Electrical demulsification of oil-in-water emulsion

Colloids and Surfaces A: Physicochem. Eng. Aspects 302 (2007) 581–586

Electrical demulsification of oil-in-water emulsion Tsuneki Ichikawa ∗ Division of Materials Chemistry, Graduate School of Engineering, Hokkaido University, Sapporo 060-8628, Japan Received 10 January 2007; received in revised form 8 March 2007; accepted 19 March 2007 Available online 23 March 2007

Abstract Application of a weak external electric field destroys stable oil-in-water emulsions by accelerating the coalescence of oil droplets. The acceleration is induced by the reduction of repulsive double layer force due to electric field-induced migration of ions adsorbed on the surface of oil droplets. The potential energy for the front surfaces of the approaching two droplets is given by U=

εl κζ 2 e−κw 8(h + 1)



[4(h + 1) + 3h(a1 − a2 )E0 cos η/ζ]2 [3h(a1 + a2 )E0 cos η/ζ]2 − −κw h + 1 + (h − 1) e h + 1 − (h − 1) e−κw



−

AH 12πw2

where h = zs eζ(s+,0 + s−,0 )/[kT(s+,0 − s−,0 )], zs is the valence of surface ions, e the unit charge, s+,0 and s−,0 the number densities of positive and negative surface ions, kT the thermal energy at temperature T, εl the dielectric constant of water, κ the Debye reciprocal length, ζ the zeta potential, w the separation distance between the front surfaces of approaching two droplets with radii a1 and a2 , E0 the intensity of the external electric field, η the angle between the axis of approach and the external field, and AH is the Hamaker constant of the droplets, respectively. The above equation indicates that two oil droplets are coalesced into one droplet by applying the external electric field of

   2[zs eζ(s+,0 + s−,0 ) + kT (s+,0 − s−,0 )]    3zs e(s+,0 + s−,0 )a

|E0 | ≥ 

where a is the radius of the larger droplet. © 2007 Elsevier B.V. All rights reserved. Keywords: Electrical demulsification; Oil-in-water emulsion; DLVO theory; Double layer potential; Coalescence; Surface charge migration

1. Introduction Emulsion systems have been widely used in our daily life as foods, cosmetics, medicines and so on. Emulsions are divided into two types, oil-in-water and water-in-oil. Three types of forces are known to prevent the destruction of oil-in-water emulsions by the coalescence of the oil droplets. They are the electrical double layer force acting between electrically charged oil droplets [1,2], the short-range hydration force acting between hydrated oil surfaces [3,4], and the steric force acting between oil surfaces adsorbing macromolecules [5,6]. The double layer force is generated by the overlap of diffuse electric double layers of adjacent droplets and is the most fundamental force for stabilizing charged oil droplets in water. The energy barrier pre-

∗

Tel.: +81 11 706 6747; fax: +81 11 706 7897. E-mail address: [email protected].

0927-7757/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.colsurfa.2007.03.036

venting the coagulation of two charged droplets is estimated by the DLVO theory [1,2]. According to the theory, the barrier height is determined by the attractive van der Waals force and the repulsive double layer force that is composed of the attractive Maxwell’s electric field stress and the repulsive osmotic pressure. The strength of the double layer force is determined by the concentration of ions in water and the surface charge densities of adjacent droplets. Although the DLVO theory is a fundamental theory for explaining the stability of charged particles in water, except for our recent work [7], the theory has not been strictly applied to oilin-water emulsions. The approach of two charged oil droplets closer than the thickness of the double layers causes electrostatic interactions between the two surfaces, which results in the migration of ions adsorbed on the surfaces. The double layer force should therefore be determined by taking the change of the surface charge densities and the surface electrostatic potentials into account. However, the force has been generally estimated by

