Effect of glycerol on the binary coalescence of water drops in stagnant oil phase

chemical engineering research and design 8 7 ( 2 0 0 9 ) 1640–1648

Contents lists available at ScienceDirect

Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd

Effect of glycerol on the binary coalescence of water drops in stagnant oil phase Wei Wang a,b , Jing Gong b , Kwun Ho Ngan a , Panagiota Angeli a,∗ a b

Department of Chemical Engineering, University College London, Torrington Place, London WC1E 7JE, United Kingdom Beijing Key Laboratory of Urban Oil and Gas Distribution Technology, China University of Petroleum, Beijing, PR China

a b s t r a c t The binary coalescence of water drops forming through capillaries at low inlet flow rates in an immiscible stagnant oil phase was studied and the evolution of the coalescence process was recorded using a high speed video camera. An increase in the inlet flow rate as well as in the drop size was found to increase the time required for coalescence. Interfacial tension was also varied by adding glycerol in the water phase. Although glycerol reduced the interfacial tension, the drop–drop coalescence time decreased in contrast to what has been reported in the literature. Experiments with the oil phase saturated with glycerol demonstrated that the decreased coalescence times could only partly be explained by mass transfer. The reduced water drop coalescence times in the presence of glycerol were also considered to be responsible for the decreased water fraction required for the phase inversion of the organic–aqueous dispersion. © 2009 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. Keywords: Binary drop coalescence; Interfacial tension; Mass transfer; Phase inversion

1.

Introduction

Coalescence of liquid drops dispersed in another immiscible liquid plays an important role in many industrial applications which include liquid–liquid extraction, emulsification, separation and multiphase transportation. During dispersed liquid–liquid flow, coalescence will influence the drop size distribution as well as the phase inversion phenomenon. The coalescence process between two drops involves three steps. In the first step, the drops come into contact driven by the applied forces of the flow field. Secondly, the drops flatten during their approach and a thin liquid film is formed between them which starts to drain with a rate that depends on parameters such as liquid properties, capillary pressure inside the drops and applied forces. Finally, the film reaches a critical value at which the intermolecular forces, e.g. van der Waals forces, become dominant and cause the film to rupture. The present study deals with the last two stages of the drop–drop coalescence process. There are a large number of experimental studies on the coalescence of liquid drops with flat interfaces (Nielsen et al., 1958; Charles and Mason, 1960a,b; Mackay and Mason, 1963a,b;

∗

Vrij and Overbeek, 1968; Hodgson and Lee, 1969; Hodgson and Woods, 1969; Burrill and Woods, 1973; Chen et al., 1998; Dreher et al., 1999; Ghosh, 2004). Investigators have conducted experiments with either pure chemicals or in the presence of added components that affect interfacial properties where the effects of drop size, temperature and mass transfer of the impurities across the interface were investigated. It is commonly accepted that with large drops the large contact area reduces the film drainage rate resulting in larger coalescence time (also called rest-time) compared to small drops. Results by Dreher et al. (1999) show that the coalescence time depends almost linearly on drop size. Moreover, for easily deformable drops, coalescence time and drop stability increase with drop size (Mackay and Mason, 1963a; Chen et al., 1998). With decreasing surface/interfacial tension, film drainage rate will be reduced, which leads to longer coalescence times (Hartland and Wood, 1973; Li and Slattery, 1988). Hartland and Wood (1973) found that during the coalescence of a liquid drop with a flat interface the drainage rate decreased with a decrease in interfacial tension and applied force or with an increase of the drop volume. Li and Slattery (1988) confirmed that the coalescence time of nitrogen bubbles increased

Corresponding author. Tel.: +44 0 20 7679 3832; fax: +44 0 20 7383 2348. E-mail address: [email protected] (P. Angeli). Received 2 December 2008; Received in revised form 13 May 2009; Accepted 24 May 2009 0263-8762/$ – see front matter © 2009 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.cherd.2009.05.004

