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Liquid-liquid two-phase flow patterns in ultra-shallow straight and serpentine microchannels

  • Zan Wu
  • Bengt Sundén
Open Access
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Abstract

Water-butanol and water-hexane flows were visualized in ultra-shallow straight and serpentine microchannels with a cross-junction. At the inlet cross-junction, three major flow patterns including tubing/threading, dripping and jetting were mapped using the aqueous Capillary number versus the organic Weber number. Correspondingly, in the main microchannel, annular flow, slug flow and droplet flow were mapped using combined dimensionless numbers (Weber number times Ohnesorge number) of both phases. The flow pattern transitions were explained based on a force analysis, considering the phase flow rates, junction angle between the side feeding channels and the central feeding channel as well as aspect ratios. Compared to the straight microchannel, the dripping regime at the inlet junction and the slug flow occupy larger zones in serpentine microchannels because the centrifugal force tends to break up the organic annular core into slugs and droplets over the bends.

Nomenclature

Bo

Bond number, (ρa-ρo)gdh2/γ

Ca

Capillary number, μu/γ

Ce

A dimensionless number representing the ratio of centrifugal to interfacial forces, ρu2dh2/(γR)

d

Channel diameter, μm

dh

Hydraulic diameter, μm

g

Gravitational acceleration, m/s2

h

Channel depth, μm

j

Superficial velocity, m/s

L

Channel length, m

Oh

Ohnesorge number, μ/(dhργ)0.5

Q

Volumetric flow rate, ml/h

q

Flow rate ratio of organic to aqueous phases

R

Bending curvature radius of the channel centerline, m

Re

Reynolds number, ρjdh/μ

u

Average velocity (the overall volumetric flow rate of the two phases divided by the cross-sectional area), m/s

w

Channel width, μm

We

Weber number, ρj2dh/γ

Greek symbols

γ

Interfacial tension, N/m

μ

Dynamic viscosity, Pa∙s

ρ

Density, kg/m3

Subscript

ave

Average

a

Aqueous phase

c

Continuous phase

d

Dispersed phase

o

Organic phase

1 Introduction

Concerning process intensification and scale miniaturization, micro-structured devices (e.g., microscale heat exchangers, microreactors, micromixers) are widely used because they possess merits such as high heat and mass transport rates, enhanced mixing, fast reaction, energy and raw material savings, and easiness of numbering up [1]. Two-phase micro-structured systems are significant in extraction, emulsification, polymerization, nitration, nanoparticle synthesis, phase-transfer catalysis, pharmaceutical and biochemistry etc. Two-phase flow patterns at microscale are not much covered, e.g., refs. [2, 3, 4, 5, 6] for gas-liquid flow, and refs. [7, 8, 9, 10, 11, 12] for liquid-liquid flow. Inlet microchannels intersect at junctions which define local flow fields causing interface deformation. A cross-junction, as a hydrodynamic focusing geometry, consists of three microchannels that intersect at a certain angle, with one phase from two side inlets and with the other from the central inlet [11, 13]. The cross-junction creates approximately an extensional flow, a common feature of flow-focusing geometries [14]. Various flow patterns occur when two phases meet at the junction. For example, Cubaud and Mason [15] observed tubing, threading, displacement, dripping and jetting flow regimes for various immiscible fluid pairs in a cross-junction of straight microchannels with square cross sections, covering more than an order of magnitude of difference in viscosity ratios and interfacial tensions. Squeezing, dripping and jetting were realized by De Menech et al. [16] to form droplets for microfluidic T-junctions. Fu et al. [17] identified viscous displacement, tubing, dripping and jetting in a microfluidic cross-junction for silicone oil-water flow. Recently, Wu et al. [11] mapped flow patterns at cross-junctions and studied slug hydrodynamics for five liquid-liquid systems flowing in three square glass microchannels of channel depths from 200 μm to 600 μm.

