Flow properties of nanobubble mixtures passing through micro-orifices

International Journal of Heat and Fluid Flow 40 (2013) 106–115

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Flow properties of nanobubble mixtures passing through micro-orifices Akiomi Ushida a,⇑, Tomiichi Hasegawa b, Takatsune Narumi b, Toshiyuki Nakajima c a

Center for Fostering Innovative Leadership, Institute for Research Collaboration and Promotion, Niigata University, 8050-2 Ikarashi, Nishi-ku, Niigata-shi, Niigata 950-2181, Japan Faculty of Engineering, Niigata University, Niigata 950-2181, Japan c TECH Corporation Co. Ltd., Japan b

a r t i c l e

i n f o

Article history: Received 28 June 2012 Received in revised form 4 December 2012 Accepted 22 January 2013 Available online 17 February 2013 Keywords: Orifice flow Nanobubble Water Complex liquid Pressure drop

a b s t r a c t Mixtures containing microbubbles or nanobubbles (NBs), as well as their applications, are one of the most interesting research areas in fluid mechanics. In the present study, pressure drops were observed for several types of NB mixtures—NB/water, NB/surfactant, and NB/polymer—when passing through capillary tubes and micro-orifices. Pressure drops of a NB/water mixture agreed with those of water and numerical predictions for a 100-lm orifice, but were lower than both of these results for orifices of 50-lm diameter or less. Agreement was not found between the pressure drops of three NB/surfactant (anionic, nonionic, and cationic) mixtures and those of water or the respective surfactant only in all experimental cases. Moreover, the experimental pressure drops of an NB/polymer (polyethylene glycol) mixture were higher than those of the polymer only. Factors including slip wall, interfacial tension effect, an electric interface phenomenon, and elasticity were examined in experiments and are discussed in this paper. Ó 2013 Elsevier Inc. All rights reserved.

1. Introduction The drag reduction of complex liquids—for example, dilute surfactant and polymer solutions—has been studied previously by several researchers (Hershey and Zakin, 1967; Patterson et al., 1969; Liaw et al., 1971; Sureshkumar et al., 1997; Burger et al., 1982; Smith et al., 1994; Zakin et al., 1996; Sreenivasan and White, 2000). As a consequence, the drag reduction associated with a surfactant or polymer additive is well-known. In contrast, the drag reduction, washing, and purifying effects of microbubble and nanobubble (NB) mixtures have recently been examined. Merkle and Deutsch (1992), Xu et al. (2002), and Ferrante and Elghobashi (2005) have investigated the drag reduction effects of microbubble mixtures, and showed that the turbulent intensity is reduced in the turbulent boundary layer. Kodama et al. (2000) reported that the friction acting on ships’ hulls is decreased as a result of microbubbles. Zhang et al. (2011) and Ushida et al. (2012a) conducted studies on the washing effects of nanobubble mixtures. Measurements by Liu et al. (2012) showed that less coagulant is needed to treat wastewater from dying processes by using microbubbles. Choung et al. (1993), Li et al. (2003), and Miyamoto et al. (2007) explored the washing effects of microbubbles. Fujiwara et al. (2003) investigated water purification using microbubbles, and Matsumoto et al. (2005) subsequently reported their biological applications.

⇑ Corresponding author. Tel./fax: +81 25 262 6712. E-mail addresses: [email protected], [email protected] (A. Ushida). 0142-727X/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.ijheatfluidflow.2013.01.013

Takahira et al. (2005) examined the pressure field generated by microbubbles and some applications of this. Harting et al. (2010) observed NB behavior in lattice Boltzmann simulations. As can be seen from the above, microbubble/water and NB/water mixtures have been investigated in a number of previous studies. Biomedical Engineering, washing effect, purifying effects, and drag reduction effect is reported using microbubbles or NBs, and technological development has spread to various fields. However, the study of mixtures involving microbubbles or NBs and complex liquids has been limited; in particular, the examination of NB mixtures has been rare. In view of this situation, several types of NB mixtures (NB/water, NB/surfactant, and NB/polymer) were passed through capillaries and micro-orifices and their pressure drops experimentally measured. Shen et al. (2008), Dailey and Ghadiali (2010), and Ushida et al. (2012b) determined that the rheological properties of dilute polymer solutions change with the addition of microbubbles. Generally, as used complex liquids, it is important that the rheological properties. The effect of mixing NBs for rheological properties was verified. Their flow and rheological behavior was also examined. 2. Test liquids Water, three types of surfactant solutions, and a dilute aqueous solution of polyethylene glycol were tested in experiments, as well as each liquid’s corresponding NB mixture. Ion exchanged water (GSR-200, ADVANTEC Co. Ltd.) was prepared before experiments (simply referred to as water hereinafter). Three types of surfactant

