [7] that such microreactors,
utilizing internal partitions, obstacles, turns, and irregularities, transform
the initial laminar flow into turbulence, facilitating more efficient mixing
through the development of forced convection. In the present study, similar
outcomes are achieved through the mechanism of natural convection, eliminating
the need to use reactors with complex geometries.
In the second case, we examined the development of
soluto-capillary Marangoni convection. Our study involved a two-layer system
with stable density stratification, consisting of an aqueous solution of
isopropyl alcohol and water. To trigger Marangoni convection, a gas bubble was
formed near the top boundary of the microchannel at a distance of 1.1 cm from
the T-junction, creating a liquid-gas interface. We visualized the spatial
distribution of the solute using the Fizeau interferometer. Figure 3 depicts
the optical scheme and provides examples of interferograms. The interference
pattern was formed by a pair of plane-parallel glass plates of interference
quality with semitransparent coating (2 and 4), which formed the Fizeau
interferometer cell. The side walls of the microfluidic channel were positioned
at a slight angle to the optical axis of the interferometer to prevent the
reflected light from the reactor walls from entering the camera's aperture. While
glass plate 2 remained fixed, the angle of plate 4 was adjustable. In position
I, where the plates were precisely parallel to each other and perpendicular to
the optical axis, the interferometer allowed us to observe patterns in the
infinite fringe mode (see interferogram I in Figure 3). This optical
configuration allowed the investigation of the emerging flow structure and
provided a qualitative assessment of the mixing intensity of the liquids.
Figure 3. Scheme of the
optical setup: 1, 2 – interference glass plates forming the measuring cell of
the Fizeau interferometer; 3 - microreactor; 4 - CCD camera, 5 - He-Ne laser.
The vertical size of each interferogram is 0.2 cm.
In order to observe the mixing process in the mode of fringes of
equal thickness, the interferometer was readjusted using special screws (see
Interferogram II in Figure 3). This adjustment involved introducing a slight
angle (~0.3°) between the glass plates of the interferometer. Interferograms
obtained in this manner were suitable for qualitative analysis and quantitative
assessment of the refractive index distribution resulting from the non-uniform
concentrations of the dissolved substance (specifically, alcohol in this
study). For the quantitative analysis, we employed the spatial phase shift
method [16]. We processed the interferograms and measured the quantitative
parameters using the IntelliWave software (Mahr GmbH, Germany).
No specific requirements were imposed on the quality of the glass
walls of the microreactor when implementing this optical scheme. It was
sufficient for the utilized glasses to be visually free from any noticeable
optical distortions, such as internal striae and surface deformations. The
spacer, which defines the channel geometry, should possess a consistent and
uniform thickness. This requirement is essential to minimize the measurement
error of the refractive index difference of the liquid, ultimately enabling
precise determination of the concentration gradient across different segments
of the microreactor. For instance, the silicone spacer had a thickness of 200±5
μm, resulting in a relative measurement error of ±2.5%.
The interferograms (fringes of equal thickness) enabled the
reconstruction of two-dimensional optical path difference (OPD) fields using
the phase shift method. Moreover, essential parameters of the study, such as
the distribution of refractive index or the concentration of the dissolved
substance, could also be calculated. The interferogram, obtained by reflecting
light from the coatings on the interference glass plates, contained integral
information about the optical path difference (OPD). This OPD consisted of
information obtained from the light passing through the investigated liquid
system (a signal), the microfluidic cell walls, and the air space between the
interference plates and microchannel (a noise). To extract the OPD of the
desired signal, we captured a reference image that contained only noise. This
reference image was an interferogram obtained for a microchannel filled only
with pure water. Subsequently, the IntelliWave software functions were employed
to extract the OPD of the reference image to reconstruct the wrapped phase
difference field and the corresponding OPD field. Figure 4a illustrates the
interferogram of the water-filled microreactor and corresponding wrapped phase
difference and OPD fields.
Figure 4. The main stages of
image processing shown in the example of interferogram analysis obtained at
Q
=0.004
ml/min. From top to bottom: an interference pattern (fringes of equal
thickness), the corresponding wrapped phase difference field, and the OPD field
acquired in a microreactor filled with (a) water (reference image) and (b) the
system alcohol-water. (c) The resulting OPD field, representing the alcohol
concentration distribution obtained by subtracting the OPD of the reference
image. The bubble position is
x
=1.1 cm. The working region of the
channel is indicated by a black frame, aligned with the chosen coordinate axes
shown in Figure 1a. Each image has a vertical size of 0.2 cm.