Besides the flow regimes at the inlet junction, flow regimes downstream in the main microchannel are of equal importance for transport processes and reactions. For flow patterns captured at downstream locations “far” from the inlet, a different flow-pattern terminology was used, e.g., annular, slug and droplet. The same flow pattern captured at the inlet junction may evolve along the downstream microchannel into different flow patterns [5, 11]. For example, as stated in Wu et al. [11], the tubing/threading pattern at the cross-junction either evolves into an annular flow or a slug flow at downstream locations in the main microchannel; the dripping regime at the cross-junction either develops into a slug flow or a droplet flow at downstream axial locations. Slug hydrodynamics (e.g., slug size and velocity) and their dependence on Ca and q have been analyzed [14, 17, 18, 19].

Few works are devoted to serpentine or meandering microchannels even if such an arrangement is preferable as a mixer or a reactor for a long flow path on a small chip and for secondary flows to enhance mixing [20, 21, 22, 23, 24, 25, 26]. Bends and curved channels affect single-phase and two-phase flows differently [24]. For one-phase flow through a bend, there are two counter-rotating Dean vortices within the microchannel cross section [27]. For two-phase flow, the centrifugal force generates two different sized vortices providing a three-dimensional (3D) asymmetrical recirculation in serpentine and meandering microchannels [28]. The asymmetrical motion intensifies as the centrifugal force increases by reducing the bend curvature radius or by increasing the flow rates. Table 1 provides a brief summary of relevant works on two-phase flows in serpentine/meandering micro−/mini-channels. Among them, most of the reported works considered gas-liquid flows; works focused on liquid-liquid flows are very limited. Besides, the works focused on channels of aspect ratios <2.7. In this work, the aspect ratio equals the channel width over its depth.
Table 1

Relevant works on two-phase flow in serpentine or meandering micro/minichannels

Authors

Inlet junction

Channel geometry (mm)

Phase system

Superficial velocities (m/s)

Observed flow patterns

Remarks

Gunther et al. [20]

T-junction

PDMS; rectangular;

w = 0.40, h = 0.15, R = 0.60, L = 1063

Ethyl alcohol solutions, air

jc: 0.005–0.02,

jd: 0.005–0.2

slug flow

3D recirculation in liquid slugs enhancing mixing

Kirpalani et al. [21]

T-junction

-; circular;

d = 0.96, R = 3.9, L = 200

water, air

jc: 0.1–7.0

jd: 0.03–14.0

annular, slug and bubbly flows

Flow pattern transitions occurred due to bends

Fries and von Rohr [22]

T-junction

PDMS; rectangular;

w = 0.2 and 0.4, h = 0.15, R = 1.0 and 2.0, L = 40–230

Ethanol, nitrogen

jc: 0.01–0.07, jd: 0.08

slug flow

Small bend radii enhance mass transfer efficiently over the channel center line

Dessimoz et al. [23]

T-junction,

Y-junction

glass; circular; d = 1.0, R unspecified, L = 250

water, CO2

jc: 0.01–0.2,

jd: 0.004–10.0

annular and slug flows

Interfacial tension and inertia mainly determine the flow patterns

Roudet et al. [24]

T-junction

PMMA; circular;

d = 0.75, R = 1.5, L = 340

water, air

jc: 0.069–0.208,

jd: 0.015–0.675

slug-annular flow, slug flow

Dominant inertia effects on bubble shape; a larger slug-annular regime

Sarkar et al. [25]

cross-junction

glass; ~rectangular;

w = 0.4, h = 0.25, R ~ 0.7, L ~ 1000

water-succinic acid-n-butanol

jc: 0.008–0.30,

jd: 0.008–0.30

annular, slug, droplet flows

Continuous phase and organic phase alternate depending on inlet junction and flowing conditions

Li et al. [26]

T-junction

PDMS and glass; rectangular;

w = 0.1, h = 0.06, R = 0.65, L = 50

Silicon oil, viscoelastic aqueous solution

jc: 0.00006–0.0025,

jd: 0.00004–0.0015

slug flow, tailed slug flow, droplet flow

Slug dynamics of viscoelastic liquid in oil

As flow structures are closely coupled with heat and mass transport processes [2, 11], this study intends to experimentally investigate liquid-liquid flow patterns both at/near the cross-junction and at downstream locations “far” from the cross-junction in the main microchannel of quasi-trapezoidal straight and serpentine microchannels with an aspect ratio of 5.3 by employing water-butanol and water-hexane systems.