582

T. Ichikawa / Colloids and Surfaces A: Physicochem. Eng. Aspects 302 (2007) 581–586

assuming either the surface electrostatic potentials are constant [8] or the surface charge densities are constant [9,10]. The migration of surface ions under an electrostatic field plays a crucial role in the external electric field-induced destruction of oil-in-water emulsions. Formation of emulsions is troublesome in solvent extraction processes since the processes are stopped until the emulsions are separated into oil and water. To find an efficient method of demulsification without contaminating the systems has therefore been expected. We have recently found that dense oil-in-water emulsions are demulsified very quickly by applying a low electric field of less than 10 V/cm [11,12]. Based on the experimental and theoretical analyses of this new phenomenon, we have concluded that the applied field induces the rearrangement of surface ions on each oil droplet to compensate the external field-induced potential gradient, which causes the polarization of surface electrostatic potentials and therefore results in the hetero-coagulation and coalescence of oil droplets in homogeneous emulsion systems. However, the theory developed in Ref. [12] is still imperfect. The distributions of surface charges on approaching two charged droplets under the external electric field should be determined by the external field and the surface charges of adjacent droplets, though the latter effect has not been included in the theory. Here we will rebuild the theory by taking the both effects into account. 2. Theory 2.1. Isolated oil droplet We treat an emulsion system composed of oil droplets adsorbing positive and negative ions with the valences ±zs and the average surface number densities s±,0 , respectively, in water dissolving positive and negative ions with the valences ±z and the average number density c0 . The radii of the droplets a are much longer than the thickness of diffuse electric double layers generated at the interface of the solution and the charged surfaces. Although the spatial distribution of ions around the droplets under an external electric field cannot be given by the static Boltzmann distribution, since the external field induces the continuous flow of ions and therefore changes the static distribution of ions, the detailed theoretical analysis has revealed that the external field affects the distribution only through the change of the surface charge density, unless the intensity of the external field exceeds 104 V/cm [12]. The electrostatic potential φ in the solution is then given by the following Poisson–Boltzmann equation: ∇ 2 φ − κ2 φ = 0 where  κ=

2c0 z2 e2 εl kT

(1)

(2)

is the Debye reciprocal length, e the unit charge, kT the thermal energy at temperature T, and εl is the dielectric constant of the solution. The Debye–H¨uckel approximation of sinh(zeφ/kT) = zeφ/kT has been used in Eq. (1). The second term

Fig. 1. Coordinate used for the calculation of double layer force acting between two charged oil droplets in water.

in the left side of Eq. (1) attenuates the electrostatic potential by shielding it with ions in water. The electrostatic potential on the surface of the oil droplet is related to the surface charge density through the boundary condition of     ∂φi ∂φ ∂φ zs e(s+ − s− ) = εi ≈ − εl (3) − εl ∂n ∂n surface ∂n surface where s+ and s− are the number densities of positive and negative surface ions, n the normal to the surface, and φi and εi are the electrostatic potential and the dielectric constant in the droplet. The εi ∂φi /∂n term in Eq. (3) is negligible, since εl is usually much higher than εi and, because of the shielding of electric field by ions in water, ∂φ/∂n is much larger than ∂φi /∂n. The Poisson–Boltzmann equation under the polar coordinate shown in Fig. 1 is expressed as   1 ∂2 ∂φ 1 ∂ sin θ = κ2 φ (rφ) + (4) r ∂r 2 r 2 sin θ ∂θ ∂θ Using the relation of ∂φ/∂r  ∂φ/∂θ, the solution of Eq. (4) for a droplet of radius a is given by φ ≈ φs

a e−κ(r−a) r

(5)

where φs is the electrostatic potential on the surface arising from adsorbed surface ions. Eq. (5) is practically the same as the exact solution of the Poisson–Smoluchowski equation [12] as long as E0  104 V/cm. Substitution of Eq. (5) into Eq. (3) gives zs e(s+ − s− ) ≈ εl κφs

(6)

Here the relation of κa  1 has been used. The distribution of surface ions is given by the Boltzmann distribution under the electrostatic field arising from the surface ions and an external electric field E0 . Eq. (6) is then expressed as    zs e(φs − Ea cos θ) zs e S+ exp − kT   zs e(φs − Ea cos θ) − S− exp (7) = εl κφs kT

