Generation of Air–Water Two-Phase Flow Patterns ... - ACS Publications

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Generation of Air−Water Two-Phase Flow Patterns by Altering the Helix Angle in Triple Helical Microchannels Sambasiva Rao Ganneboyina† and Animangsu Ghatak†,‡,* †

Department of Chemical Engineering, Indian Institute of Technology, Kanpur, 208016 India INM-Leibniz Institute for New Materials and Saarland University, Campus D 2 2, 66123 Saarbruecken, Germany

‡

S Supporting Information *

ABSTRACT: Flow of a liquid inside a helical tube is composed of axial and circumferential components, the latter arising because of its specific geometry. For a gas−liquid two-phase flow inside a helical tube, the coupled effect of these two flow components leads to a variety of flow patterns, for example, slug, bubble, and stratified flow. We present here a novel triple-helical microchannel, in which, the two-phase flow is found to engender several additional flow patterns not observed with the conventional geometries, for example, the parallel and oscillating annular flow and even simultaneous occurrence of several such patterns. We show that the transition between these patterns depends not only on the fluid rates of the two liquids but also on the helix angle. We have presented detailed phase diagrams to elaborate these effects. We have examined also the effect of channel geometry on the specific features of these flow patterns.

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INTRODUCTION Gas−liquid two-phase flow is central to variety of practical and industrial applications, for example, oil recovery, manufacturing of food and cosmetic products, heat pipe applications, firefighting devices and so on. Most of these processes involve several different flow regimes depending on the flow rates of the gas and liquid, which have significant bearing on both the quality, quantity, and finally the cost of the products. However, at the microscale, the confinement of the geometry and the tortuous flow path affect significantly the transition between different flow regimes. In this context, miniaturization of fluidic channels,1−3 specially three dimensionally oriented channels, can be of immense help because of a variety of reasons: the three-dimensional geometry nearly follows many actual situations, small dimension allows the flow to be laminar, the effect of gravity is eliminated, a significantly smaller volume of material has to be handled, and effect of interfacial/surface tension gets inherently integrated as the formation of bubbles and slugs depends also on the interfacial tension between different phases and that between the fluid and the rigid wall, in addition to the interfacial shear forces. While the effect of most of these parameters have been studied to some detail,4−13 the effect of geometry of the channel, importantly its threedimensional orientation on gas−liquid two-phase flow, has not been investigated to sufficient extent. The objective of this report is to investigate and explore a variety of gas−liquid twophase flow patterns that can be observed in a helical geometry. Flow through a planar curved tube was first analyzed by Dean14,15 where he showed that in such a tube, an incompressible fluid is subjected to centrifugal forces which result in a pressure gradient in the radial direction.16 As a consequence, the fluid element in the central plan is driven toward the outer wall and that at the inner wall is driven toward the central plane generating two sets of symmetric secondary flow cells in the transverse plane. A helical tube is however different from a planar curved tube, in that, it has two geometric © 2012 American Chemical Society

features: curvature and torsion, both of which affect the secondary flow. With increase in torsion of the tube geometry, the two cell structure turns asymmetric, one growing larger at the expense of the other; eventually for low Reynolds number flow, the two cells merge to generate a single recirculation cell.17,18 Nevertheless, with this single circulating cell too the secondary flow persists in the transverse plane; importantly, it remains stationary with respect to time, unlike eddies in turbulent flow.19−22 Here, we have extended these ideas in designing a novel multihelical microchannel system in which several helical flow paths are conjoined along their contour leading to a single multihelical flow geometry. We show that in such channels air and water can flow in several different flow regimes in addition to the stratified and annular flow commonly observed in macroscopic single-helical pipes. An example is the “parallel flow” of gas and water in which these two fluids flow along two or more different helical flow paths. Similarly, we observe also “partial parallel” flow in which an air stream flows in a helical path in parallel to slug flow or wavy flow in the rest of the helical paths. These flow patterns are all specific to the multihelical geometry presented here and we show that they can be tuned by controlling the helix angle in addition to the flow rates of air and water.