2 Experimental setup and procedure

As seen in Fig. 1, organic solvents and water were delivered to microchannels and controlled by two syringe pumps (New Era). Test sections (straight and serpentine microchannels) were placed horizontally. A stereo microscope (Motic) and a camera (Olympus) were used to capture the flow patterns inside the microchannels. Two quasi-trapezoidal microchannels, one straight and one serpentine, fabricated by isotropic wet etching in glass with a glass lid bonded on the top, were used as test sections with excellent chemical resistance. The straight and serpentine microchannel layouts are shown in Fig. 2. The inlet and outlet junctions of the two microchannels are cross-junctions, with an angle of 45° between the side channel and the central channel. The length of the straight main microchannel is 50 mm. For the serpentine microchannel, as shown in Fig. 2b, there is a straight section of 2.8 mm between the inlet junction and the first 90° bend, and a straight section of 4.2 mm between the last 90° bend and the outlet junction. The two 90° bends have a curvature radius of the channel centerline (R1) of 3.5 mm, while the eight 180° bends between the two 90° bends have a curvature radius of the channel centerline (R2) of 2.25 mm. Between two adjacent 180° bends, there is a straight section of a length of 13.35 mm connecting them. As shown in Fig. 2c, the straight and serpentine microchannels have the same quasi-trapezoidal cross sectional dimensions, with a long base size, a short base size and a height of 1140 ± 20 μm, 990 ± 20 μm, and 200 ± 20 μm, respectively.
Fig. 1

Drawing of the test rig

Fig. 2

Description of the configuration and the cross-section geometry of a the straight microchannel and b the serpentine microchannel

Two liquid-liquid systems were employed. Fluid properties are given in Table 2. The organic solvents are 1-butanol (Acros Organics, ≥ 99.5%) and n-hexane (Acros Organics, ≥ 99.36%), flowing into the cross-junction through the central microchannel. The aqueous phase is de-ionized water, which is fed from the two side microchannels. The soluble nature of 1-butanol in water is expected to present a negligible effect on flow patterns considering the short contact time between the two liquids, especially at the inlet junction. Minute amount of phenol red was added into water for a better clarity between the two phases. The flow patterns and evolutions were visualized at seven visualization windows (VWs), i.e., for the straight microchannel VW1 (@ cross-junction) and VW2 in the microchannel of 30 mm downstream from the junction; for the serpentine microchannel, VW3 at the inlet junction, VW4 and VW6 in the central zone of straight sections between two 180° bends, and VW5 and VW7 at 180° bends, as indicated in Fig. 2b. Experimental works were performed at 20.0 ± 0.5 °C.
Table 2

Fluid properties at 20.0 ± 0.5 °C

 

Organic phase

Density, ρ(kg/m3)

Viscosity, μ (Pa∙s)

Interfacial tension, γ (N/m)

Water

 

998.2

0.001

 

Butanol

810.0

0.00294

water-butanol: 0.0018

 

Hexane

654.8

0.0003

water-hexane: 0.051

Firstly, water was supplied to saturate the microchannel for 10 min. Secondly, Qo was maintained constant while increasing Qa. The uncertainties for the volumetric flow rates Qo and Qa were ± 0.5% according to the specified accuracy of the syringe pumps. Snapshots were captured at steady-state conditions. The test ranges of some dimensionless numbers are provided in Table 3. The microchannels were cleaned and dried properly when completing each set of measurements.
Table 3

Operating dimensionless numbers for straight and serpentine microchannels

Liquid-liquid system

q

Rea, ρajadh/μa

Reo, ρojodh/μo

Caa, μaja/γ

Cao, μojo/γ

Wea, ρaja2dh/γ

Weo, ρojo2dh/γ

Ceo, ρou2dh2/(γR)