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2.1. Nanobubble mixtures

2.2. Rheology 2.2.1. Viscosity Fig. 2a shows a schematic of the viscometer. Fig. 2b then plots the wall shear stress, sw (=DcDp/4Lc, where Dc and Lc are the inner

[ 106] 2.0

Peak diameter ; Dp = 70 nm Averaged diameter ; Dave. = 110 nm

Nb [ml-1]

1.0

0.5

0

0

100

(b)

102 Capillary Dc = 1.20 mm

101 water ( T = 18.3 °C ) NB water ( T = 18.4 °C ) LAS ( T = 18.6 °C ) NB/LAS ( T = 18.9 °C ) BC ( T = 24.1 °C ) NB/BC ( T = 18.0 °C ) AE ( T = 17.8 °C ) NB/AE ( T = 18.3 °C ) PEG ( T = 22.2 °C ) NB/PEG ( T = 22.5 °C )

100

A NB/water mixture (hereinafter NB water) was prepared by using a NB generator (HANDS-S-10, Daiko Engineering Co. Ltd.). Air was mixed into the water through high swirling flows. Fig. 1 plots the NB number density, Nb, against NB particle size, Db and shows that the peak diameter, Dp = 70 nm and the averaged diameter, Dave. = 110 nm as determined on a nanoparticle analyzer (NanoSight LM1-HS, Quantum Design Japan Co. Ltd.). The resulting mixture contained 1.0 vol% NBs. NB mixtures were prepared as follows: (1) the surfactant and PEG solutions outlined above section were first prepared at a concentration twice as high as that required for the final mixtures, and (2) these solutions were mixed into an equivalent volume (2.0 L) of NB water. The prepared mixtures are henceforth termed NB/LAS, NB/BC, NB/AE, and NB/PEG for simplicity.

1.5

(a)

τ w [Pa]

solutions were also prepared, where the critical micelle concentration (CMC) of each was taken from previous research (Karasawa et al., 2007; Amaki et al., 2008; Hasegawa et al., 2008; Ushida et al., 2010); laurylbenzenesulfonic acid sodium salt (Nacalai Tesque Co. Ltd.; molecular weight (MW) = 349, CMC = 150 ppm, concentration: 1.0 wt%) as an anionic surfactant, benzalkonium chloride (MP Biomedicals LLC; MW = 355, CMC = 400 ppm, concentration: 1.0 wt%) as a cationic surfactant, and polyoxyethylene (23) lauryl ether (Wako Pure Chemical Industries Ltd.; MW = 1214, CMC = 100 ppm, concentration: 1.0 wt%) as a nonionic surfactant. These surfactants are referred to as LAS, BC, and AE hereinafter, respectively. The CMC of each surfactant denotes the concentration above which spherical micelles are found to form (Mukerjee and Mysels, 1971; Robson and Dennis, 1977; Cates and Candau, 1990; Jafvert et al., 1994; Wilcoxon and Provencio, 1999). Here, the surfactant concentrations used in the experiments were greater than the CMCs such that spherical micelles were considered to be present in the aqueous solutions. As a polymer, a 1.0 wt% aqueous solution of polyethylene glycol (PEG) with MW = 2.0  104 was also prepared. Finally, the above liquids were mixed with NBs.

200

300

400

Db [nm] Fig. 1. NB number density, Nb, plotted against NB particle diameter, Db.

10-1 102

103

104

105

-1

SRw [s ] Fig. 2. (a) Schematic of capillary viscometer and (b) wall shear stress, sw, plotted against wall shear rate, SRw (=8Vc/Dc).

diameter and length of the capillary, respectively, and Dp is the measured pressure drop), against the wall shear rate, SRw (=8Vc/ Dc for mean velocity Vc passing through the capillary) when the tested liquids are under laminar capillary flow (Dc = 1.20 mm, SUS304). The viscosities of all liquids followed Newton’s Law, and were almost the same as that of water within the bounds of experimental error.