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EXPERIMENTAL SECTION Materials. The microchannels were fabricated in crosslinked blocks of poly(dimethylsiloxane) (PDMS) (Sylgard 184, Dow Corning product). Flexible nylon threads of diameter 50 μm were procured from local market and were used for generating the templates for fabrication of microchannels. Received: Revised: Accepted: Published: 9356

June 16, 2011 May 23, 2012 June 15, 2012 June 27, 2012 dx.doi.org/10.1021/ie201249g | Ind. Eng. Chem. Res. 2012, 51, 9356−9364

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Chloroform was used as solvent for swelling the cross-linked PDMS. Deaerated, deionized (DI) water, and air at ambient conditions (room temperature, ∼25 °C) were used as the two different fluids for carrying out the two-phase flow experiments. Dispovan syringes (volume ca. 20−50 mL), along with syringe pumps (Harvard apparatus, model PHD 2000 Infuse/Withdraw) were used for pumping the fluids. Flexible silicon tubing and micropipet tips were used for connecting the syringes to the inlet of the channel. Two-phase flow patterns inside the channels were visualized under microscope (Nikon corporation, model TE2K -U) at an optical magnification of 6× to 40× (× refers to 10 times). The flow patterns were captured at frame rate: 60−73000 fps and at an image resolution: 128 × 16 to 1024 × 1024 pixels using a high frame rate camera (Photron Fastcam, model 100K). Preparation of Microchannels. Triple-helical microchannels were generated inside cross-linked blocks of PDMS by using a template generated by twisting three strands of nylon monofilaments to a desired helix angle.23,24 The template consisting of a triple helical straight portion with three free strands at its ends was placed inside a pool of Sylgard 184 prepolymer liquid mixed with the cross-linker (10:1 weight ratio). The prepolymer liquid was cured at 80 °C for 30 min followed by swelling it inside a pool of a suitable solvent such as chloroform. The filaments were then withdrawn by gently pulling out of the swollen block which was then deswelled back by slow drying at controlled condition.23 The surface of the channels was found to be optically smooth without any imperfection. For all cases, the straight helical portion of the channel was maintained at 10 mm. The PDMS block was prepared enough thick, ∼10 mm, so that the channel crosssection does not deform because of internal pressure. Two of the three inlet flow paths were used for pumping the two fluids while the third inlet was kept blocked. A tiny hole was punctured on one of the two inlet paths to place a pressure transducer probe for measuring the inlet pressure of air. Channel Geometry. Optical micrographs in Figure 1b show the cross-section of a typical channel, the area of which is expressed as: As = (5π/8 + √3/4)d2 and the wetted perimeter as WS = 5πd /2; here d is the diameter of a constituent single helical path. Notice that for channels with different helix angle, although the relative orientation of the three constituent flow paths rotates differently along the axial length, the crosssectional area and hydraulic diameter of the channel remains identical. For example, for d = 50 μm, the hydraulic diameter: Dh = 4As /WS is calculated as 61 μm and the cross-sectional area as 5993 μm2, both remaining the same irrespective of the pitch of the helix or the helix angle. The helix angle θ is measured as the angle made by the tangent, drawn in the plane of helical path at the axis of the channel as shown in Figure 1c. The helix radius ρ is the radius of the helical flow path. The radius of curvature 9 and torsion τ of a single helix are defined in terms of helix angle θ and helix radius ρ as 1/9 = sin 2 θ /ρ and τ = sin θ cos θ/ρ,25 respectively. It has been shown earlier that for flow through a helical tube, the secondary circumferential flow occurs as perturbation to the primary Poiseuille flow with τ /9 = (sin 3 θ cos θ )/ρ2 as the perturbative parameter.18,26 The resultant perturbation expansion and its substitution in the Navier−Stokes equation yield a solution which shows that the effect of torsion is present only in the second order, whereas that of curvature is in first order. This result implies that for a spiral channel, that is, a plainer helix,

Figure 1. Schematic of air−water two-phase flow experiment in triple helical microchannels. (a) The experimental setup. (b and c) The cross-sectional and the side view of the channel geometry. (d) Optical micrograph of the side and top views of the inlet to the triple helical channels. The scale bar represents 100 μm.