Straight microchannel

water-butanol

1.0E-2~12

0.22~130

0.06~1.44

3.6–4~0.22

1.1E-3~2.6E-2

7.9E-5~28.3

6.4E-5~3.7E-2

water-hexane

6E-3~12

0.22~1.30

0.48~11.4

1.3E-5~7.7E-3

3.8E-6~9.2E-5

2.8E-6~1.0

1.8E-6~1.0E-3

Serpentine microchannel

water-butanol

1.0E-2~96

0.22~130

0.06~5.76

3.0E-5~6.0E-2

5.6E-4~5.6E-2

7.9E-5~28.4

6.4E-5~0.59

8.5E-5~4.6

water-hexane

1.0E-2~24

0.3~157

0.7~68

1.9E-5~9.2E-3

5.8E-6~5.5E-4

6.2E-6~1.44

4.1E-6~3.8E-2

2.4E-6~0.15

3 Results and discussion

3.1 Flow patterns at the inlet cross-junction

Tubing/threading, dripping and jetting were identified at inlet junctions VW1 and VW3, as seen in Fig. 3. For a detailed description of their flow characteristics, see Wu et al. [11].
Fig. 3

Flow pattern photos at cross-junctions, for the straight microchannel at VW1 a tubing, Qo = 15.0 ml/h for hexane and Qa = 4.0 ml/h, b dripping, Qo = 3.0 ml/h for hexane and Qa = 45.0 ml/h, and c jetting, Qo = 1.0 ml/h for butanol and Qa = 60.0 ml/h; and for the serpentine microchannel at VW3 d tubing, Qo = 3.0 ml/h for butanol and Qa = 6.0 ml/h, e dripping, Qo = 3.0 ml/h for hexane and Qa = 20.0 ml/h, and f jetting, Qo = 3.0 ml/h for butanol and Qa = 80.0 ml/h

Figure 3b and e show typical flow configurations of the dripping regime. The imposed flow of water from the two side microchannels at an angle of 45° exerts a force on the organic phase with one vertical force component and one horizontal force component. As Qa increases at a relatively low Qo, on one hand, the vertical force component due to imposed feeding flow of water increases and thus narrows and squeezes the organic phase when the front of the organic core thread partially obstructs the main microchannel. Therefore, a curved neck region is formed which connects the organic feeding flow and the organic core front. On the other hand, the horizontal force component tends to promote stretching of the organic core as the main microchannel is mostly obstructed by the front of the organic core. Besides, the organic core stretches further into the main microchannel due to the viscous shear force generated by the water film flow between the organic phase front and the microchannel walls. Therefore, the neck becomes thinner and the radii of curvature at the neck region decrease. Thus, the interfacial tension force increases and dominates to destabilize the interface at the neck region. Therefore, the neck breaks up into slugs or droplets and these detached organic components are convected downstream.

If Qo is comparably larger than Qa, tubing/threading regime prevails. As shown in Fig. 3a and d, there are a continuous organic core flow and an annulus aqueous film flow. As seen from Fig. 3a, small undulations fluctuate along the interface with time and space at a relatively high flow rate of hexane. However, no thread breakup occurs within the viewing zone of 5 mm × 5 mm. At high Qo, it is hard to form an organic neck region in the cross-junction, which is typical of the dripping regime, as the liquid inertia of the organic phase at a high flow rate dominates over the vertical force component generated by the imposed continuous flow of water from the side microchannels at a comparably low flow rate. In other words, the interfacial tension force diminishes in tubing/threading compared to dripping. Besides, as the organic core flows faster than the annulus water flow, there is a viscous shear force exerted on the organic core, trying to decelerate and hold back the organic core flow. The viscous shear force is approximately balanced by the horizontal force component because of feeding of the aqueous phase which tries to push the organic core downwards.

When Qa increases further at a relatively low Qo, jetting occurs (Fig. 3c and f). During jetting, the organic phase thread can penetrate into the main microchannel as a single jet, whose length is normally larger than the junction size and up to several times of the channel size before droplet pinch-off at the tip [14]. The jet diameter is typically much less than the channel size. In jetting, the vertical force component generated by the fast imposed aqueous flow quickly thins the organic core thread in the junction, while the horizontal force component quickly carries the thin organic core thread downwards out of the inlet junction. The viscous shear from the continuous water flow further elongates the inner organic core thread, and interfacial instabilities are also convected downstream. Thus it is not able to develop a curved neck region at/near the cross-junction similar to the one in dripping due to dominant aqueous inertia and its induced viscous shear over interfacial tension and organic inertia. Therefore, jetting prevails at a comparably high Qa and a relatively low Qo. Further downstream in the microchannel, the jet propagates thread undulations induced by Rayleigh-Plateau instabilities and overcomes the viscous shear or inertia to generate slugs or droplets.