1641

chemical engineering research and design 8 7 ( 2 0 0 9 ) 1640–1648

when the surface tension was decreased by changing the concentration of NaCl in the aqueous continuous phase. In addition, viscosities of the dispersed and continuous phases, presence of surfactants and mass transfer between the phases also affect the film drainage rate (Bazhlekov et al., 2000; Chesters and Bazhlekov, 2000; Yeo et al., 2003; Chevaillier et al., 2006; Giribabu and Ghosh, 2007). Accurate experiments using image reflectometry (ellipsometry) on film drainage behaviour have elucidated the effects of mass transfer, viscosity, presence of electrolyte and other liquid properties on coalescence (Bazhlekov et al., 2000; Goodall et al., 2002; Kumar et al., 2002; Zdravkov et al., 2003; Chevaillier et al., 2006). The thinning rate of the liquid film to its critical thickness depends on the rigidity and mobility of the colliding interfaces (Chesters, 1991). Interfacial rigidity determines how much the colliding interfaces will flatten and is influenced by drop size and surface/interfacial tension. If the interface is undeformable, which means that the pressure in the liquid film is lower than the Laplace pressure inside the drops, the film can easily be drained. Interfacial mobility is governed by the tangential stresses exerted on the film by the drops (Abid and Chesters, 1994; Saboni et al., 1995) and depends on the viscosity ratio of the dispersed and continuous phases. Three types of interfacial behaviour during coalescence are identified based on the dispersed/continuous phase viscosity ratio: (1) immobile interfaces, when the dispersed phase viscosity is much higher than the continuous phase one, or when surfactants are present that retard the drainage of the liquid film; (2) fully mobile interfaces, when the continuous phase viscosity is very large compared to that of the dispersed phase; (3) partially mobile interfaces, when the viscosity ratio is moderate (10−2 –102 ) (Chesters, 1991; Abid and Chesters, 1994; Saboni et al., 1995), which are the most common ones. Film drainage between partially mobile interfaces appears as a plug flow, which is controlled by viscous forces exerted by the dispersed phase (Lee and Hodgson, 1968; Bazhlekov et al., 2000). Based on the above, a number of film drainage models have been developed, with early ones considering coalescence to be a purely hydrodynamic phenomenon and assuming the drainage to happen between parallel plates (Reynolds, 1886; Gillespie and Rideal, 1956; Mcavoy and Kintner, 1965). Hartland (1969) derived an expression for the drainage of the film beneath a rigid sphere or a liquid drop approaching a deformable fluid interface with the assumption of constant force. To account for interfacial mobility, an empirical parameter, n, was introduced with values n = 1 when the fluid–fluid interface is fully mobile and n = 2 when both interfaces are immobile: 3n2 c A2 t= 16F



1 1 − 2 h2 h0

tions: 3c R2 F immobile interfaces, t = 16 2

partially mobile interfaces, t =

fully mobile interfaces, t = −



1 1 − 2 h2 h0

d F1/2 2(2/R)

3R h ln 2 h0

3/2

 (2)

1 h

−

1 h0

 (3)

(4)

More recently, Borrell and Leal (2008) proposed a simple drainage model for the film between two drops, assuming a disk-like interface, by applying a constant inlet flow rate of the forming drops instead of using constant approaching force or velocity:

t=

RQ2d  1 8 2

h

−

1 h0

2 (5)

where  is the interfacial tension, Q is the inlet flow rate, d is the viscosity of the dispersed phase. Similar to Eq. (1), a decrease in interfacial tension will increase the coalescence time. However, the draining film thickness may not be uniform and more accurate numerical models using lubrication theory have been proposed to couple the interface deformation with film drainage flow and fluid circulation within the drops (Chen et al., 1984; Hahn et al., 1985; Abid and Chesters, 1994; Jeelani and Hartland, 1994; Saboni et al., 1995; Klaseboer et al., 2000; Yang et al., 2001). Most of the models though assume simple boundary conditions, such as constant interaction force or constant approach velocity, while in reality both will vary during the collision of a drop with a flat interface or with another drop. In this paper, the binary coalescence of water drops within a stagnant organic phase was investigated experimentally. The coalescence behaviour of pure deionized water drops was found to be in accordance with previous research. However, the addition of glycerol at various concentrations in the water phase, which decreased the interfacial tension, resulted in a decrease of the coalescence time in contrast to literature results for systems with decreased interfacial tension.

 (1)

where A is the area of the draining film, A = 2␲R2 (1 − cos c ), R is the drop radius, c is the angular inclination of the edge of the draining film to the radial axis, h0 and h are the initial and final film thickness, F is the applied force and c is the viscosity of the continuous phase. According to Eq. (1), film mobility will influence the drainage time, while for any value of n a decrease in interfacial tension will enlarge the contact area between the drop and the interface leading to longer coalescence time. Chesters (1991) summarized the film drainage models for drop–drop coalescence with deformable interfaces with the assumption of constant force, in the following equa-

Fig. 1 – Experimental setup for the drop–drop coalescence studies.

1642

chemical engineering research and design 8 7 ( 2 0 0 9 ) 1640–1648

Table 1 – Properties of test fluids (at 20 ± 0.4 ◦ C). Properties 3

Density (kg/m ) Viscosity (mPa s) Surface tensiona (mN/m) Interfacial tensiona (mN/m) a

2.

Exxsol D140 oil

Deionized water

1% glycerol solution

10% glycerol solution

828.10 5.50 28.30

973.20 0.84 72.60 34.02

976.80 0.85 71.70 32.70

1000.02 0.921 68.90 26.60

Drop volume method.