with negligible torsion, the dimensionless quantity that characterizes the secondary flow is a modified Reynold’s number, called the Dean’s number: (d/ρ) 1/2 Re which incorporates the effect of curvature of the channel. Similarly, for channels with finite curvature and torsion, the Reynold’s number is modified to (d/ρ)1/2 (sin3 θ cos θ)1/4Re; thus, the effect of helix angle θ gets incorporated through the quantity, f(θ) = (sin3 θ cos θ)1/4. Notice that for these channels the helix angle takes into account also the effect of inlet angle to the channel. The optical micrographs in Figure 1d depict the magnified side and top views of the inlet at which the three separate flow paths join together to form the triple helical channel. Since these flow paths merge tangentially, the inlet angle for these channels remains same as the helix angle. Flow Experiment. In a typical experiment, the two fluids: air and deionized (DI) water, filled in syringes were pumped into the channel at a desired volume flow rates. The outlet of the channel was connected to a tube of internal diameter 2.2 mm in which both water and air formed slugs over the whole range of the flow rates. The volumetric flow rates for each stream were then estimated as the net volume of respective slugs flowing through this tube per unit time. The superficial velocities of water and air: Vw and Va were calculated by dividing this volume flow rate with the channel cross-section As.

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RESULTS AND DISCUSSION The optical micrographs in Figure 2 depict different two-phase flow patterns observed at different water and air flow rates and different helix angles. The domains of occurrence of these patterns are presented in phase diagrams with superficial velocities of water and air: Vw and Va as the two axes. Figure 3a shows an example of such a plot for helix angle, θ = 9°; similar others are obtained also for different other helix angles. These data show that for small velocities of water and air: Vw = 0.01− 0.1 m/sec and Va = 0.01−0.1 m/sec, the flow within channels with small θ remains similar to that in straight tubes, that is, 9357

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not understood; however, it suggests that the slugs of air possibly do not occupy the whole cross-section of the channel after all, possibly a thin film of water always remains present surrounding it. In a phase diagram for small helix angle of 9°, (Figure 3a) the region OABCDO depicts the slug flow regime, within which the lengths of the air and water slugs change with the superficial velocities: Va and Vw. Figure 3b shows a typical plot of slug length of air and water: La and Lw with Va for a constant Vw; with increase in Va, slug length of air, La, increases but that of water, Lw, decreases. The reverse happens for La and Lw for an increase in Vw, at constant Va. Figure 4a shows that the slug lengths vary also with helix angle, θ. Here at Va = 0.3 m/sec and Vw = 0.4 m/sec, La decreases from 0.22 mm to 0.2 and 0.11 mm, respectively, for θ = 9°, 19° and 32°; the micrographs shows that at θ = 32°, the slug almost turns to bubble flow. The combined effect of Vw, Va, and θ can be accounted by defining a quantity ξ = (Vw/Va)f(θ) against which we can plot the slug lengths. Figure 4c shows such a plot for slug length of water Lw with ξ, while Figure 5 shows similar plot for slug lengths of air, La. Notice that for a given (Vw/Va), Lw increases with f(θ) while La decreases, suggesting that the helical geometry tends to stabilize more the water slugs than air slugs, possibly because of the centrifugal effect, which is more prominent for water that has a larger density. A question arises of how do these slug lengths compare with that in a conventional straight microchannel with regular cross sections. We present in the inset of Figures 4c and 5 the slug length data for θ = 0° calculated from a correlation proposed by Qian, D. and Lawl, A.27 The slug length of water is calculated to be smaller than that in the helical channels which corroborates with our observation in Figure 4c that, with decrease in ξ, Lw decreases; it finally reaches 0.02 mm for θ → 0. This value is somewhat smaller than 0.1 mm as obtained from the inset of this figure in the limit Vw/Va → 0. This discrepancy could happen because, θ = 0 for our case would mean a channel with three parallel channels of circular cross section conjoined together, whereas, the inset of Figure 4c represents a straight channel with circular crosssection. For very large value of helix angle, for example for θ = 32°, the shearing effect of the secondary flow tends to break the water slugs, for which, slug lengths of both water and air

Figure 2. Optical micrographs of typical air−water two-phase flow patterns observed at different fluid velocities. The scale bar represents 100 μm.