2.2.2. Elasticity Determining the elasticities of the liquids was important to understand their rheological properties. However, their viscoelasticities were too small to measure with a commercial rheometer. Therefore, the jet thrust of each liquid was instead examined because this is related to viscoelasticity (Oliver and MacSporran, 1969; Metzner and Metzner, 1970; Waters and King, 1971; Boger and Denn, 1980; Hasegawa et al., 2003; Ushida et al., 2012c). The experimental apparatus are shown in Fig. 3a. A jet of test liquid was ejected from a capillary (Dc = 0.40 mm, SUS304) into a cup immersed in a water-filled vessel. Since the cup opening was considerably greater than the cross-sectional area of the out-flowing jet, the momentum flux flowing out of the beaker was made negligible by cords connecting the beaker to an electric balance (GR-200; A&D Co. Ltd.). The jet force measured by this method is denoted Tm, and Tm values are plotted as a function of SRw in Fig. 3b, where the solid line represents the values predicted under a Poiseuille flow. All data except those corresponding to PEG and NB/PEG agree with the predictions, no differences can be seen among them. The lower values of PEG and NB/PEG are considered to be due to their elasticity. In contrast, the other liquids have the same jet thrust as that of water within the bounds of experimental error, and therefore do not possess measurable elasticity in this shear rate range.

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(a)

Fig. 4. Experimental apparatus for measuring pressure drops.

4. Numerical analysis

(b)

Fig. 5a shows the model of the present channel employed in the numerical analysis by using Navier–Stokes equations and continuity equation under the cylindrical coordinate system (r, h, z),

10-1

Capillary Dc = 0.40 mm

Tm [N]

10-2

10

Poiseuille Flow water ( T = 19.2 °C ) NB water ( T = 21.1 °C ) LAS ( T = 18.3 °C ) NB/LAS ( T = 19.9 °C ) BC ( T = 23.3 °C ) NB/BC ( T = 18.6 °C ) AE ( T = 22.1 °C ) NB/AE ( T = 19.5 °C ) PEG ( T = 20.4 °C ) NB/PEG ( T = 19.0 °C )

-3

10-4

10-5

103

104

105

106

107

( )      @uz @p 1 1 @ @ 2 uz  @uz  @uz  @uz ; þ þ u þ u ¼  þ r r z @t @r  @z @z Re r  @r  @r  @z @z " #     @ur @p 1 @ 1 @    @ 2 ur  @ur  @ur þ ur  þ uz  ¼   þ r ur þ   ; Re @r  r  @r  @t @r @z @r @z @z @uz 1 @     þ r ur ¼ 0: @z r  @r The azimuth, h, is ignored here, because the axisymmetric flow can be assumed to have zero tangential velocity. ur and uz are the velocity components in the r and z directions, respectively, and t is time. Index  denotes the dimensionless components, where

-1

SRw [s ] Fig. 3. (a) Schematic of measuring jet thrust and (b) measured jet thrust, Tm, plotted against wall shear rate, SRw.

(a)

3. Experiments 3.1. Micro-orifice

3.2. Experimental apparatus Fig. 4 shows the experimental apparatus for measuring pressure drops. This set up is similar to that used in previous studies (Hasegawa et al., 2007, 2009; Ushida et al., 2010, 2011, 2012d). Test liquid was injected using a syringe pump (JP-HP1, Furue Science Co. Ltd.) through a micro-orifice attached at the base of a circular acrylic channel of diameter 25 mm into a liquid stored in an acrylic vessel. The flow rate, Q, was constant throughout. The pressure drop, Dp, between the channel interior and the external water level was measured at a position 150 mm upstream of the orifice with a differential pressure transducer (SDP-11, Tsukasa Sokken Co. Ltd.).