Phase superficial velocities or dimensionless numbers are generally used to map flow patterns. The Caaa ja/γ) and Weo (ρo jo2 dh/γ) were adopted to map the observed flow patterns at cross-junctions, where ja and jo are superficial velocities of aqueous and organic phases, respectively. The dh is 335 μm, the same for the two microchannels, which was calculated as four times the cross-section area over the perimeter of the cross section. Figure 4 shows flow pattern maps at VW1 for the straight microchannel while Fig. 5 provides maps at VW3 for the serpentine microchannel.
Fig. 4

Flow pattern maps at the cross-junction VW1 based on Caa and Weo

Fig. 5

Flow pattern maps at the cross-junction VW3 based on Caa and Weo

For water-butanol flow in the straight microchannel as given in Fig. 4a, the flow regime is tubing or threading at low to medium Caa. At high Caa, the flow regime is jetting. There is a small dripping regime between the two flow regimes at low to medium Weo. At high Weo or at high Caa, the dripping regime can hardly survive when either the organic liquid inertia or the aqueous viscous shear dominates over the interfacial tension force. The transitional lines from Wu et al. [11] for the same liquid-liquid system in square channels with a dh of 400 μm were shown in Fig. 4a for comparison. There are two major differences. The tubing/threading regime is much larger while the dripping regime is much narrower compared to those in Wu et al. [11]. Similarly for water-hexane flow, dripping prevails over the entire experimental range in Wu et al. [11] with a similar range of phase flow rates, while in this work dripping becomes much narrower (Fig. 4b). Tubing/threading dominates at low to medium Caa and medium to high Weo. Jetting appears at high Caa. The smaller junction angle in the present work probably attributes to the expansion of tubing/threading and the narrowing of dripping. In Wu et al. [11], the three feeding microchannels intersect at right angles, i.e., with a junction angle of 90°, while in the present work the two side microchannels meet the central microchannel with the same junction angle of 45°. Considering the two works with similar cross-sectional areas and the same water flow rate, in Wu et al. [11] the vertical force component is much larger, accelerating the thinning of the organic core thread in the junction, while the horizontal force component is much less, providing longer time for the front of the organic core thread to fill up the main microchannel. Therefore, it is much easier to form a curved thin neck in Wu et al. [11] than in this study, which indicates that dripping covers a much larger zone in Wu et al. [11] while instead tubing/threading covers a much larger region in this work. Comparing water-butanol and water-hexane flows, the former has a much smaller dripping regime mainly because the former has a much less interfacial tension.

At VW3 of the serpentine microchannel, the three regimes mentioned above were observed, as shown in Fig. 5. The first 90° bend, 2.8 mm downstream from the cross-junction at VW3, redistributes the phases and gradually changes the flow direction by 90°, which might promote an asymmetric upstream flow to the channel centerline at the cross-section at low flow rates of the aqueous phase. By comparing Figs. 4b and 5b for water-hexane flow, the tube/threading regime becomes narrower while the dripping regime becomes larger especially at low Weo values. The centrifugal force changes the flow direction, produces chaotic advection and improves phase interaction to enhance break-up of the organic core thread at the 90° bend, thus causing transition from tubing/threading to dripping. As shown in Fig. 4a for the straight microchannel and in Fig. 5a for the serpentine microchannel, water-butanol flow is much less affected by the downstream bend compared to water-hexane flow. The interfacial tension of water-hexane flow is one order of magnitude larger than that of water-butanol flow. Accordingly, interfacial instability is much more intense and apparent for the former than the latter. The asymmetrical flow at the cross-junction and the directional change of the flow are supposed to augment interfacial disturbances and waves in water-hexane flow.