Experimental procedure

The experiments of binary drop coalescence were carried out using the experimental set up shown schematically in Fig. 1. The coalescence cell was a vertical rectangular acrylic cell with a square cross-section of side length 15 cm and height 25 cm.

The two drops were formed at two stainless-steel capillaries (OD = 0.7 mm) each connected to a larger stainless steel delivery tube. The two tubes were then connected to the syringes (gas tight 10 ml glass, Hamilton 1010LT) of a dualsyringe infusion pump (KDS101). This configuration allows steady delivery in each syringe of flow rates between 10 and

Fig. 2 – Binary coalescence of water drops for capillary separation distance = 2.93 mm and inlet flow rate Q = 10 ␮l/min. (a-1) t = 50.84 s; (a-2) t = t0 = 54.38 s; (a-3) t = 68.12 s; (a-4) t = t = 68.14 s; (a-5) t = 68.20 s; (b-1) t = 50.84 s; (b-2) t = t0 = 54.38 s; (b-3) t = t = 68.14 s; (b-4) t = 68.20 s.

chemical engineering research and design 8 7 ( 2 0 0 9 ) 1640–1648

1643

Fig. 3 – Coalescence time of deionized water drops at inlet flow rate 10 ␮l/min and capillary separation distance 2.93 mm. 30 ␮l/min, required in this work. The flow rates delivered by the syringe pump were checked against the measured volumes of the formed drops (following the methodology given by Gnyloskurenko et al., 2003) and excellent agreement was found. The capillaries entered the coalescence cell through specially made ball joints at the wall that allowed them to move freely without leaking. The distance between two vertical capillaries could be adjusted by moving the delivery tubes forward or backward. The continuous liquid level in the acrylic cell was maintained at 30 mm above the outlet of the capillaries. The coalescence was captured with a high speed video camera (Phantom v7.1), which has a CMOS sensor with a maximum resolution of 1024 × 1024 pixels. The average recording rate used throughout the coalescence process was 200 fps, while even higher recording rates up to 8000 fps were necessary to capture the formation of the liquid bridge between the two drops as soon as coalescence started. When necessary, back-lighting was provided by a fiber optic cold light (M1000 Mille Luce, Stocker & Yale) to avoid generating temperature gradients. Exxsol D140 oil (non-polar aliphatic oil, water insoluble) was used as the continuous phase in all the experiments. The aqueous dispersed phase was either deionized water or deionized water with different glycerol concentrations. The properties of the fluids are shown in Table 1, while glycerol is also insoluble in Exxsol D140 oil. The continuous oil phase was placed in the acrylic container while the dispersed aqueous phase was injected through the capillaries. Before each experiment the coalescence cell was rinsed several times with deionized water and was left to dry in the atmosphere. The syringes were also rinsed with the relevant aqueous phase before the experiment. Care was taken not to touch the capillaries inside the cell after the cleaning. The continuous organic phase was then fed into the cell while the aqueous phase was delivered to both capillaries. Pairs of drops formed in the capillaries and their coalescence process was observed with the high speed camera. The drops subsequently detached from the capillaries and settled at the bottom of the cell. At the low flow rates used the drops formed in each capillary were well separated from subsequent ones and did not interfere with each other and with the coalescence process. For each set of conditions 60–100 pairs of drops were formed and at the end of it the coalescence cell was emptied and cleaned again. This procedure ensured that within one set of conditions the change in the liquid level height in the cell was insignificant and did not affect the coalescence process.

Fig. 4 – Effect of drop size on the coalescence time of deionized water drops. (a) Q = 10 ␮l/min, (b) Q = 20 ␮l/min and (c) Q = 30 ␮l/min.

The coalescence between two drops can be affected by factors such as external vibrations, temperature variations and temperature gradients (Charles and Mason, 1960a; Davies, 1992). To avoid any such effects, during the experiment the cell was placed in a thermostatic environment where temperature was controlled to be at 20.0 ± 0.4◦ C. In addition, the prepared aqueous solution was placed in the thermostatic environment for 12 h before the experiment, to eliminate any temperature gradients, while the solution was kept covered to avoid any dust precipitating on the interface. Particular care was also taken to eliminate vibrations and the coalescence cell was put to a separate bench from the rest of the set up to avoid any disturbances mainly from the pump but also from the computer and the camera. The coalescence process between two drops is shown in Fig. 2. According to Ban et al. (2000), as coalescence time (tcoalescence = t − t0 ) is defined the difference between the time the two drops come into contact, t0 , and the time the two drops begin to coalesce, t . The evolution of coalescence is depicted in Fig. 2(a) while in Fig. 2(b) some photographs have been magnified to show more clearly the drop–drop contact and the formation of the bridge. Fig. 2(a1 and b1) are taken at