(b)

102

101 2 2Δ p / ρV [-]

Nickel micro-orifices with diameters of between D = 20 and 100 lm and with a thickness of L = 20 lm were used in experiments, giving a thickness ratio L/D = 0.20–1.00. A previous study (Hasegawa et al., 2009, 2011) showed that the present orifices have relatively smooth surfaces and burrs on their edges. Furthermore, it could be seen in that study that the front surface of each orifice has a rounded corner leading into the aperture, whereas the corner on the back surface is at a right angle. However, no difference was found in the properties of the flows in either direction (Hasegawa et al., 2009). In the current experiments, the flow direction was from the front to back of the orifices.

100

10

-1

10-2 10-1

L / D = 0.20 The present result Kusmanto et al. 2004 Hasegawa et al. 2009

100

101

L / D = 1.00 The present result Kusmanto et al. 2004 Hasegawa et al. 2009

102

103

Re [-] Fig. 5. (a) Schematic of numerical region and (b) Numerical results for pressure drops when thickness ratio, L/D = 0.20 and 1.00.

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(a)

102

Orifice 100 µm L / D = 0.20

101 2 2Δ p /ρV [-]

ur = ur/V, uz = uz/V, r = r/D, z = z/D, p = p/qV2, and t⁄=tV/D. Here, V and D are the characteristic velocity and length, respectively. In the present study, D is the orifice diameter and V is the mean velocity of the liquid passing through the orifice. The diameter of the tube upstream and downstream of the orifice was 40D. The length upstream of the orifice was 40D in the z-direction and that downstream was 1000D. The finite volume method for a Newtonian fluid was adopted, in which the velocities and pressures were expressed on a staggered grid with a two-dimensional cylindrical coordinate system. Coupling of velocity and pressure was achieved by the SIMPLE method. The convective term and the viscous term were discretized by the first-order upwind difference and by the second-order central difference, respectively. The following boundary conditions were applied: (1) Poiseuille flow existed at the inlet boundary, (2) the velocity and pressure in the radial direction were zero, (3) the radial velocity component was zero on the center line, and (4) all velocities were zero at the channel and orifice wall. Fig. 5b plot the dimensionless form of 2Dp/qV2 against Re for the smallest and largest thickness ratios, respectively, together with those determined previously (Kusmanto et al., 2004; Hasegawa et al., 2009). The three sets of results are almost concurrent in both cases.

100 Prediction o water (T = 18.5 C) o NB water (T = 14.1 C)

10-1

10-2 100

101

102

103

104

Re [-]

(b)

5. Experimental results

102

Orifice 50 µm L / D = 0.40

101

Fig. 6a–c shows plots of 2Dp/qV2 (where V = 4Q/pD2 is the mean velocity of the liquid passing through an orifice) against Re = qVD/l (where q and l are the density and viscosity of the liquid, respectively) for each of the orifices. Previous water results (Hasegawa et al., 2009) are also presented for comparison. Experimental pressure drops agree with numerical predictions for the 100-lm orifice (Fig. 6a). However, the experimental drops for NB water when D = 20- and 50-lm are lower than those of water (Figs. 6b and c). This reduction in the experimental values from those predicted grows as the orifice size is decreased. Furthermore, the NB water values are almost half those of water. These results are in accord the results of the previous study (Ushida et al., 2012d).

2 2Δ p /ρV [-]

5.1. NB water

100

10-1

10-2 0 10

Prediction water (T = 18.1 o C) o NB water ( T = 14.3 C)

101

102

103

104

Re [-]

(c)

102

5.2. NB/surfactant mixtures

100

10-1 Prediction o water (T = 20.7 C ) o ( NB water T = 15.9 C )

10-2 100

101

102

103

104

Re [-]

5.3. NB/PEG Fig. 10a–c shows the 2Dp/qV2–Re plots for PEG only and NB/ PEG. NB/PEG pressure drops are lower than those of water, but higher than those of NB water and PEG only. PEG and NB/PEG both have elastic properties from Fig. 3b, although NB/PEG’s elasticity is about twice that of PEG. Drag reduction occurs based on a liquid’s elastic properties (Toms, 1948; Virk, 1975; Kulicke et al., 1989; Escudier et al., 1998; Hasegawa et al., 2003) and the experimental results here show this reduction accordingly.