essentially axial. However, at higher Vw and Va the effect of helix angles becomes more prominent leading to several flow patterns in addition to those observed in the conventional geometries like straight or single helical channels. These patterns remain steady with time and invariant along the length of channel. In what follows we will describe these patterns in detail. Slug Flow. Figure 2a shows the slug flow patterns characterized by plugs of air separated by plugs of water, with both apparently occupying the whole cross-section of the channel and both moving at equal velocities. Importantly, a frame rate of at least 10 000 fps had to be used in order to distinctly capture the air and water slugs. Interestingly, the interface of a water and air slug is not found to remain perfectly normal to the surface of the channel, nor does it form a contact angle greater 90°, as can be expected of a hydrophobic surface like PDMS. The three phase contact line forms a contact angle θc = 40o−60o for helix angles varying from θ = 9°−32°, suggesting that the surface behaves apparently hydrophilic in the dynamic condition. The reason for this apparent hydrophilic behavior for a known hydrophobic material like PDMS is

Figure 3. (a) Phase diagram prepared using superficial velocities of air and water as coordinates shows regimes of two-phase flow patterns in a triple helical microchannel of helix angle, θ = 9°. (b) The lengths of air (open symbols) and water plugs (filled symbols) obtained in θ = 9°, are plotted as a function of the air velocity with water velocity kept constant at Vw = 0.06 m/sec. The error bars represent the standard deviation of data obtained in several experiments. 9358

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Figure 5. The slug lengths of air in channels of different helix angle θ = 9°−32° are plotted as a function of the quantity ξ−1 = [(Vw/Va) × (sin3 θ cos θ)1/4]−1. The symbols ○, △, ◊ and □ represent channels with helix angle 9°, 19°, 24°, and 32°, respectively. The solid line in the inset represents the slug length of air in straight microchannels as calculated using correlations suggested by Qian, D. and Lawl, A.27

microscopy, in which a fluorescent dye was mixed with the water prior to pumping it into the channel. At ∼60 fps, the channel appeared bright all along its length, but such a low frame rate was not sufficient for distinguishing between the slugs; at higher frame rates, the intensity of light was not sufficient enough to be captured by the optical sensor of the camera. Therefore, the existence of this thin water film could not be conclusively established. Notice also that for almost all helix angles, the experimentally measured slug velocity was larger than the superficial velocity of water, Vw = 0.4 m/sec, as expected, except for θ = 32°, for which, Vs remains slightly smaller than Vw. This discrepancy possibly occurs because for such a large helix angle, the channel does not remain exactly straight axially. As a result, the area of cross-section possibly gets somewhat underestimated, leading to slight overestimation of Vw. Bubble Flow. Beyond slug flow, the flow pattern that appears is the bubble flow, for example, at water velocities beyond 1.0 m/sec. Here, the air bubbles do not span the whole cross section of the channel but remain immersed in a pool of water (optical micrographs in Figure 2b). The two sequences of images: A, B, C and D, E, F in Figure 6a further capture the effect of helix angle and water flow rate on the shape and size of the air bubbles. Notice that, in contrast to conventional flow geometries, here the bubbles do not assume any regular threedimensional shape, like that of sphere or cylinder, but their shape is rather dictated by the internal helical structure of the channel, which it occupies. A magnified image of a typical air bubble presented in Figure 6C reveals this nonregular shape. A similar image of a solid cylindrical gel prepared inside these channels is presented in Supporting Information, Figure S1 which too captures the nonregular shape of the particle, one advantage of which is that the surface area of these bubbles or particles exceeds significantly that of a cylinder or sphere of equivalent diameter. The bubble size, db, estimated by averaging their dimensions in horizontal and vertical directions, and the bubble velocity, Vb, are plotted in figure 6b, which shows that bubbles decrease in size with helix angle with a corresponding increase in the bubble velocity. An estimate of bubble diameter can be made by considering that energy spent per unit time by the drag force is used in