1644

chemical engineering research and design 8 7 ( 2 0 0 9 ) 1640–1648

Table 2 – Parameters of the cumulative coalescence time curves, maximum (tmax ), half (t1/2 ) and mean (tmean ) coalescence times. Dispersed phase

Interfacial tension (mN/m)

Flow rate (␮l/min)

34.02

10.0

Deionized water

Distance (mm)

20.0 30.0

1% glycerol in water solution

32.70

10.0 20.0 30.0

10% glycerol in water solution

26.60

10.0 20.0 30.0

a

Maximum time, tmax (s)

Half time, t1/2 (s)

Mean time, tmean (s)

2.54 2.93 2.54 2.93 2.54 2.93

Nonea None None None None None

10.9 16.5 12.5 16.7 18.1 17.5

13.9 37.9 17.3 33.2 29.2 34.5

2.54 2.93 2.54 2.93 2.54 2.93

35.1 42.6 22.2 40.3 18.0 53.2

8.2 8.8 9.6 9.4 9.2 12.3

11.9 13.9 10.8 13.9 14.7 17.9

2.54 2.93 2.54 2.93 2.54 2.93

15.7 17.9 26.9 25.5 29.4 28.1

6.1 6.0 6.6 7.5 7.2 7.5

9.4 9.2 11.6 12.0 12.6 13.8

None indicates that some pairs of drops finally detached separately without coalescence.

time 50.84 s from when the drops first started forming at the capillaries. The gap between the two drops is about 60 ␮m, corresponding to two pixels for the magnification of the current lens. Time t = 54.38 s, when the two drops first come in contact as shown in Fig. 2(a2 and b2), is taken as t0 . The start of coalescence, where a liquid bridge can clearly be seen between the two drops, occurs at time t = 68.14 s and is shown in Fig. 2(a4 and b3). Finally, Fig. 2(a5 and b4) shows the evolution of the liquid bridge at a later time, t = 68.20 s after the beginning of coalescence. Because of the difficulty in determining the initial drop contact time, t0 , 1–1.5 s variation may exist. In Fig. 3 the distribution of coalescence times as well as the cumulative coalescence time distribution can be seen for binary coalescence of deionized water drops in oil at an inlet flow rate of 10 ␮l/min and centre to centre separation distance between the capillaries of 2.93 mm. The y-axis denotes the percentage of drop pairs from all drop pairs that formed which coalesced at a particular coalescence time. The distribution of coalescence times can be attributed to chemical impurities in the system and the random nature of disturbances which cause the film to break (Charles and Mason, 1960a; Vrij and Overbeek, 1968; Davies, 1992; Dreher et al., 1999). It should also be noted that in this example the cumulative coalescence time does not reach 100% because some drop pairs break away from the capillaries without the drops coalescing.

3.

Results and discussions

3.1.

Experimental results

Fig. 4 illustrates the cumulative coalescence time distributions obtained during binary water drop coalescence at two centre-to-centre capillary separation distances. When the two drops come into contact their diameter is equal to the capillary separation distance and this is taken as the drop size for the coalescence experiment. By increasing the distance

between the two capillaries the sizes of the drops that are brought into contact are also increased. The sigmoidal shapes of the time distributions are similar to those obtained from drop to liquid–liquid flat interface coalescence (Nielsen et al., 1958; Charles and Mason, 1960a,b; Mackay and Mason, 1963a; Vrij and Overbeek, 1968; Chen et al., 1998). In Table 2 three characteristic parameters of the coalescence time curve are given for comparison, namely maximum time (tmax ), half time (t1/2 ), which represents the time where 50% of drop pairs coalesced and mean time (tmean ), which is the arithmetic average of the coalescence time; the minimum coalescence time (tmin ) is not included because there were uncertainties involved in the measurement of very small times. It is found that at all inlet flow rates, an increase in drop size causes an increase in coalescence time; the curves in Fig. 4 shift to the right while the characteristic coalescence times (Table 2) are increased with the 2.93 mm separation distance compared to the 2.54 mm one. These findings are in good agreement with results by other investigators, as discussed in Section 1 (Mackay and Mason, 1963a; Chen et al., 1998; Dreher et al., 1999). The force pressing the drops together and causing the film to drain depends on capillary pressure and on van der Waals forces as given by p = (2/R) + (AH /6h3 ) (Marrucci, 1969), where AH is the Hamaker constant. The disjoining pressure of the electric double layer force can be neglected for water drop coalescence in an organic continuous medium. An increase in drop radius will decrease the overall pressure and lead to longer coalescence times. As the inlet flow rate increases the effect of drop size on coalescence time diminishes (Fig. 4) which again is in accordance with previous results on flow-induced coalescence (Borrell and Leal, 2008; Leal, 2004). An increase in the inlet flow rate for the same capillary separation distance, on the other hand, leads to an increase in the coalescence time. With increasing inlet flow rate, Q, the flat film area between the two drops increases (A = a2 ) as suggested by the following equation for coaxial drop coalescence

chemical engineering research and design 8 7 ( 2 0 0 9 ) 1640–1648

Fig. 5 – Coalescence time of 1% glycerol/water drops at inlet flow rate 10 ␮l/min and capillary separation distance 2.93 mm.