Orifice 20 µm L / D = 1.00

101 2 2Δ p /ρV [-]

Figs. 7a–c, 8a–c, and 9a–c show the pressure drops for the three surfactant solutions. As a comparison, previous experimental results (Ushida et al., 2010, 2011) for cases where the corresponding surfactant solutions only were tested are also given in the figures. LAS-only results agree well with those of water and those predicted for the 100-lm orifice (Fig. 7a). For other orifice diameters, the experimental pressure drops for NB/LAS are lower than those of LAS only, but are higher than the pressure drops for NB water (Figs. 7b and c). NB/AE values are lower than those of water and higher than those of AE only (Fig. 8a–c). A distinctive change in behavior is also seen in this case, since AE-only pressure drops increase sharply, whereas NB/AE drops do not. The NB/BC case shows the same trends as the MB/AE case (Fig. 9a–c).

Fig. 6. Dimensionless pressure drops, 2Dp/qV2, plotted against Reynolds number, Re, for water and NB water when D = (a) 100 lm, (b) 50 lm, and (c) 20 lm.

6. Discussion 6.1. NB water Hasegawa et al. (2007, 2009) and Ushida et al. (2012c) discussed the elasticity of water passing through a micro-orifice.

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(a)

(a)

102

102

Orifice 100 µm L / D = 0.20

Orifice 100 µm

L / D = 0.20

101 2 2Δ p /ρV [-]

2 2Δ p /ρV [-]

101

100

10-1

Prediction o water (T = 18.5 C ) o water T NB ( = o14.1 C) LAS (T = 16.2 C ) NB/LAS (T = 14.6 o C)

10-2 100

1

10

10

2

10

100 Prediction water (T = 18.5 o C) NB water (T = 14.1 oC) BC (T = 18.8 oC) o NB/BC (T = 14.7 C)

10-1

3

10

10-2 100

4

101

Re [-]

(b)

(b)

102

Orifice 50 µm 2 2Δ p /ρV [-]

2 2Δ p /ρV [-]

10

100

10-1

10-2 100

Prediction water ( T = 18.1 oC) o NB water ( T = o14.3 C) LAS ( T = 15.3 C) o NB/LAS (T = 12.6 C)

101

102

103

100

10-1

10-2 100

104

Prediction o water (T = 18.1 C) o NB water ( T = 14.3 C) o BC (T = 19.2 C) o NB/BC (T = 12.8 C)

101

(c) Orifice 20 µm L / D = 1.00 2 2Δ p /ρV [-]

2 2Δ p /ρV [-]

10-2 100

Prediction o water ( T = 20.7 C) o NB water ( T = 15.9 C) LAS (T = 15.4 oC) o NB/LAS (T = 14.2 C)

102

104

Orifice 20 µm L / D = 1.00

1

100

Prediction o water ( T = 20.7 C ) o NB water (T =o 15.9 C ) BC (T = 24.2 C ) o NB/BC (T = 12.9 C )

10-1

10-2 101

103

102

10

100

10-1

102

Re [-]

102

101

104

Orifice 50 µm L / D = 0.40

Re [-]

(c)

103

102

101

L / D = 0.40

1

102

Re [-]

103

104

100

101

Re [-] 2

Fig. 7. 2Dp/qV –Re plots for LAS only and NB/LAS when D = (a) 100 lm, (b) 50 lm, and (c) 20 lm.

However, the effect of elasticity increases cannot reasonably be considered in the case of NB addition. The results instead strongly suggest that slip occurs at interface between the orifice wall and the NBs. Ushida et al. (2012b) have numerically investigated this slip wall.

102

103

104

Re [-] Fig. 8. 2Dp/qV2–Re plots for AE only and NB/AE when D = (a) 100 lm, (b) 50 lm, and (c) 20 lm.

6.2. NB/surfactant mixtures An electronic interface between surfactant charges and the electric double layer (Davis et al., 1978; Manne et al., 1994; Srinivas and Hermann, 1995; Fedorov and Kornyshev, 2008) was observed.