3.2 Flow patterns in the main microchannel

Flow patterns were observed at VW2 for the straight microchannel, and at VW4, VW5, VW6 and VW7 for the serpentine microchannel. Three main flow patterns, i.e., annular, slug and droplet flows were observed for the two channels. For example, Fig. 6 shows several typical flow patterns observed at VW5 of the serpentine microchannel. Flow patterns for the straight microchannel at VW2 and for the serpentine microchannel at VW6 were mapped by using the organic phase and aqueous phase superficial velocities, as shown in Figs. 7 and 8, respectively. In annular flow, the organic phase flows continuously in the core of the microchannel, surrounded by the annulus aqueous phase, e.g., Fig. 6a. As the water flow rate increases, the organic core thread becomes thinner. The thin annular core can be stable up to a high water flow rate, e.g., Fig. 6b. If the organic core thread breaks up into slugs in the junction or close to the inlet or even after a certain distance depending on flow conditions, slug flow was observed. Interfacial tension dominates slug flow. The slug shape depends on Caa and flow rate ratios. The slug length is normally larger than the hydraulic diameter of the microchannel, see., e.g., Fig. 6c. Periodic deformations of the slug end were noticed in the serpentine microchannel due to centrifugal forces, which was also observed in Roudet et al. [24] for a meandering microchannel. In Fig. 6d, at the same Qo of hexane, a larger Qa exerts a larger pressure and a larger viscous shear on the interface, accelerating the neck thinning and break-up to form slugs and droplets. Smaller droplets may coalesce to form larger droplets or slugs, which tend to attach channel walls. This phenomenon stems from the partial wetting behaviours of water and organic liquids on glass microchannel walls. Regular and ordered slug flow and droplet flow of uniform slug or droplet size may be achieved by adding surfactants to prevent the coalescence of droplets [29], which will be investigated in the near future. The slug-droplet flow shown in Fig. 6d was also categorized as slug flow in the present study. As Qa further increases, the slug size decreases and droplets are formed depending on the liquid-liquid systems. Figure 6e shows droplet flow for water-butanol in the serpentine microchannel. From visualization, the organic jet was observed to break up near the inlet junction and droplet flow was formed.
Fig. 6

Flow pattern photos at VW5 a annular flow, Qo = 3.0 ml/h for butanol and Qa = 6.0 ml/h, b annular flow, Qo = 3.0 ml/h for butanol and Qa = 40.0 ml/h, c slug flow, Qo = 3.0 ml/h for hexane and Qa = 6.0 ml/h, d slug flow, Qo = 3.0 ml/h for hexane and Qa = 40.0 ml/h, e droplet flow, Qo = 3.0 ml/h for butanol and Qa = 80.0 ml/h

Fig. 7

Flow pattern maps at VW2 based on jo and ja

Fig. 8

Flow pattern maps at VW6 based on jo and ja

For the straight microchannel, the annular flow at VW2 corresponds to most of the tubing/threading regime observed at VW1; the slug flow at VW2 occupies a large fraction of the dripping regime and a small fraction of the tubing/threading regime at VW1; and the droplet flow at VW2 covers the jetting regime and a small fraction of the dripping regime at VW1. Therefore, the reasoning regarding flow pattern transitions at the inlet junction presented above is still valid for flow pattern transitions downstream in the main microchannel.

Comparing Fig. 7 at VW2 and Fig. 8 at VW6, the slug flow regime at VW6 is larger than that at VW2. The change of the flow direction in the serpentine microchannel causes a centrifugal force, generating chaotic advection and enhancing phase interaction at and near the bends. Besides, there is a tendency to force the heavier fluid towards the outside and the lighter fluid towards the inner side of the bend, though this movement is not noticeable from flow pattern images for most cases as the density values of the organic and aqueous phases do not differ much. Such liquid movement tends to give rise to a slip between the phases and complicates the flow structure. As a result, depending on flow conditions, the organic annular core breaks up into slugs and long slugs break up into short slugs and droplets. Therefore, flow pattern may vary along the flow direction due to centrifugal forces in bend regions. For example, at Qo = 6 ml/h and Qa = 30 ml/h, annular flow occurred and the organic core is continuous over VW4, while slug flow was observed at VW6 after flowing through four 180° bends. Therefore, slug flow prevails over a larger regime while annular flow shrinks at VW6 in the serpentine microchannel.