1645

Fig. 6 – Coalescence time of 10% glycerol/water drops at inlet flow rate 10 ␮l/min and capillary separation distance 2.93 mm.

(Borrell and Leal, 2008):

 a≈

tQ + a20 2R

(6)

where a is the deformed film radius and a0 is its initial value, equal to 0 for drop–drop coalescence. Increased area between the two drops will increase the time for the film to drain to its critical value thus increasing the coalescence time; the correlation between flow rate and coalescence time was given in Eq. (5). In the current experiments the drop size during coalescence also increased from its initial value when the drops first come into contact and this, in addition to flow rate, would increase coalescence time. The change in drop size will be larger at the higher flow rates and as a result both increased drop size and flow rate will contribute to the increased coalescence times obtained at high flow rates compared to the low ones. In the absence of interfacial tension gradients (Marangoni phenomena), it is commonly accepted that film drainage time will be increased with decreasing interfacial tension (see also Eqs. (2)–(5)). In order to study the effect of interfacial tension on coalescence time glycerol was added in the water phase. Glycerol was chosen because it does not behave like a common surfactant that would stabilize the interface and retard film drainage and is not soluble to oil that would cause mass transfer between the two phases which can affect coalescence. The properties of the two glycerol concentrations used, 1% and 10%, can be seen in Table 1. Coalescence time distributions for 1% and 10% glycerol concentrations in water and inlet flow rates 10 ␮l/min are shown in Table 2 and Figs. 5 and 6. It can be seen that with the addition of glycerol the film drainage rate is enhanced. In the case of 1% glycerol in water 80% of drops coalesced within 15 s of drop–drop contact time, while in the case of 10% glycerol in water the same percentage of drops coalesced within 10 s. In comparison, when pure deionized water was used 80% of the drops required 35 s to coalesce while there was also a small percentage of drops that did not coalesce (see Fig. 3). Cumulative coalescence times for different glycerol concentrations in the aqueous phase and Q equal to 10 and 30 ␮l/min are shown in Figs. 7 and 8 for two capillary separation distances respectively, while similar results were found for 20 ␮l/min. In the presence of glycerol similar effects of drop size and inlet flow rate on coalescence time are observed as in pure water. In addition, the coalescence rate is enhanced when glycerol is added in the water phase, while the percent-

age of coalesced drop pairs reaches 100%. This is not the case with the coalescence of deionized water drops, where some drop pairs detached from the capillaries without coalescing (see Table 2). This enhancement appears to be small for small drops at the lower flow rate used (Fig. 8(a)). This is probably because with small drop sizes and low inlet flow rates coalescence happens more easily and as a result addition of glycerol offers only small improvements. The above results show that the addition of glycerol in water drops enhances coalescence. Given that with the addition of glycerol interfacial tension is reduced, these results appear to contradict what is commonly accepted that decreased interfacial tension increases coalescence time (see also Eqs. (2)–(5)) and will be further discussed below.

Fig. 7 – Effect of glycerol concentration in water on the cumulative coalescence time distribution of water drops for capillary separation distance 2.93 mm. (a) Q = 10 ␮l/min and (b) Q = 30 ␮l/min.

1646

chemical engineering research and design 8 7 ( 2 0 0 9 ) 1640–1648

Fig. 8 – Effect of glycerol concentration in water on the cumulative coalescence time distribution of water drops for capillary separation distance 2.54 mm. (a) Q = 10 ␮l/min and (b) Q = 30 ␮l/min.

3.2. Coalescence behaviour in the presence of glycerol in the aqueous phase It has been suggested that even when there is a slight solubility of a component into the opposite phase, mass transfer will occur that will affect coalescence. Nielsen et al. (1958) found that coalescence taking place in mutually saturated phases always results in longer coalescence times compared to the unsaturated ones. Charles and Mason (1960b) also suggested that the enhanced coalescence rate of water drops in chloroform observed when ethanol was dissolved in water could be attributed to mass transfer of ethanol to the non-polar chloroform even though its solubility to it is small. In order to check the effect of any mass transfer on coalescence times, experiments were carried out using oil phase saturated in glycerol. To prepare the saturated oil phase, small volumes of oil were placed in contact with large volumes of the aqueous phase (oil/aqueous phase volume ratio = 1:10) that had different glycerol concentrations (1% and 10%) for more than 24 h. The saturated oil phase for each concentration was then placed into the coalescence cell to perform experiments using the respective glycerol–water solution. The coalescence times with the unsaturated and saturated oil phase reveal that coalescence times increase obviously in the saturated mixtures (Fig. 9) in agreement with the data by Nielsen et al. (1958). When glycerol is transferring to the oil phase then a concentration gradient of the glycerol within the drop can appear. This is because the film region between the drops will become more easily saturated to glycerol compared to the rest of the oil phase. As a result there would be higher glycerol concentration on the side of the drops facing the film than the rest which could give rise to Marangoni flows that will help film drainage (Davies, 1992).