Figure 4. (a) Optical micrographs show the air slugs in channels with different helix angle for a constant Vw = 0.4 m/sec and Va = 0.3 m/sec. (b) The bar chart shows the air and water slug velocities Vs as a function of the helix angle. The open and filled bars represent the slug velocities calculated from the superficial velocity of water (Vs = Vw (1 + La/Ls)) and the actual slug velocities as measured from experiments. The dashed line represented the corresponding superficial water velocity. (c) The slug lengths of water in channels of different helix angle θ = 9°−32° are plotted as a function of the quantity ξ = (Vw/Va) × (sin3 θ cos θ)1/4. The symbols ●, ▲, ⧫, and ■ represent channels with helix angle 9°, 19°, 24°, and 32°, respectively. The inset represents the slug lengths as a function of the ratio of fluid velocities, in straight microchannels. These data are calculated using correlations suggested by Qian, D. and Lawl, A27.

decrease, and eventually we observe bubbles instead of the slug flow. Similar to slug lengths, the velocity of the water and air slugs Vs also vary with the helix angle as represented by the bar charts in Figure 4b. For example, for Va = 0.3 m/sec, Vw = 0.4 m/sec, and θ = 9°, the slug velocity is observed to be Vs = 0.7 m/sec, but it decreases to 0.4 m/sec in channel with θ = 32°. An estimate of the slug velocity can be made by considering that it should vary with the superficial velocity of water as: Vs = Vw(1 + La/Ls), in which all quantities in the right-hand side of the equation are experimentally measured. The bar chart in Figure 4b, however, presents a somewhat different picture. Here, the calculated values of Vs exceed significantly that measured from experiments. The difference is more prominent for smaller helix angles but diminishes with increase in helix angle. This discrepancy between experimental and estimated slug velocities could not be accounted for by any other mechanism other than that a thin film of water is indeed always present through which water flows at a velocity significantly higher than the slug velocity Vs. An attempt was made to ascertain the presence of this water film and to measure its thickness by fluorescence 9359

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Figure 6. (a) Optical micrographs show air bubbles in channels with helix angle 9° and 32° for increasing superficial velocity of water Vw = 1.1−2.6 m/sec and air velocity Va = 0.63 m/sec. The scale bar represents 100 μm. (b) The bubble diameter (open symbol) and the bubble velocity (filled symbol) are plotted as a function of the water velocity with air velocity kept constant at Va = 0.63 m/sec. The symbols ○ and □ represent channels with helix angle 9° and 32°, respectively. The solid lines are guide to eye. (c) Magnified image of air bubble captured in the θ = 24° channel. The scale bar represents 25 μm. (d) In a typical bubble flow regime, θ = 9°−32°. The size of the air bubble db for different helix angles θ = 9°−32° are plotted with respect to ζ. The symbols ○, □, and △ represent channels with helix angle 9°, 24°, and 32°, respectively. The solid line at the inset of the figure represents air bubble diameter as calculated in straight microchannels using a correlation proposed by Qian, D. and Lawl, A.27

Figure 7. Optical micrographs depict simultaneous occurrence of several different flow patterns. (a) The image represents a parallel-slug flow pattern in a channel with helix angle θ = 9° at Vw = 0.6 m/sec and Va = 0.14 m/sec. (b) The flow pattern changes to parallel-bubble flow as air velocity is increased to Va = 0.42 m/sec.

defined in terms of the superficial velocity of water and bubble diameter as cd = 24/Reb, where Reb = dbVwρw/μw. The net surface energy of the bubbles which are generated per unit of time can be written as γaw(πdb2)ṅ, where γaw is the air−water interfacial tension, ṅ = 6Q̇ a/(πdb2) is the number of air bubbles generated per unit time and Q̇ a is the volume flow rate of air through the channel. Balancing these two energies, one obtains a scaling law for the bubble diameters as

generating new surfaces of bubbles. The drag force of water on a bubble of diameter db can be written as (cd′ ρwVw2/2)Ad = (cd′ ρwVw2/2)(πdb2/4), where cd′ is the drag coefficient. Therefore the kinetic energy of water that gets converted to the surface energy of the bubbles per unit time can be written as ∼(cd′ ρwVw2/2)(πdb2/4)Vw. Notice that the drag coefficient should account for the helical geometry of the channel and also the velocity profile of liquid in the channel. However, in the absence of a clear knowledge of the velocity profile inside the channel, we will define the drag coefficient somewhat semiempirically as cd′ = cd f (θ) = cd(sin3 θ cos θ)1/4, where cd is the drag coefficient for a bubble in a straight tube and can be