Dimensionless numbers are also employed to map flow patterns in microchannels. To begin with, Fig. 9 presents the operating ranges of dimensionless numbers, i.e., We, Ca, Bo and Ce. The Ce number indicates a comparison between centrifugal forces and interfacial tension forces. The u was used in the Ce number instead of superficial velocities. Figure 9a and b gives comparisons of dimensionless numbers for the two phases flowing in the straight microchannel. The Weo and Cao numbers of water-butanol flow are at least two orders of magnitude larger than those of water-hexane flow, at a similar range of Reo from 0.1 to 10, suggesting that interfacial tension is significant for water-hexane flow even at a high Reo. For the aqueous phase, the relatively higher Wea values at high Rea indicate that the liquid inertia of the aqueous phase tends to present a considerable effect on the organic phase. As for the serpentine microchannel in Fig. 9c for the organic phase, the ranges of Weo and Cao are similar to those for the straight microchannel. For each Reo, Ce increases when the average flow velocity increases. It seems that effect of the centrifugal forces at and near the bends are important, especially at relatively high flow velocities. For the serpentine microchannel, the Wea and Caa ranges of the aqueous phase are similar to those in Fig. 9b and the Ce range is similar to that in Fig. 9c. Therefore, comparison of non-dimensional numbers for the aqueous phase is not given here.
Fig. 9

Ranges of several dimensionless numbers, showing the ratios of the buoyancy force to the interfacial tension (Bo), the inertia force to the interfacial tension (We), the viscous shear force to the interfacial tension (Ca), and the centrifugal force to the interfacial tension (Ce)

The dimensionless group WeOh, proposed by Yagodnitsyna et al. [29] for water-ionic liquid flow in microchannels, was used to present flow pattern observations. The Ohnesorge number (Oh) equals Ca over the square root of We. Figure 10 shows water-butanol and water-hexane flows at VW2 of the straight microchannel. Flow pattern transitional lines can be obtained from the flow pattern map for the two liquid-liquid systems. The red dashed line indicates the slug-droplet transition, while the black solid line indicates the annular-slug transition and also the annular-droplet transition at high WeaOha values. It can be seen from Fig. 10 that the newly developed transitional lines can estimate the flow pattern data of both water-butanol flow and water-hexane flow. The transitional lines were compared with the flow pattern transition points in Cao et al. [30] for water-butanol and water-oil flows in a square cross-junction channel with a junction angle of 90° and a channel width of 400 μm, as shown in Fig. 11. In general, the annular flow is much larger and the slug flow is much smaller at VW2 of the straight microchannel than those of the square microchannel in Cao et al. [30]. The difference at the inlet junction, i.e., the junction angle of the quasi-trapezoidal straight microchannel in the present work and the square microchannel in Cao et al. [30] is one of the main reasons attributing to this phenomenon, with a similar argument as for Fig. 4a.
Fig. 10

Flow pattern maps at VW2 based on a combined dimensionless number WeOh. The solid and dashed lines correspond to the new flow pattern transitional lines based on the experimental data

Fig. 11

Comparisons of the newly developed flow pattern transitional lines (the solid and dashed lines) for the straight microchannel at VW2 to those flow pattern transitional data points in Cao et al. [30] for water-butanol and water-oil flows in a square microchannel

Flow pattern maps employing dimensionless number groups WeoOho and WeaOha were shown in Fig. 12 for VW4-VW7 of the serpentine microchannel. The transitional lines for the straight microchannel at VW2 were shown for comparison in Fig. 12a for VW4, a straight section after a 90° bend and an 180° bend. The three flow patterns are located in zones similar to those in the straight microchannel. However, the slug flow regime becomes larger towards the annular flow regime and the droplet flow regime becomes slightly larger towards the slug flow regime at VW4 because the centrifugal force might break up the organic annular core into slugs and also break up the slugs into droplets over the bends. Based on the same reasoning, by comparing the flow pattern maps along the flow direction of the serpentine microchannel from VW4 to VW7, the slug flow regime expands further towards the annular flow regime after more 180° bends, while the droplet flow regime expands slightly.
Fig. 12

Flow pattern maps for the serpentine channel based on a combined dimensionless number WeOh along the flow direction at: a VW4, b VW5, c VW6, and d VW7. The solid and dashed lines in Fig. 12a correspond to the newly developed annular-slug and the slug-droplet transitional lines for the straight microchannel at VW2, respectively

