Volume-of-Fluid Simulations of Gas-Liquid-Liquid Flows in Microchannels

Microreactors are miniaturized and continuous devices, often comprised of several
channels (of different size and shape) with characteristic dimensions of the
order of 10 - 1000 μm. Microreactors
offer several advantages and the key advantage is that they offer a large
interfacial area (per unit volume) in comparison to conventional reactors.
 Micro−reactors have been used to
intensify processes involving gas−liquid and liquid−liquid reactions.
However, applications of microreactors for catalytic reactions
involving gas−liquid−liquid (G/L/L) flows still remain unexplored.
An extensive literature survey showed that several experimental and numerical
studies were performed to understand two−phase gas−liquid and liquid−liquid
flows in microchannels (e.g. Shao et al., 2010; Raj et al., 2010). However, only a very few experimental studies were reported on
characterization of hydrodynamics of gas−liquid−liquid flows in microchannels (e.g.
Khan and Duraiswamy, 2009; Wang et al., 2010 and Yue
et al., 2014).

For development of microreactors to intensify
processes involving three−phase G/L/L reactions, it is important to understand the
hydrodynamics of G/L/L flows in microchannels. In
particular, it is important to understand three−phase flow regimes and
formation of bubbles/drops or slugs of gas and liquid into another liquid.
Moreover, it is important to understand how to manipulate distributor
configurations and flow rates to produce desired flow patterns and to control
bubble/drop or slug sizes. While there exists significant literature on
numerical simulations of gas−liquid and liquid−liquid flows using
various numerical methods e.g. the Volume−of−Fluid (VOF) or the
Level Set or the Lattice−Boltzmann method; to the best of author?s
knowledge, numerical simulations of three−phase flows using interface
tracking/capturing methods have not been attempted so far. The objective of the
present contribution is to perform the VOF simulations of gas (air) and liquid
(water) in another liquid (kerosene) immiscible
with the first liquid flowing continuously
in a microchannel for different flow regimes and understand the formation dynamics of bubbles/drops or slugs
under different flow conditions and to verify the predictions using experiments.

Experiments
were performed using a single T−junction microchannel
with a rectangular cross−section (H = 950 μm;
W = 1000 μm, L_inlet
= 30 mm, L_channel =210 mm) machined on a
PMMA sheet (Figure 1a). The machined plate was glued with another PMMA sheet with a thin glue sheet. Air and water were
pumped from the side inlets and kerosene was pumped through the main channel
(Figure 1(a)), to generate bubbles/drops or slugs of air and water in kerosene
(continuous phase). The Sodium Dodecyl Sulfate (SDS) was used as the surfactant in the present
work with the concentrations of 0.3 and 2 wt/wt%.  The surface/interfacial tensions of air−water (air−water+SDS
(0.3 wt/wt %) = 0.035; air−water+SDS (2 wt/wt %) = 0.031) and oil-water (oil−
water+SDS (0.3 wt/wt %) = 0.005; oil−water+SDS
(2 wt/wt %) = 0.003) were measured using Tensiometer
(Kruss GmbH, Germany). A high − speed
digital camera was used (at 2000 fps) to visualize the formation dynamics of
bubble / drop / slug and the G/L/L/ flow regimes. These observed flow regimes
and formation mechanisms of bubble / drop or slugs and their lengths were
further used to verify the numerical predictions.

Numerical simulations were performed using the VOF method implemented in commercial CFD solver Fluent
14 (Ansys Inc, USA) to
simulate the formation dynamics of bubbles/drops in different flow regimes for
0.3 and 2 wt/wt% SDS
mixture. The channel geometry and dimensions (see Figure 1 (b)) used in the simulations were the same as that
considered in the experiments (1000 µm x 950 µm). Simulations were performed
with air as the gas phase (ρ_air =
1.78 kg/m³, μ_air= 1.37 x
10⁻⁵Pa.s) and water+SDS
as dispersed liquid phase (ρ_water =
998.2 kg/m³, μ_water= 0.001
Pa.s) and kerosene as the continuous liquid phase (ρ_kerosene = 780 kg/m³, μ_kerosene= 0.00115 Pa.s).
The volumetric flow rates of phases were used in the
simulations ranges of Q_oil = 3?15 ml/min; Q_air= 5.24 ? 11.18 ml/min; Q_water =
0.85?5.61 ml/min. The predictions were verified using the experiments. In this
abstract few key results are reported. The volumetric flow rates of phases were
used in the simulations ranges of Q_oil = 3?15 ml/min; Q_air= 5.24 ? 11.18 ml/min; Q_water = 0.85?5.61 ml/min. The predictions were verified
using the experiments. In this abstract few key results are reported. A
time step of 5x10⁻⁶ s was used for the numerical simulations.
 Further details of the computational model and numerics
will be provided in the full length manuscript.