T. Ichikawa / Colloids and Surfaces A: Physicochem. Eng. Aspects 302 (2007) 581–586

Here Ea cos θ is the intensity of the electrostatic potential generated on the surface by the external field, that is defined by Ea cos θ =

3εl E0 3E0 a cos θ ≈ a cos θ εi + 2εl 2

It is convenient to rewrite Eq. (7) as  ze s G+ exp − (φs − ζ − Ea cos θ) kT z e ε κφ s l s − G− exp (φs − ζ − Ea cos θ) = kT zs e

(8)

(9) and (11). The surface potentials are linearly dependent on the external field, which indicates that Eq. (9) can be approximated as a linear function of Ea cosθ. Using the approximation of exp[±zs e(φs − ζ − Ea cos θ)/ kT] ≈ 1 ± zs e(φs − ζ −Ea cos θ)/kT, Eq. (9) gives φs =

(9)

where ζ is the surface electrostatic potential under no external electric field that is related to the average surface charge density as zs e(s+,0 − s−,0 ) ζ= (10) εl κ ζ is approximately the same as the zeta potential of the droplet. The constants G+ and G− are determined from the conservation of the total numbers of positive and negative ions, respectively:

1  ze s 4πa2 s+,0 = 2πa2 G+ exp − (φs − ζ − Eacosθ) d cos θ, kT −1

1 z e s 4πa2 s−,0 =2πa2 G− exp (φs − ζ−Ea cos θ) d cos θ kT −1 (11) The surface electrostatic potential under the external field is obtained by solving Eq. (9) numerically under the normalization conditions of Eq. (11). The advantage of using Eq. (9) instead of Eq. (7) is that the exponents become close to zero, so that the accurate numerical calculation can be achieved without using small cos θ increment. Fig. 2 shows the surface electrostatic potentials of the isolated droplet at θ = 0 that are obtained as numerical solutions of Eqs.

(G+ − G− ) + (G+ + G− )(zs e/kT )(ς + Ea cos θ) (12) (εl κ/zs e) + (G+ + G− )(zs e/kT )

Using the relation of ζ = zs e(s+,0 − s−,0 )/εl κ and the approximation of exp[±zs e(φs − ζ − Ea cos θ)/kT] ≈ 1 ± zs e(φs − ζ − Ea cos θ)/kT, substitution of Eq. (12) into Eq. (11) gives G+ = s+,0 ,

G− = s−,0

(13)

which leads to φs = ζ +

h Ea cos θ 1+h

(14)

where h=

zs eζ s+,0 + s−,0 kT s+,0 − s−,0

(15)

As shown in Fig. 2 the values of electrostatic potentials obtained from Eq. (14) are in good agreement with the exact ones. 2.2. DLVO theory under external electric field Since the approach of two oil droplets deforms the droplets, the shape of the droplets are no more spherical. However, since the sizes of the droplets are generally much larger than the thickness of the double layers, 1/κ, the front surfaces of the droplets to be attached at first can be regarded as two parallel planar plates separated by distance w, no matter whether the droplets are spherical or not. According to the DLVO theory, the force acting between charged particles in water is given as a sum of the double layer force and the van der Waals force. The double layer force acting between the front surfaces of approaching two charged droplets is obtained by solving the Poisson–Boltzmann equation for two parallel plates along the axis of approach (θ = 0). The solution of the Poisson–Boltzmann equation under the Debye–H¨uckel approximation is then given by φ = C e−κx + D eκ(x−w)

Fig. 2. Effect of electric field E on the surface electrostatic potential φ1 at θ = 0 of charged oil droplet. ζ and a are the zeta potential and the radius of the droplet, respectively; s+,0 :s−,0 , the ratio of the average number densities of positive and negative surface ions with valences ±zs . The thick straight lines show the approximate values obtained from Eq. (14).