⎛ γ ⎞1/2 ⎛ Q̇ ⎞1/2 1 db = 0.8⎜⎜ aw ⎟⎟ ⎜⎜ a ⎟⎟ ⎝ μw ⎠ ⎝ f (θ ) ⎠ Vw 9360

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The plot of db against ζ = (γaw/μw)1/2 (Q̇ a/f(θ))1/2 1/Vw as in Figure 6d shows that the data of bubble sizes from experiments for Va = 0.63 m/sec and θ = 9°−32° all fall on a straight line: db(mm) = 0.11ζ + 0.03. In the limit of very high water velocity and/or large helix angle, that is, at which ζ→0, the minimum bubble diameter that can achieved is 30 μm, which is almost equal to that of the overlapped inner circular area between the three single helices. This result signifies that the above relation for bubble diameter, albeit semiempirical, presents a simple yet effect way to rationalize the data. In the inset of figure 6d, we present also the bubble diameters in straight microchannels that is, for θ = 0° as a function of Va/Vw. This data is calculated from the same correlation used for obtaining the slug length of air as described in the previous section.27 Similar to air slugs, here too the bubble diameter remains significantly smaller in the helical channels as compared to that in the straight channels. In the phase diagram of Figure 3a, the bubble flow regime is depicted by the region IABH which shows that within the water velocity range Vw = 0.5−2.0 m/sec, this regime is very narrow so that with slight change in the velocities it changes either to the single phase water or slug flow. In addition to these known flow patterns, some additional patterns also appear; for example, the optical micrographs in Figure 7 show that bubbles of air flow along one helical path of the channel, while continuous flow of water occurs in the remaining two helical paths. This particular image is captured in a channel with a helices angle of θ = 9° at Vw = 0.6 m/sec and Va = 0.14 m/sec and at 27 00 fps. Importantly, these patterns show that, in these channels it is possible to restrict the flow of bubbles at a desired trajectory, unlike in conventional geometries. Similar to slug and bubble flow, these flow patterns also remain stable as observed in experiments carried over long period. Parallel Flow. In the slug flow regime, the length of the air slugs increases with the air velocity, and eventually, beyond a threshold limit, a radial rather than axial segregation of gas and liquid takes place, resulting in air and water occupying the channel cross-section only partially: air flows only along the helical path at which it enters the channel, while water flows through the two other helical paths. Figure 3b shows that the length of the air plug increases drastically as the air flow rate exceeds a threshold limit. At Vw = 0.06 m/sec, this limit is found to be Va = 0.14 m/sec at which “parallel flow” of air and water sets in as shown by Figure 2c. Notice that similar parallel flow is not observed with straight channels except where the density difference between two fluids results in “stratified flow”, nor is it observed in the conventional single helical channel. Thus this unique flow pattern occurs because a centrifugal effect for the multihelical channel gives stability to the individual fluid streams. However, the transition from slug to parallel flow does not occur abruptly. In fact, for most velocity ranges it goes through a “partial parallel flow regime” in which two different flow patterns simultaneously appear as shown in Figure 8. Here, the sequence of optical micrographs depicts the evolution of parallel flow regimes for an increase in air flow rate at a constant water flow rate of Vw = 0.14 m/sec. Initially at low air flow rate, Va = 0.14 m/sec, we see parallel flow with water flowing along two helical paths, whereas air is restricted to flow along one single helical path (Figure 8a). With increase in Va to 0.56 m/sec, the continuous flow of water in one of the helical paths breaks up into slugs, while along two other helical paths air and water continue to flow separately (Figure 8b). With further increase in Va to 1.4 m/sec, the water slug length

Figure 8. Sequence of optical micrographs depict different parallel flow patterns in a channel with a helix angle of 19°. Images A−D are obtained respectively for Va = 0.14, 0.56, 1.4, and 2.8 m/sec and Vw = 0.14 m/sec. Image A depicts parallel flow with water flowing along two helical paths and air in one helical path. Image B: Flow of water and air along two different helical path and slug flow in one helical path. Image C: The slug length of water decreases in the third helical path. Image D depicts flow of water along one inlet path while air flows in the remaining two helical paths.