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(a)

(a)

102

100

Prediction o water (T = 18.5 C ) NB water (T = 14.1 o C ) AE (T = 16.3 o C ) NB/AE (T = 14.4 o C )

10-1

10

10

1

10

2

10

100

Prediction water ( T = 18.5 o C ) NB water (T = 14.1 o C ) PEG (T = 19.3 o C ) MB/PEG (T = 16.7 o C )

10-1

10-2 100

10-2 0

L / D = 0.20

101

L / D = 0.20

2 2Δ p /ρV [-]

2 2Δ p /ρV [-]

Orifice 100 μm

Orifice 100 μm

101

102

3

10

4

101

Re [-]

(b)

10

(b)

2

2 2Δ p /ρV [-]

Prediction o water (T = 18.1 C )o NB water (T = 14.3 C ) AE (T = 15.2 o C )o NB/AE (T = 12.2 C )

L / D = 0.40

100

Prediction o water ( T = 18.1 C ) NB water (T = 14.3 o C ) PEG (T = 19.9 o C ) NB/PEG (T = 17.2 o C )

10-1

10-2

10-2 100

101

102

103

104

100

101

Re [-]

(c)

10

(c) Orifice 20 μm L / D = 1.00

10-2 100

2 2Δ p /ρV [-]

Prediction o water (T = 20.7 C )o NB water (T = 15.9 C ) AE (T = 15.3 o C )o NB/AE (T = 13.3 C )

101

102

103

104

102

100

10-1

103

Prediction o water (T = 20.7 C )o C) NB water (T = 15.9 o PEG (T = 16.6 C ) o NB/PEG (T = 14.8 C )

101

100

10-1

102

Re [-]

2

101 2 2Δ p /ρV [-]

104

Orifice 50 μm

101

100

10-1

103

102

Orifice 50 μm

L / D = 0.40

101 2 2Δ p /ρV [-]

102

Re [-]

104

10-2 100

Re [-] Fig. 9. 2Dp/qV2–Re plots for BC only and NB/BC when D = (a) 100 lm, (b) 50 lm, and (c) 20 lm.

Moreover, a sharp increase in AE pressure drops was discussed in terms of breaking the micelle structure at very high strain velocity. The previous studies (Ushida et al., 2010, 2011) show relationship between Re (which was steep rise points of pressure drops) and D. Re  D was found to increase broadly with D, but it was nearly

Orifice 20 μm

L / D = 1.00

101

102

103

104

Re [-] 2

Fig. 10. 2Dp/qV –Re plots for PEG only and NB/PEG when D = (a) 100 lm, (b) 50 lm, and (c) 20 lm.

constant, the following relationship was obtained: Re  D = 2.0  102 m. As in those discussions, the electronic interaction between the electric double layer and NB/surfactant mixtures is examined here. Different results were found for the three types of surfactant (LAS, AE and BC). In addition, the microbubble

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Fig. 11. Schematic of setup to measure (a) surface tension and (b) force balance of liquid film.

particle size remains unchanged in laminar flows (Cho et al., 2005; Kukizaki and Goto, 2008; Elmahdy et al., 2008; Terasaka et al., 2009). We consider that nanobubbles show the same trend in the case here. Interfacial tension effects caused by surface tension must also be discussed. Fig. 11a shows apparatus employed to measure surface tension, rs, by the du Noüy method (du Noüy, 1919; Zuidema and Waters, 1941; Lunkenheimer and Wantke, 1981; Goebel and Lunkenheimer, 1997). A brass ring with inner diameter r1 = 7.75 mm and outer diameter r2 = 7.50 mm was used. A Petri dish filled with a test liquid was set on a z-stage. When the ring came into contact with the liquid surface, the height of the zstage, h1, was measured. As the stage was lowered, the liquid film elongated until breaking, at which point the height of the z-stage, h2, and the maximum value of the force, FB, were measured. The difference in height, h1  h2, was thus the height, Dh, of the elongated liquid film (Fig. 11b). By this method, FB is calculated through the following force balance equation:

F B ¼ 2pðr1 þ r2 Þrs þ pðr21  r 22 Þqg Dh; where q and g are the test liquid density and gravitational acceleration (=9.81 m/s2), respectively. The first term on the right-hand side is the surface tension, and the second term is the gravitational force. Rearranging, rs is then expressed as follows:

rs ¼

FB ðr 1  r 2 Þqg Dh  2 2pðr 1 þ r 2 Þ

Table 1 shows rs for the cases of LAS, AE, and BC. Although rs of NB/LAS was smaller than that of LAS-only, Pressure drops of NB/ LAS was almost agree with those of LAS-only. The rs values of NB/AE and NB/BC agree with those of AE and BC, respectively, even Table 1 Estimated surface tension, rs, of test liquids. Test liquid

r (mN/m)