583

(16)

Although the approach of the two droplets modifies the surface charge distribution, the effect is limited within a very small region where the double layers overlap with each other. The constants G+ and G− are thereby scarcely changed by the overlap of the double layers, and the boundary conditions at the front surfaces of the two droplets are given by  ze εl κ s (C − D e−κw )=s+,0 exp − (C + D e−κw − ζ − Ea1 ) zs e kT z e s − s−,0 exp (17) (C + D e−κw − ζ − Ea1 ) kT

584

T. Ichikawa / Colloids and Surfaces A: Physicochem. Eng. Aspects 302 (2007) 581–586

 ze εl κ s (D − C e−κw )=s+,0 exp − (C e−κw + D − ζ + Ea2 ) zs e kT z e s −κw −s−,0 exp + D − ζ + Ea2 ) (18) (C e kT Using the approximation of exp[±zs e(φs − ζ ± Ea)/kT] ≈ 1 ± zs e(φs − ζ ± Ea)/kT, the above equations give the solutions of C=

(h + 1)a1 +(h − 1)a2 e−κw (h + 1)ζ + hE (h + 1) + (h − 1) e−κw (h + 1)2 − (h − 1)2 e−2κw (19)

D=

(h + 1)ζ (h − 1)a1 e−κw + (h + 1)a2 − hE (h + 1) + (h − 1) e−κw (h + 1)2 − (h − 1)2 e−2κw (20)

The double layer force P is given as a sum of the Maxwell’s electric field stress and the osmotic pressure as         εl dφ 2 zeφ zeφ P= − +exp − −2 +kTc0 exp − 2 dx kT kT (21) Since the double layer force is the same everywhere between x = 0 and x = w, by taking x = 0, the force is expressed as  −κw )  εl κ2 −κw 2 2 ze(C + D e ] +4kTc0 sinh [C−D e P= − 2 2kT (22) Application of the Debye–H¨uckel approximation of sinh(zeφ/ kT) = zeφ/kT to Eq. (22) gives   (h + 1)ς + h(a1 − a2 )(E/2) 2 2 −κw P = 2εl κ e (h + 1) + (h − 1) e−κw 2  h(a1 + a2 )(E/2) (23) − (h + 1) − (h − 1) e−κw which is rewritten as P=

[(h + 1)ζ−ha2 E][(h + 1)ζ + ha1 E][2εl κ2 e−κw (h − 1)2 ] [(h + 1) + (h − 1) e−κw ]2 [(h + 1) − (h − 1) e−κw ]2   (h + 1)[(h + 1)ζ + ha1 E] −κw × −e (h − 1)[(h + 1)ζ − ha2 E]   (h + 1)[(h + 1)ζ − ha2 E] × (24) − e−κw (h − 1)[(h + 1)ζ + ha1 E]

Analysis of Eq. (24) under the condition of h > 1 reveals that the double layer force is always attractive as long as a2 E/ζ > 1 + 1/h. Since |ζ| > 25 mV and therefore h > 1 for most of emulsion systems stabilized by the double layer force, the critical external electric field for inducing the coagulation and coalescence of two spheres is given by    2[zs eζ(s+,0 + s−,0 ) + kT (s+,0 − s−,0 )]    (25) |E0 | ≥   3zs e(s+,0 + s−,0 )a

Fig. 3. Double layer potential for front surfaces of two charged oil droplets under an external electric field E0 . w, κ, εl , ζ and a are the separation distance of the surfaces, the Debye–H¨uckel reciprocal length, the dielectric constant, the zeta potential, and the radius of the droplets, respectively.

where a is the radius of larger droplet. Addition of large oil droplets to an emulsion system composed of tiny oil droplets is therefore very effective for destroying the system by a low external electric field. Integration of Eq. (23) gives the double layer potential of