Once the OPD field of the reference image was obtained, we
initiated the pumping of the working liquids and created a gas bubble inside
the channel. In the presence of an interfacial boundary within the system, an
additional mixing mechanism arises due to soluto-capillary Marangoni
convection. Isopropyl alcohol acts as a surfactant and reduces the surface
tension of the solution. As a result, a surface tension gradient forms along
the free surface adjacent to the diffusion zone between water and alcohol. It
initiates the development of intense capillary flow both at the interfacial
surface and in the vicinity of the bubble. The resulting convection homogenizes
the distribution of alcohol, leading to the disappearance of the surface
tension gradient and the decay of convection. However, due to the continuous
supply of working liquids, the initial concentration distribution near the free
surface is reinstated, thereby reinitiating the Marangoni mechanism. Thus, the
system enters an oscillatory regime of soluto-capillary Marangoni convection
[12] that acts as a local micro-mixer that stirs the liquids near the bubble
surface. An example interferogram demonstrating the process of liquid mixing
under the development of Marangoni convection, along with its corresponding
reconstructed wrapped phase difference and OPD fields (raw signal, without
noise signal subtraction), are depicted in Figure 4b. The resulting OPD field,
which demonstrates the refractive index changes of the mixed liquids within the
channel, is presented in Figure 4c.
For any vertical cross-section of the two-dimensional OPD field,
we can calculate the refractive index distribution
n
(z). Then,
using the concentration-dependent refractive index dependence
n
(C)
for each vertical cross-section, concentration profiles
C
(z) can
be obtained, which further allows calculating the concentration difference
Δ
C
in the cross-section. This parameter served as a criterion for
assessing the efficiency of mixing. By analyzing how the initial concentration
difference Δ
C
between layers changes along the channel, we
quantitatively evaluated the mixing efficiency in the presence of Marangoni
convection. Figure 5 presents the results obtained from experiments conducted
under the same initial conditions (flow rate
Q
= 0.004 ml/min, alcohol
concentration
C
= 9.6%, bubble position
x
= 1.1 cm) but for
different bubble sizes. The bubble size was determined by the ratio of the
vertical bubble size to the vertical channel size,
s
=
hb
/
h.
Figure 5a shows the interferograms and corresponding two-dimensional OPD fields
obtained for different bubble sizes. Figure 5b presents the corresponding
dependencies characterizing the variation of the initial concentration
difference ΔC
along the channel. Additionally, for comparison, the
dependency obtained in an experiment conducted under the same flow rate but in
the condition of pure diffusive mixing (in the absence of a bubble) is also
presented.
The shaded area on the graph (Figure 5b) represents the region
where the bubble position was masked during processing. We did not perform the
OPD calculation for this region. It is evident that at the beginning of the
channel, the liquids are weakly mixed due to the diffusion process. Near the
bubble, the mixing intensifies due to the activation of the convective
mechanism. Analysis revealed that the mixing process enhanced with increasing
bubble size. It is explained by the fact that the intensity of soluto-capillary
Marangoni convection increases with the expansion of the free surface area.
Figure 5. (a) Interferogram
(top) showing the mixing process of liquids during the development of Marangoni
convection, along with its corresponding OPD field (bottom). Each image has a
vertical size of 0.2 cm. (b) Dependencies characterizing the variation of the
initial concentration difference between the initial liquids along the channel,
obtained for different sizes of gas bubbles. The experimental parameter: flow
rate
Q
= 0.004 ml/min, alcohol concentration
C
= 9.6%, bubble
position
x
= 1.1 cm.
By employing optical interferometry, we successfully captured and
visualized the dynamic mixing process of two continuously flowing liquids
within a microreactor, as influenced by two different types of hydrodynamic
instabilities. In order to visualize the convective flow driven by the
instabilities, we utilized two optical schemes adapted to each specific
instability type. The shearing interferometer was employed to reveal the
significant inhomogeneities arising from double-diffusion convection. The Fizeau
interferometer allowed us to investigate the weaker inhomogeneities associated
with soluto-capillary Marangoni convection. The results obtained from our
experiments demonstrated the remarkable capabilities of interferometry, even in
the context of microreactors with limited spatial dimensions. Despite the
challenges posed by confined spaces, the resolution of our experimental
apparatus was enough to provide high-quality visualization of the intricate
liquid mixing dynamics. The analysis of the interferograms obtained using the
Fizeau interferometer yielded qualitative insights and quantitative information
about the refractive index distribution within the system. Using the calculated
refractive index fields, we derived dependencies that accurately described the
variation in the initial concentration difference along the channel. This
quantitative assessment enabled us to evaluate the efficiency of the mixing
process under different initial system configurations, with varying sizes of
the free surface (a gas bubble). This study effectively demonstrates the
prowess of interferometry as a powerful tool for both visualizing and analyzing
convective flows within microchannels. Our findings have significant
implications for the optimization of microreactors and other microdevices,
particularly in the context of achieving efficient liquid mixing.
The work was financially supported by the Russian Science
Foundation (grant 19-11-00133).
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DOI:
10.1080/09500349514551621