Water LAS BC AE NB water NB/LAS NB/BC NB/AE

70.2 41.1 39.2 40.2 60.0 30.6 40.9 38.9

Fig. 12. Model of interface phenomenon for (a) NB/LAS, (b) NB/AE, and (c) NB/BC.

though the corresponding pressure drops are different. Therefore, the interfacial tension effect was negligible in the experimental results. Kim et al. (2000), Takahashi (2005), and Jin et al. (2007) have reported that the zeta potential of NBs ranges from 102 to 101 mV. Furthermore, the zeta potential of the electric double layer ranges from +100 to +101 mV (Schellman and Stigter, 1977; Yoon and Yordan, 1986; Fisher et al., 2002; Taki et al., 2008). Maoming et al. (2010) have additionally reported that microbubbles and NBs are negatively charged, and Hampton and Nguyen (2010) stated that the interface between the bubbles and the liquid was important for bubble flows. Generally, a solid wall in a liquid is negatively charged and the surroundings are positively charged. This is the well-known electric double layer (Gurney, 1935; Grahame, 1947; Devanathan and Tilak, 1965). In contrast, Fig. 12a shows a schematic of NB/LAS mixture flow around an orifice wall, where the LAS micelles and NBs in the aqueous solution are negatively charged. The size of the micelles for all three surfactants was similar to that of NBs (Robson and Dennis, 1977; Paradies, 1980; Almgren and Swarup, 1983). The LAS micelle and NB mixture phase was formed near the orifice wall because of their negative charges. Hence, a gas phase was established due to the existence of NBs. However, the slip rate was less than that for NB water (LAS only < NB/LAS < NB water). For the nonionic AE surfactant, the number of micelle near the orifice wall was less than for the LAS case. Fig. 12b shows a schematic of NB/AE mixture flow. Because of the increased number of NBs, the NB/AE slip rate of NB/ AE was greater than that in the NB/LAS case. Finally, the BC micelles were positively charged, namely, they were counter charged. Fig. 12c shows a schematic of the NB/BC mixture flow. The NB existence rate was greater than that of NB/AE. Ergo, the interface near the orifice wall was similar to that for the NB water flow. 6.3. NB/PEG The pressure drops measured for the NB/PEG mixtures containing 1.0 vol% nanobubble, when passed through micro-orifices,

A. Ushida et al. / International Journal of Heat and Fluid Flow 40 (2013) 106–115

113

where ‘‘water’’ and ‘‘PEG, NB/PEG’’ indicate experimental pressure drops of water, and PEG or NB/PEG, respectively (Tomita and Mochimaru, 1980; Hasegawa et al., 1988; Hasegawa and Nakamura, 1991; Gorder et al., 2009; Ushida et al., 2012b). Fig. 14 plots estimated ES values against V. The elastic stress of NB/PEG is less than that of PEG only. Hence, the existence of NBs in the PEG solution leads to a reduction in elasticity. 7. Conclusion

Fig. 13. Schematic images of the fluid structure for the case of (a) PEG and (b) NB/ PEG flow.

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Several types of nanobubble (NB) mixtures were passed through micro-orifices in this study. The following results were obtained. Measured pressure drops for a NB/water mixture (NB water) passing through 650-lm orifices were lower than those of water only and those numerically predicted by Navier–Stokes equations. Different results were observed for each of the NB/surfactant mixtures. For anionic surfactant (LAS and NB/LAS), the pressure drops were always such that LAS only < NB/LAS < NB water. For nonionic (AE and NB/AE) and cationic (BC and NB/BC) surfactants, inverse relations to the LAS case were obtained. Moreover, an interface phenomenon between the orifice wall and NB/surfactant mixtures was discussed, and the slip wall was numerically investigated. The experimental results are approximately equivalent to the values given by a half-slip wall. Pressure drops for a NB/polymer mixture (NB/PEG) were higher than those for the polymer solution only (PEG).The existence of NBs in the PEG solution was discussed, and it was shown the estimated elastic stress of NB/PEG was lower, corresponding to the experimental results. Acknowledgments