decreases (Figure 8c). Thus both slug and parallel flow coexist within an intermediate range of air flow rate unlike any other known systems. Finally at Va = 2.8 m/sec, water flows along one flow path while air flows in the remaining two paths (Figure 8d). The phase diagram in Figure 3a shows that the parallel flow regime remains stable over a wide range of air and water velocities: Va = 0.55−11.7 mm/sec and Vw = 0.05−1.4 mm/sec. Experiments for a long period, ∼1/2 h, show that these flow regimes do not change over time but remain stable so long as air and water velocities remain unaltered. Annular Flow. A set of different flow patterns are observed as air velocity is increased beyond the phase boundary CBH in Figure 3a. Annular flow patterns with air slugs in the core, surrounded by water film appear beyond the slug and bubble flow regimes. For small helix angles, these air slugs are rather long but decrease in length for a larger helix angle of the channel. However, unlike other flow patterns, here the interface between the gas and the liquid does not remain stationary but oscillates with a frequency whose value depends upon the helix angle and the flow velocities. The sequence of video micrographs [a−f] in Figure 9a shows such annular flow patterns in a helical channel with θ = 32°, captured at a time resolution of 1/18000 s. The variation in height of the vertical bars in this figure depicts the oscillatory nature of the interface. At some locations, in this set of images the interface between the air and water does not appear sharp but blurry and diffused because of insufficient time resolution at which the video could be captured. The fractional thickness of the air with respect to the projected width of the channel, f = Wa/Wc is plotted as a function of time in Figure 9b. The data suggest the existence of two different time scales: a long time through which the thickness of the air stream remains unaltered and a relatively small time within which the thickness of the air decreases to a very small value and then increases again, both occurring catastrophically. A detailed analysis of this phenomenon has not yet been done. But preliminary experiments show that the characteristic times of such cycles increase with helix angle as τ ≈ f(θ) implying that helical geometry gives stability to the annular film of liquid. Thus, in contrast to all known examples of annular flow of a liquid surrounding a core of air,28,29 the flow pattern here essentially remains stable because of the effect of centrifugal flow field. Intuitively, any perturbation in thickness of the annular water film generates a region where the flow area for water increases, leading to a decrease in water 9361

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Figure 9. (a) A sequence of video micrographs depict the wavy nature of the interface between air and water in an annular flow regime. The images [a−f] are obtained for Vw = 1.4 m/sec and Va = 4.2 m/sec in θ = 32° channel and captured at 0, 37, 74, 111, 148, and 259 μs, respectively. The vertical bar, on each image represents the thickness of air stream on its two-dimensional projection. (b) Plot of fractional thickness of air stream with respect to the total thickness of the channel shows oscillations with particular frequency.

Figure 10. Phase diagrams depict the flow regimes of air and water in channels with helix angle (a) θ = 19°and (b) 32°.

Figure 11. The critical superficial velocities of water and air for crossover from one flow regime to other are plotted as a function of the quantity f(θ).

increases the curvature. Thus these two forces arrest the growth of perturbations and provide stability to the system. In addition, because of the channel geometry, the perturbations inherently become asymmetric which also are known to impede the growth of instability. As a result, we observe that the annular flow remains stable. At any location along its length, the diameter of the air core decreases but rarely breaks to form slugs. Effect of Helix Angle on Transition of Flow Patterns. In Figure 10, we present the phase diagrams for two different

velocity, as a result of which pressure at that point increases. But an increase in the flow area of water is accompanied by a decrease in that of air, due to which, the air flow rate increases with consequent decrease in air pressure at the same location. Thus the hydrodynamic pressure difference across the interface tends to drive the perturbations to grow. However an inward increase in thickness of the water ring results in an increase in centrifugal force on water because of the circumferential component of flow. Along with this, also the surface tension of water tends to impede the growth of perturbations because it 9362