εl κζ 2 e−κw [4(h + 1) + 3h(a1 − a2 )E0 /ζ]2 UD = 8(h + 1) [h + 1 + (h − 1) e−κw ]  [3h(a1 + a2 )E0 /ζ]2 − (26) [h + 1 − (h − 1) e−κw ] It is noted that substitution of E0 = 0 into Eq. (26) gives the double layer potential under no external field that has been obtained in the previous paper [7]. Fig. 3 shows the double layer potential as a function of the separation distance. The double layer potential changes to an attractive one, once E0 exceeds 2(1 + 1/h)ζ/3a. For more general case that the axis of approach is declined at angle η from the external electric field, the double layer potential is obtained from Eq. (26) simply by replacing E0 with E0 cos η. The total potential energy including the van der Waals energy is finally given by

εl κζ 2 e−κw [4(h + 1) + 3h(a1 − a2 )E0 cos η/ζ]2 U= 8(h + 1) h + 1 + (h − 1) e−κw  AH [3h(a1 + a2 )E0 cos η/ζ]2 − − (27) −κw h + 1 − (h − 1) e 12πw2 where AH is the Hamaker constant [13]. Fig. 4 shows the shape of the potential barrier between the front surfaces of two identical droplets. The external electric field significantly reduces the height of the barrier. The barrier disappears at 3aE/2ζ = 1 + 1/h, which indicates that the van der Waals force scarcely affects the electrical demulsification.

T. Ichikawa / Colloids and Surfaces A: Physicochem. Eng. Aspects 302 (2007) 581–586

Fig. 4. Potential energy barrier between front surfaces of approaching two identical oil droplets. w, κ, ζ and a are the separation distance of two spheres, the Debye–H¨uckel reciprocal length, the electrostatic potential of the isolated spheres, and the radius of the spheres, respectively. Parameters used for the calculations areζ = −60 mV, kT = 4.1 × 10−21 J, κ = 4.6 × 107 m−1 , s+,0 = 0, z = zs = 1, εl = 80ε0 , η = 0 and AH = 5 × 10−21 J.

The total potential energy for two charged droplets can be obtained by dividing the surfaces of the particles with tiny parallel plates and applying Eq. (27) to each segment [14]. 3. Comparison with experimental data Fig. 5 shows the effect of external electric field on the stability of oil-in-water emulsion that is prepared by shaking 3:2 mixture of oil (1:1 mixture of benzyl alcohol and tetrahydropyran) and water (containing 2 × 10−4 mol/dm3 of sodium 2-naphthyl sulfonate as a surfactant) in a separatory funnel more than 100 times. The emulsion layer thus prepared has a lifetime of more than 1 h. Application of an external electric field higher than 4 V/cm shorten the lifetime to less than 20 s. The acceleration of demulsification is never observed on the water-in-oil emulsion that is occasionally prepared by increasing the water content more than 1:1. The acceleration is induced neither by electrophoresis nor electrolysis, since the fusion of the droplets takes place not only near the electrodes but everywhere in the emulsion layer [11].

585

Fig. 5. Effect of external electric field on the lifetime of oil-in-water emulsion.

The emulsion used for the electrical demulsification is characterized by ζ = −60 mV, T = 298 K, s+,0 = 0, εl = 80ε0 , c0 = 2 × 10−4 mol/dm3 , a = 25–30 ␮m and AH = 5 × 10−21 J [15]. Substitution of these values and E0 = 4 V/cm into Eq. (25) gives the radius of a = 140 ␮m. Although the droplets with a > 140 ␮m are scarcely observed on the microscope image, a small number of droplets with a > 140 ␮m may act as seed droplets for the demulsification. The electrical demulsification is accelerated once the coalescence starts, since the external field-induced coalescence is more effective for larger droplets. Fig. 6 depicts the mechanism of electrical demulsification. Surface ions migrate under an external electric field in such a way to minimize the difference of the electrostatic potential induced by the external field. The surface charge density is therefore the lowest at the right surface of the largest droplet perpendicular to the external field. Since the height of potential energy barrier decreases with decreasing surface charge density, a small droplet adjacent to the surface with the lowest surface charge density is absorbed at first by the largest droplet. Absorption of the droplet increases the volume of the largest droplet, so that the charge density on the right surface of the largest droplet is further lowered. Lowering of the surface charge density lowers the barrier, and causes the acceleration of the coalescence. The external electric field thus breaks the emulsion.