Fig. 9 – Effect of mass transfer on the cumulative coalescence time of water drops at different glycerol concentrations for capillary separation distance 2.93 mm. (a) Q = 10 ␮l/min and (b) Q = 20 ␮l/min. However, as can be seen from Fig. 9, even when there is no mass transfer, the cumulative coalescence time in the presence of glycerol reaches 100% in contrast to that in pure water. In addition, and particularly for the 10% glycerol system, film drainage times are still faster than in pure water. This suggests that mass transfer alone cannot fully account for the increased coalescence efficiency in the presence of glycerol in water. By adding glycerol in water the interfacial tension is reduced which would make the interface easier to deform. Non-uniform distribution of surface active agents on the interface has been shown to cause fusion of drops because of fluctuations generated at the interfaces (Evans and Wennerström, 1999). This phenomenon could appear when glycerol is dissolved in water and be further enhanced because the interface can deform easily in this case. In addition, and in contrast to common surfactants, the hydrophobic part of glycerol within the oil phase is not long enough to generate steric interactions that would prevent drops from approaching very closely and would delay coalescence (Tadros, 1996). Furthermore, the HLB (hydrophilic–lipophilic balance) value of glycerol is 11.09 (Griffin’s method (Griffin, 1954)), indicating an o/w emulsifier, that would tend to invert the dispersed aqueous phase into continuous and result in instability and easier coalescence. The coalescence enhancing properties of the glycerol– water solutions compared to pure water were also demonstrated in phase inversion experiments. Phase inversion of a liquid–liquid dispersion is the phenomenon whereby the continuous phase changes to become dispersed and vice versa. Enhanced drop coalescence compared to break up rates has been suggested as a possible reason for the appearance of phase inversion (Kato et al., 1991; Norato et al., 1998; Bin et al., 2005).

1647

chemical engineering research and design 8 7 ( 2 0 0 9 ) 1640–1648

Table 3 – Phase inversion of the aqueous-oil dispersion in a stirred tank at 400 rpm impeller speed for different glycerol concentrations in the aqueous phase. Oil volume

Water volume

Water volume fraction

Type of dispersion

Deionized water–unsaturated oil 700 725

500 500

41.67% 40.82%

o/w w/o

1% glycerol–unsaturated oil 700 750 800 825

500 500 500 500

41.67% 40.00% 38.46% 37.74%

o/w o/w o/w w/o

10% glycerol–unsaturated oil 700 800 850 875

500 500 500 500

41.67% 38.46% 37.04% 36.36%

o/w o/w o/w w/o

Phase inversion experiments were carried out in an acrylic stirred tank (diameter = 16.9 cm) using unsaturated oil and water with different glycerol concentrations, 0%, 1% and 10%, as test fluids. The dispersion was formed using a Heidolph rotating stirrer (RZR 2041) with a six blade Rushton impeller and rotating speeds 300 and 400 rpm. In all experiments 500 ml of water were placed in the tank, while the initial amount of oil varied. The propeller was put within the water and close to the oil–water interface. The mixture was stirred for 2 min and the continuous phase was determined from its appearance as well as its separation characteristics when stirring was stopped. A small amount of oil (increments of 25 ml) was added and the continuity of the new mixture was checked. The experiment continued until water became the dispersed phase. Indicative results are shown in Table 3 for 400 rpm stirring speed. It can be seen that when glycerol was added the amount of water required for the dispersion to be water continuous decreased with increasing glycerol concentration (water fractions at phase inversion are between 0.408–0.417, 0.377–0.385, and 0.364–0.370 for 0%, 1% and 10% glycerol respectively). This indicates that the enhancement of water drop coalescence with the addition of glycerol favours the aqueous phase to be the continuous one in an oil–water dispersion.

4.