Figure. 2a shows the predicted formation dynamics of
air slug (by iso surface of volume fraction) at 1^stT−junction for Q_oil=
5 ml/min for 0.3 wt/wt % of
water+SDS mixture. As shown in Figure. 2a the magnitude of shear
force exerted on the air−oil interface
at 1^stT−junction was less
compared to the surface tension force which opposes the slug movement and as a
result slugs were grown and occupy the main channel cross-section and that led
to obstruct the continuous phase flow. Then the pressure was build up in the downstream
of air−oil interface at the 1^stT−junction. The increase in pressure drop across the slug led
to its squeezing and the slug was finally detached at the 1^stT−junction as shown at t = 21 ms in
Figure. 2a. This
regime was referred as the squeezing regime. In addition, simulations of bubble
formation in dripping formation regime were performed (results not shown here).

The pressure in the dispersed and continuous phase was
identified as essential element to understand the formation dynamics of bubbles/drops
or slugs. In the present work, simulated point pressure at both 1^stT−junction (see Figure.
3(a)) and 2^nd
T−junction (see Figure. 3(b)) was considered to
analyse the formation dynamics of bubbles/drops or slugs. The time history of
pressures was recorded at each time step at the aforementioned points in the
solution domain for Q_oil = 5 and 15 ml/min as shown in Figure. 3.  The detailed
pressure analysis (see Figure. 3 (b)) during the squeezing and dripping regime will be reported
in the full length manuscript.

Figure. 4(a) shows the predicted formation dynamics of
a water slug at the 2^nd T−junction for 0.3 wt/wt
% of water+SDS mixture. Figure. 4(b) shows the time
evolution of pressure at point P2. Air slug formed at the 1^st
T−junction led the detachment of water+SDS−oil
interface at the 2^ndT−junction as shown in Figure. 4(a). At t =0 ms, rear end of air slug
was attached to the water-oil interface and water slug started entering into
the main channel. It should be noted that addition of 0.3 wt/wt % SDS led to reduction in the interfacial tension force
between water+SDS and oil (0.005 N/m) compared to
that between the pure water and oil (0.046 N/m). As time progressed, the
deformed water+SDS-oil interface was dragged into the
main channel as shown at t = 4 - 8 ms. Then the water+SDS-oil interface at the 2^nd T−junction was squeezed by the incoming air slug as shown at
t = 14 and 16 ms and the corresponding interface was
detached at t = 18 ms as shown in Figure 4(a). The corresponding
experimental image is shown as the first image in Figure. 5(c) and the predicted
detachment mechanism and water slug shape agreed very well with the experiments.

A comparison of the experimental and predicted flow
regimes for SDS concentrations in aqueous phase of 0.3 wt/wt% is shown in Figure. 5. In the images shown in Figure. 5 (a) ? 5(d), the first two images correspond to the experiments, in
which the first image was captured at the 2^nd T−junction, and second
image was captured at a distance of 4.6 cm downstream the 2^nd T−junction. The corresponding predicted flow regime is shown
in the third image of Figure. 5(a) ? 5(d). In experiments and numerical investigations, air
bubbles/slugs were formed at the 1^st T−junction (not visible in the figures) and in all situations
these bubbles/slugs lead to the detachment of water drops/slugs at the 2^nd
T−junction as shown in the first images
of Figure. 5(a) ? 5(d). The predicted three−phase
flow regimes (third image) showed an excellent agreement with an experimental
flow regimes (1^st image) viz. the Bubble−Drop (B−D) (Figure. 5(a)) and Slug−Slug (S−S) (Figure.5 (b) ? 5(d)) flow regimes. The corresponding 3D images (of predicted
flow regimes) are shown in Figure. 6.

While the predicted flow regimes and detachment mechanisms agreed well
with those observed in experiments, a quantitative verification was performed
by comparing the predicted and measured lengths of bubbles/drops or slugs with the effects of Q_oil (figure not shown here),
Q_air (see Figure. 7) and Q_water
(see Figure. 8).
The predictions showed quantitative agreement with experiments as shown in
Figure. 7 and Figure. 8. The detailed analysis
(with the help of dimensionless numbers such as Ca_oil,
We_air and We_water)
of results obtained from the present work will be reported in the full length
manuscript. The understanding of formation mechansims
and flow regimes, experimentally validated computational model is expected to
help in devising distributors and optimizing flow conditions to control
bubble/drops/slug sizes and flow patterns in microchannels.
   

References