Fig. 6. Schematic representation of the mechanism of electrical demulsification.

586

T. Ichikawa / Colloids and Surfaces A: Physicochem. Eng. Aspects 302 (2007) 581–586

4. Conclusion It has been shown that the migration of ions adsorbed on the surface of oil droplets in water plays a significant role in the stability of oil-in-water emulsions under external electric fields. The mathematical expression of the potential energy barrier preventing the coalescence of charged oil droplets has been obtained as a function of the external field by solving the Poisson–Boltzmann equations for ions in water and on the surfaces of the droplets. The potential energy barrier between the front surfaces of two oil droplets is expressed as a sum of the double layer potential and the van der Waals potential:

εl κζ 2 e−κw [4(h + 1) + 3h(a1 − a2 )E0 cos η/ζ]2 U= 8(h + 1) h + 1 + (h − 1) e−κw  AH [3h(a1 + a2 )E0 cos η/ζ]2 − − −κw h + 1 − (h − 1) e 12πw2 respectively, where h = zs eζ(s+,0 + s−,0 )/[kT(s+,0 − s−,0 )], zs is the valence of surface ions, e the unit charge, s+,0 and s−,0 the number densities of positive and negative surface ions; kT, the thermal energy at temperature T, εl the dielectric constant of water, κ the Debye reciprocal length, ζ the zeta potential, w the separation distance between the front surfaces of approaching two droplets with radii a1 and a2 , E0 the intensity of the external electric field, η the angle between the axis of approach and the external field, and AH is the Hamaker constant of the

droplets, respectively. Although the double layer potential under no external electric field prevents the coalescence of oil droplets, the double layer potential assists the coalescence if the external electric field is strong enough to satisfy the condition of    2[zs eζ(s+,0 + s−,0 ) + kT (s+,0 − s−,0 )]    |E0 | ≥   3zs e(s+,0 + s−,0 )a where a is the radius of larger droplet. The emulsion system is thereby destroyed by the external electric field. References [1] B.V. Derjaguin, L.D. Landau, Acta Physicochim. U.S.S.R. 14 (1941) 633. [2] E.J.W. Verway, J.T.G. Overbeek, Theory of the Stability of Lyophobic Colloids, Elsevier, Amsterdam, 1948. [3] B.V. Derjaguin, N.V. Churaev, M.V. Muller, Surface Forces, Plenum, New York, 1987. [4] M. Manciu, E. Ruckenstein, Langmuir 17 (2001) 7061. [5] R. Evans, D.H. Napper, J. Colloid Interf. Sci. 52 (1975) 260. [6] E.J. Clayfield, E.C. Lumb, J. Colloid Interf. Sci. 22 (1966) 269. [7] T. Ichikawa, T. Dohda, Y. Nakajima, Coilloids Surf. A 279 (2006) 128. [8] R. Hogg, T.W. Healy, D.W. Fuerstenau, Trans. Faraday Soc. 62 (1966) 1638. [9] J. Gregory, J. Chem. Soc., Faraday II 69 (1973) 1723. [10] J. Gregory, J. Colloid Interf. Sci. 51 (1974) 44. [11] T. Ichikawa, K. Itoh, S. Yamamoto, M. Sumita, Colloids Surf. A 242 (2004) 21. [12] T. Ichikawa, Y. Nakajima, Colloids Surf. A 242 (2004) 27. [13] H.C. Hamaker, Physica 4 (1937) 1058. [14] B.V. Deryagin, Kolloid Z. 69 (1934) 155. [15] J. Gregory, Adv. Colloid Interf. Sci. 2 (1970) 396.