Conclusions

The evolution of the coalescence process between two water drops in a stagnant oil phase as well as the coalescence time distributions were investigated using a high speed video camera. It was found that increasing the drop size as well as the inlet flow rate increased the drainage time of the film trapped between the two colliding drops, in accordance with previous findings. In contrast to what has been reported in the literature, however, the decrease of the interfacial tension with the addition of glycerol in the water phase decreased the coalescence time. Mass transfer was found to be partly responsible for this behaviour even though glycerol has only limited solubility in the organic phase. Other possible reasons such as increased ability of the interface to deform in the presence of glycerol were also discussed. The short drop coalescence times obtained with glycerol present in water were considered to be responsible for the lower water fractions required for the phase inversion of an aqueous–organic dispersion compared to the dispersion without glycerol.

Acknowledgements W. Wang would like to thank the China Scholarship Council (CSC) and the Chinese government for providing financial support for overseas research. K.H. Ngan would like to thank Chevron Energy Technology Company for providing his studentship. The authors would like to thank the EPSRC Engineering Instrument Pool for providing the high speed camera.

References Abid, S. and Chesters, A.K., 1994, The drainage and rupture of partially-mobile films between colliding drops at constant approach velocity. Int J Multiphase flow, 20: 613–629. Ban, T., Kawaizumi, F., Nii, S. and Takahashi, K., 2000, Study of drop coalescence behavior for liquid–liquid extraction operation. Chem Eng Sci, 55: 5385–5391. Bazhlekov, I.B., Chesters, A.K. and van de Vosse, F.N., 2000, The effect of the dispersed to continuous-phase viscosity ratio on film drainage between interacting drops. Int J Multiphase Flow, 26: 445–466. Bin, H., Matar, O.K., Hewitt, G.F. and Angeli, P., 2005, Prediction of phase inversion in agitated vessels using a two-region model. Chem Eng Sci, 60: 3487–3495. Borrell, M. and Leal, G., 2008, Viscous coalescence of expanding low-viscosity drops: the dueling drops experiment. J Colloid Interf Sci, 319: 263–269. Burrill, K.A. and Woods, D.R., 1973, Film shapes for deformable drops at liquid–liquid interface III drop rest times. J Colloid Interf Sci, 42: 35–51. Charles, G.E. and Mason, S.G., 1960, The mechanism of partial coalescence of liquid drops at liquid–liquid interfaces. J Colloid Interf Sci, 15: 105–122. Charles, G.E. and Mason, S.G., 1960, The coalescence of liquid drops with flat liquid/liquid interfaces. J Colloid Interf Sci, 15: 236–267. Chen, J.D., Hahn, P.S. and Slattery, J.C., 1984, Coalescence time for a small drop or bubble at a fluid–fluid interface. AICHE J, 30: 622–630. Chen, Ch.T., Maa, J.R., Yang, Y.M. and Chang, C.H., 1998, Effects of electrolytes and polarity of organic liquids on the coalescence of droplets at aqueous–organic interfaces. Surf Sci, 406: 167–177. Chesters, A.K., 1991, The modeling of coalescence processes in fluid–liquid dispersions: a review of current understanding. Chem Eng Res Des, 69: 259–270. Chesters, A.K. and Bazhlekov, I.B., 2000, Effect of insoluble surfactants on drainage and rupture of a film between drops interacting under a constant force. J Colloid Interf Sci, 230: 229–243.