ES [N/m2]

106

105

ES = ρV PEG NB/PEG

104

103 100

10

1

10

2

2

V [m/s] Fig. 14. Estimated elastic stresses, ES, plotted against mean velocity, V, for PEG and NB/PEG.

were higher than those of the PEG-only solutions. This difference is attributed to the elastic property found in PEG in previous numerical and experimental researches (Cleland et al., 1992; Kuhl et al., 1996; Almany and Seliktar, 2005). Heymann and Grubmüller (1999) reported the elasticity of PEG was caused by the entanglement of polymer chains. In light of the above findings, our propose models of PEG flow and NB/PEG flow based on the structures were shown in Figs. 13a and b. For PEG-only, the elastic property occurs due to tangles of PEG chains (Fig. 13a). However, tangles are disturbed by nanobubbles in NB/PEG (Fig. 13b), and thus pressure drops increased in these mixtures. Because the jet thrust of NB/ PEG was smaller than that of PEG only (Fig. 3b), PEG elasticity was changed by the addition of NBs. The elastic stress, ES, of each orifice flow is expressed as

ES ¼ Dpjwater  DpjPEG;

NB=PEG ;

We thank Mr. Ryuichi Kayaba, Mr. Hiroshige Uchiyama, Dr. Keiko Amaki, Prof. Shinji Toga, Mr. Shotaro Murao, Mr. Akira Ichijo, and Mr. Takahiro Koyama for their considerable help in performing the experiments and numerical analyses, and Mr. Naoyuki Takahashi for their technical assistance in measuring surface tensions. We also thank CFIL members of Niigata University, Dr. Itaru Kourakata, and Prof. Shuji Harada for their constructive comments. References Almany, L., Seliktar, D., 2005. Biosynthetic hydrogel scaffolds made from fibrinogen and polyethylene glycol for 3D cell cultures. Biomaterial 26, 2467–2477. Almgren, M., Swarup, S., 1983. Size of sodium dodecyl sulfate micelles in the presence of additives. 3. Multivalent and hydrophobic counterions, cationic and nonionic surfactants. The Journal of Physical Chemistry 87, 876–881. Amaki, K., Hasegawa, T., Narumi, T., 2008. Drag reduction in the flow of aqueous solution of detergent through mesh screens. Nihon Reoroji Gakkaishi 36, 125– 131. Boger, D.V., Denn, M.M., 1980. Capillary and slit methods of normal stress measurements. Journal of Non-Newtonian Fluid Mechanics 6, 163–185. Burger, E.D., Munk, W.R., Wahl, H.A., 1982. Flow increase in the trans Alaska pipeline through use of a polymeric drag-reducing additive. Journal of Petroleum Technology 34, 377–386. Cates, M.E., Candau, S.J., 1990. Statics and dynamics of worm-like surfactant micelles. Journal of Physics: Condensed Matter 2, 6869–9892. Cho, S.H., Kim, J.Y., Chun, J.H., Kim, J.D., 2005. Ultrasonic formation of nanobubbles and their zeta-potentials in aqueous electrolyte and surfactant solutions. Colloids and Surfaces A: Physicochemical and Engineering Aspects 269, 28–34. Choung, J.W., Luttrell, G.H., Yoon, R.H., 1993. Characterization of operating parameters in the cleaning zone of microbubble column flotation. International Journal of Mineral Processing 39, 31–40. Cleland, J.L., Hedgepeth, C., Wang, W.I., 1992. Polyethylene glycol enhanced refolding of bovine carbonic anhydrase B. Reaction stoichiometry and refolding model. The Journal of Biological Chemistry 267, 13327–13334. Dailey, H.L., Ghadiali, S.N., 2010. Influence of power-law rheology on cell injury during microbubble flows. Biomechanics and Modeling in Mechanobiology 9, 263–279. Davis, J.A., James, R.O., Leckie, J.O., 1978. Surface ionization and complexation at the oxide/water interface. I. Computation of electrical doublelayer properties in simple electrolytes. Journal of Colloid and Interface Science 63, 480–499.

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