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different flow patterns as a function of helix angles. One important advantage of these flow patterns is the nonregular shape of the slugs and bubbles constraint by the geometry of the channel, which not only provides a specific surface area larger than conventional regular shaped channels, but also internal circulation within bubbles and slugs. In addition, we have shown also that unlike in conventional geometries, here it is possible to restrict a particular flow pattern along a specific path within the channel. All these features open up the possibility of enhanced transport of heat and mass in a host of process applications.

helix angles θ = 19° and 32° to show that the flow patterns as discussed above are observed for different helix angles albeit at a different ranges of air and water velocity. To compare the transition between different flow regimes in channels with different helix angles θ, we consider the threshold values of the superficial velocities of air and water that separate these different flow patterns. For example, transition from parallel to annular flow can be considered to happen when the centrifugal force on water due to its circumferential flow exceeds a threshold value, that is, when the circumferential component of water velocity exceeds a critical limit, Δc. As a first approximation, this condition can be written as Vwc|par−an f(θ) > Δc, so that, Vwc|par−an ≈ ( f(θ))−1. The data in Figure 11a shows the critical superficial velocity of water, Vwc|par−an beyond which the parallel flow pattern transforms to wavy annular flow, indeed scales with f(θ) as Vwc|par−an (m/sec) = 0.5(f(θ))−1 − 0.4. Since withan increase in θ, f(θ) increases, the data in Figure 11a imply that with an increase in helix angle, the transition from parallel to annular flow occurs at a smaller superficial velocity of water. Similarly the minimum water velocity at which the slug flow transforms to bubble flow is represented by Vwc|sl−bub, an estimate of which can be deduced from eq 1 which captures the experimental observation that the bubble diameter increases with a decrease in the water velocity, eventually attaining the width of the channel at which the bubbles get converted to slugs. Equation 1 can be rewritten as Vwc|sl−bub = (γaw/μw)1/2 (Q̇ a/f(θ)1/2 1/Wc, in which Wc is the width of the channel. The above relation shows that when all other parameters remain unaltered, Vwc|sl−bub = f(θ)−1/2. The data in Figure 11(b) show that the critical velocity can indeed be fitted to Vwc|sl−bub = 1.1f(θ)−1/2 − 1.3. The slope and intercept of the fit equation suggests that at large enough helix angle, θ → 48°, we are expected to observe only bubble flow instead of any slug pattern. At large enough velocity of air, the air slugs increase in length eventually transforming to annular flow. Drawing similarity from eq 1, it is natural to see that annular flow should occur when Q̇ a/f(θ) exceeds a threshold limit. The plot in Figure 11c indeed shows that the threshold air velocity Vac|sl−an at which the slug flow transforms into annular flow is obtained as Vac|sl−an = 13.4f(θ) − 2.7; that is, Vac|sl−an decreases with f(θ). In other word, longer slugs of air eventually transforming into annular flow is expected with a decrease in f(θ) as observed in Figure 5. Summary. We have presented results from experiments with air−water two-phase flow inside a novel triple-helical microchannel, which produces several flow patterns such as slug flow, bubble flow, and annular flow. In addition, we have described also several other new flow patterns, such as parallel flow and mix of several of these flow regimes. Occurrence of these flow patterns and their specific characteristics depend not only on the superficial velocity of water and air, but also on the geometry of the channel, for example, its helix angle. We have shown that here the inlet angle to these channels remains identical to the helix angle. As a result, the flow patterns and their specific features no longer depend on the spatial orientation of the inlet to the channel in contrast to conventional channels. We have developed also from the first principle a scaling analysis for estimating the bubble diameter which captures the effect of helix angle and the fluid flow rates. We have shown that the scaling law corroborates well with the bubble diameter measured from experiments. We have extended these ideas in deducing the scaling relations for critical flow rates of air and water for transition between

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ASSOCIATED CONTENT

S Supporting Information *

Optical image of a cylindrical piece of gel prepared by cross linking a gel pre-polymer solution inside a triple helical channel. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS A.G. acknowledges the financial grant DST/CHE/20080165 from Department of Science and Technology, Government of India, Mr. and Mrs. Gian Singh Bindra Research Fellowship and the Humboldt foundation for a research fellowship for this work.

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REFERENCES

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