1648

chemical engineering research and design 8 7 ( 2 0 0 9 ) 1640–1648

Chevaillier, J.P., Klaseboer, E., Masbernat, O. and Gourdon, C., 2006, Effect of mass transfer on the film drainage between colliding drops. J Colloid Interf Sci, 299: 472–485. Davies, G.A., 1992, Mixing and coalescence phenomena in liquid–liquid systems, in Science and Practice of Liquid–Liquid Extraction, Thornton, J.D. (ed). (Clarendon Press, Oxford) Dreher, T.M., Glass, J., O’Connor, A.J. and Stevens, G.W., 1999, Effect of rheology on coalescence rate and emulsion stability. AIChE J, 45: 1182–1190. Evans, D.F. and Wennerström, H., (1999). The Colloidal Domain: Where Physics, Chemistry, Biology and Technology Meet (2nd ed.). (Wiley-VCH, New York). Ghosh, P., 2004, Coalescence of air bubbles at air–water interface. Chem Eng Res Des, 82: 849–854. Gillespie, T. and Rideal, E.K., 1956, The coalescence of drops at an oil–water interface. Trans Faraday Soc, 52: 173–183. Giribabu, K. and Ghosh, P., 2007, Adsorption of nonionic surfactants at fluid–fluid interfaces: importance in the coalescence of bubbles and drops. Chem Eng Sci, 62: 3057–3067. Gnyloskurenko, S.V., Byakova, A.V., Raychenko, O.I. and Nakamura, T., 2003, Influence of wetting conditions on bubble formation at orifice in an inviscid liquid. Transformation of bubble shape and size. Colloids Surf A, 218: 73–87. Goodall, D.G., Gee, M.L. and Stevens, G.W., 2002, An imaging reflectometry study of the effect of electrolyte on the drainage and profile of an aqueous film between an oil droplet and a hydrophilic silica surface. Langmuir, 18: 4729–4735. Griffin, W.C., 1954, Calculation of HLB values of non-ionic surfactants. J Soc Cosmet Chem, 5: 249–256. Hahn, P.S., Chen, J.D. and Slattery., 1985, Effect of London–van der Waals forces on the thinning and rupture of dimpled liquid film as a small drop or bubble approaches a fluid–fluid interface. AICHE J, 31: 2026–2038. Hartland, S., 1969, The profile of the draining film between a rigid sphere and a deformable fluid–fluid interface. Chem Eng Sci, 24: 987–995. Hartland, S. and Wood, S.M., 1973, Effect of applied force on the approach of a drop to a fluid–liquid interface. AIChE J, 19: 871–876. Hodgson, T.D. and Lee, J.C., 1969, The effect of surfactants on the coalescence of a drop at an interface-I. J Colloid Interf Sci, 30: 94–108. Hodgson, T.D. and Woods, D.R., 1969, The effect of surfactants on the coalescence of a drop at an interface-II. J Colloid Interf Sci, 30: 429–446. Jeelani, S.A.K. and Hartland, S., 1994, Effect of interfacial mobility on thin film drainage. J Colloid Interf Sci, 164: 296–308. Kato, S., Nakayama, E. and Kawasaki, J., 1991, Types of dispersion in agitated liquid–liquid systems. Can J Chem Eng, 69: 222–227. Klaseboer, E., Chevaillier, J.Ph., Gourdon, C. and Masbernat, O., 2000, Film drainage between colliding drops at constant

approach velocity: experiments and modelling. J Colloid Interf Sci, 229: 274–285. Kumar, K., Nikolov, D. and Wasan, D.T., 2002, Effect of film curvature on drainage of thin liquid films. J Colloid Interf Sci, 256: 194–200. Leal, L.G., 2004, Flow induced coalescence of drops in a viscous fluid. Phys Fluids, 16: 1833–1851. Lee, J.C. and Hodgson, T.D., 1968, Film flow and coalescence. I. Basic relations, film shape and criteria for interface mobility. Chem Eng Sci, 23: 1375–1397. Li, D.M. and Slattery, J.C., 1988, Experimental support for analyses of coalescence. AIChE J, 34: 862–864. Mackay, G.D.M. and Mason, S.G., 1963a, The gravity approach and coalescence of fluid drops at interfaces. Can J Chem Eng, 41: 203–212. Mackay, G.D.M. and Mason, S.G., 1963b, Some effects of interfacial diffusion on the gravity coalescence of liquid drops. J Colloid Interf Sci, 18: 674–683. Marrucci, G., 1969, A theory of coalescence. Chem Eng Sci, 24: 975–985. Mcavoy, R.M. and Kintner, R.C., 1965, Approach of two identical rigid spheres in a liquid field. J Colloid Interf Sci, 20: 188–190. Nielsen, L.E., Wall, R. and Adams, G., 1958, Coalescence of liquid drops at oil–water interfaces. J Colloid Interf Sci, 13: 441– 458. Norato, M.A., Tsouris, C. and Tavlarides, L.L., 1998, Phase inversion studies in liquid–liquid dispersions. Can J Chem Eng, 76: 486–494. Reynolds, O., 1886, On the theory of lubrication and its application to Mr. Beauchamp Tower’s experiments, including an experimental determination of the viscosity of oil. Philos Trans R Soc London, 177: 157–234. Saboni, A., Gourdon, C. and Chesters, A.K., 1995, Drainage and rupture of partially mobile films during coalescence in liquid–liquid systems under a constant interaction force. J Colloid Interf Sci, 175: 27–35. Tadros, T.F., 1996, Correlation of viscoelastic properties of stable and flocculated suspensions with their interparticle interactions. Adv Colloid Interf Sci, 68: 97–200. Vrij, A. and Overbeek, J.T.G., 1968, Rupture of thin liquid films due to spontaneous fluctuations in thickness. J Am Chem Soc, 90: 3074–3078. Yang, H., Park, C.C., Hu, Y.T. and Leal, L.G., 2001, The coalescence of two equal-sized drops in a two-dimensional linear flow. Phys Fluids, 13: 1087–1106. Yeo, L.Y., Matar, O.K., Perez de Ortiz, E.S. and Hewitt, G.F., 2003, Film drainage between two surfactant-coated drops colliding at constant approach velocity. J Colloid Interf Sci, 257: 93–107. Zdravkov, A.N., Peters, G.W.M. and Meijier, H.E.H., 2003, Film drainage between two captive drops: PEO–water in silicon oil. J Colloid Interf Sci, 266: 195–201.