Effect of the aspect ratio on flow patterns is emphasized as follows. It is supposed that with similar cross-sectional areas and hydraulic diameters, similar inlet junctions and the same phase flow rates, a rectangular microchannel might promote tubing/threading near the junction and annular flow in the downstream microchannel. Figure 13 shows conceptual cross-sectional film distributions for the quasi-trapezoidal microchannel with an aspect ratio of 5.3, considering that the short and long bases do not differ much. At a relatively high Capillary number of the aqueous phase, above a transitional value of 0.01, Fig. 13a shows that the cross-sectional profile of the organic core looks like an ellipse or an oval as the viscous shear overcomes the interfacial tension force. At a relatively low capillary number, i.e., less than 0.01, depending on the aqueous inertia force, the cross-sectional profile of the organic phase might look like either the one shown in Fig. 13b at a relatively low Qa or the one shown in Fig. 13c at a relatively high Qa. In Fig. 13b, the film thickness is still relatively thick in the plane of the longer semi-axis. When the inertia of the aqueous phase increases, the interface might become arc-shaped in the plane of the longer semi-axis, with an even larger gap for film flow of the aqueous phase [31]. Such a large aqueous leakage flow around the organic core thread in rectangular and quasi-trapezoidal microchannels of high aspect ratios is very favorable for the persistence of tubing/threading in the cross-junction and annular flow in the downstream channel. Firstly, at the inlet junction, the force exerted by continuously imposed water flow on organic core thread decreases because a part of or most of the aqueous phase leaks through from the corners and gaps as shown in Fig. 13b and c. Besides, the resulting less aqueous flow between the front of the organic core thread and the microchannel walls gives a smaller velocity gradient normal to the wall and therefore a less shear force on the organic core front, which means a slower neck thinning and thus no break-up of the organic core. From another perspective, for slug flow in the main microchannel, due to leakage flow, the amount of liquid in aqueous slugs between two organic slugs would reduce and therefore coalesce of organic slugs is more likely to occur to form annular flow.
Fig. 13

Conceptual cross-sectional film distributions for quasi-trapezoidal microchannels of high aspect ratios at a Ca (calculated as μau/γ for this case): a much larger than 0.01, b much less than 0.01 with a low or moderate Qa, and c less than 0.01 with a relatively high Qa

4 Conclusions

Water-butanol and water-hexane two-phase flows in ultra-shallow straight and serpentine microchannels with a cross-junction were visualized for wide ranges of superficial velocities. The two microchannels have the same quasi-trapezoidal profile and the same dh of 335 μm. The aspect ratio is as high as 5.3. At the inlet junction, three major flow patterns including tubing/threading, dripping and jetting were presented using Caa versus Weo. Correspondingly, in the main microchannel, three main flow patterns were categorized, i.e., annular, slug and droplet flows. A dimensionless number group, Weber number times Ohnesorge number, was adopted to map flow regimes in the downstream microchannel. The flow pattern map, i.e., WeaOha versus WeoOho, can roughly capture liquid-liquid flow patterns. Flow pattern transitional lines for water-butanol and water-hexane flows in the main microchannel were obtained.

The flow pattern transitions were explained based on a force analysis. For the studied cross-junction with a junction angle of 45°, the vertical force component of the inertia due to the imposed water flow narrows and squeezes the organic core thread while its horizontal force component and the viscous shear promote stretching of the organic core. These forces together with the interfacial tension force of the neck connecting the feeding flow and the front of the organic core thread, and the liquid inertia of the organic phase shape the curved neck region at the inlet junction and determine whether the organic core thread breaks up or not and the resulting flow regimes. Compared to a junction angle of 90°, a junction angle of 45° tends to provide a larger tubing/threading regime at the inlet junction and a wider annular flow regime. Besides, a large aspect ratio is also favorable for tubing/threading at the inlet junction and downstream annular flow because of a large aqueous leakage flow around the organic core through the corners and gaps.

Compared to the straight microchannel, the slug flow regime becomes larger towards the annular flow regime and the droplet flow regime becomes slightly larger towards the slug flow regime in serpentine microchannels because the centrifugal force tends to break up the organic annular core into slugs and also break up the slugs into droplets over the bends.

Notes

Acknowledgments

The authors appreciate financial support from the Swedish Research Council (VR).

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of Energy SciencesLund UniversityLundSweden

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