Diffusiophoresis of Liquid Droplets and Gas Bubbles

Chapter 17

Diffusiophoresis of Liquid Droplets and Gas Bubbles

17.1 INTRODUCTION Compared with the rigid particles considered in Chapter 16, diffusiophoretic motion of a liquid droplet or a gas bubble is faster. In general, the role of the mobile droplet or bubble surface is similar to the corresponding electrophoresis of droplets or bubbles [1–4] in terms of the generation of a motionenhancing electroosmotic flow, which can also be analogized as an effective excess surface conductivity. This increase is drastic when ka is large due to the double layer suppression effect. The only question here is by what extent this increase is. As for its applications, essentially all the systems discussed in Chapter 12 for the electrophoresis of liquid droplet and gas bubble systems are also possible stages for diffusiophoresis. In practice, however, it is the biosystems such as the human stem cells or other mammal cells encountered in various situations in biochemical and biomedical fields that are particularly of interest [5–8]. Certainly, it would not be a good idea in general to apply a measurable electric field constantly and maybe over a long time upon a living biosystem, such as the human body. Diffusiophoresis, on the other hand, does not have this adverse impact upon biosystems. All one needs to do is to establish a concentration gradient of electrolytes to guide the motion of the droplet, or simply let nature take over. For instance, extraction of cells or droplet type of substances from a microcavity can be easily done with a constant flow of electrolyte solution passing over the entrance to the microcavity [9–11]. A concentration gradient is thus established across the longitudinal direction of the pore interior, which drives the droplet type of colloidal entities out from the dead end pore, as we introduced in Chapter 16. Moreover, the application in extracting surfactant-covered oil droplets from an oil-rich porous reservoir in the technology of the enhanced oil recovery [12] is very obvious. With the injection of electrolyte solution to the system, preferably the one which can result in large droplet velocity by establishing a large diffusion potential Interface Science and Technology, Vol. 26. https://doi.org/10.1016/B978-0-08-100865-2.00017-5 © 2019 Elsevier Ltd. All rights reserved.

359

360 SECTION

D Diffusiophoresis of Colloidal Particles

spontaneously, i.e., large b, the production rate of oil can be drastically increased. The mechanism is essentially the same as those mentioned above in the dead-end-pore type of application for cells, where conventional pressure-driven type of flow is proven to fail in terms of providing the driving force for the desired droplet motion [10, 11, 13–16]. Moreover, nanoemulsion and microemulsion are very promising drug delivery systems in biomedical applications due to their various merits, such as better thermodynamic stability, optical clarity, and ease of preparation [17–26]. Optimum targeted drug delivery can be achieved in principle with these nano-reservoir systems by diffusiophoresis, if some specific chemicals are released from the injury wound or infected area [27–30]. A concentration gradient would be thus established in its neighborhood, which provides the guiding signal as well as the driving force for the diffusiophoretic motion of the drug-carrying nanoemulsions. It functions like the detection and remedy of the bone-crack case by rigid quantum dots introduced in Chapter 16 [31], but here the liquid droplets of nanoemulsions or microemulsions carry the workload instead. Here, in this chapter, we focus on a sample liquid droplet system with viscosity ratio sH ¼ 0.5 as well as a gas bubble system with sH ¼ 0.01, as we did in Chapter 12 for the electrophoresis situation. The results are provided in Section 17.3.

17.2 THEORY The system diagrams for a single droplet or a gas bubble and their suspensions are shown in Fig. 17.1A and B, respectively. Note that both the governing equations and associated boundary conditions on the droplet or bubble surface are the same as those in Chapter 12 where electrophoresis is considered. The only difference is the boundary conditions at infinity or the outer virtual surface in the cell model selected, which is again the same as those selected in Chapter 12. Hence, simply replace the boundary conditions there in Chapter 12 by those in Chapter 16 where a concentration gradient is applied and we are done.

17.3 RESULTS AND DISCUSSION We examine the chemiphoresis component first, i.e., b ¼ 0. Fig. 17.2A and B show the corresponding general Henry’s charts in diffusiophoresis for a sample liquid droplet with sH ¼ 0.5 in a KCl electrolyte solution, i.e., b ¼ 0, or only the chemiphoresis component is considered. As shown in Fig. 17.2A for a close-up view of the mobility profiles when ka is relatively small, the droplet mobility increases with increasing ka in general. For a highly charged droplet (fr ¼ 5), the behavior is kind of different

Diffusiophoresis of Liquid Droplets and Gas Bubbles Chapter

17 361

z U r ÑC q a

j

x

y

(A) z U

r

ÑC q

b

a

x

j

y

(B) FIG 17.1 System diagram. (A) Single liquid droplet or gas bubble; (B) suspension of liquid droplets or gas bubbles.

362 SECTION

D Diffusiophoresis of Colloidal Particles

1

fr = 1 0.8

fr = 2 fr = 3

0.6

m*

fr = 4 fr = 5

0.4

0.2

(A)

0 –2 10

10

–1

10

0

ka

1

10

1

10

10

2

30

25

fr = 1 fr = 2

20

m*

fr = 3 15

fr = 4 fr = 5

10

5

(B)

0 –2 10

10

–1

10

0

ka

10

2

FIG. 17.2 Dimensionless mobility m as a function of ka at various fr with sH ¼ 0.5 (b ¼ 0). (A) Small scale; (B) large scale.

from the rest, but the trend is still the same. Global view shown in Fig. 17.2B indicates the large droplet mobility when ka is around 100. This behavior of drastic mobility increase when ka is large is similar to the corresponding electrophoresis phenomenon observed in Chapter 12.

17 363

Diffusiophoresis of Liquid Droplets and Gas Bubbles Chapter 1

fr = 1 0.8

fr = 2 fr = 3

0.6

m*

fr = 4 fr = 5

0.4

0.2

(A)

0 –2 10

10

–1

10

0

ka

1

10

1

10

10

2

35 30

fr = 1 fr = 2

25

fr = 3

20

m*

fr = 4 15

fr = 5

10 5

(B)

0 –2 10

10

–1

10

0

ka

10

2

FIG. 17.3 Dimensionless mobility m as a function of ka at various fr with sH ¼ 0.01 (b ¼ 0). (A) Small scale; (B) large scale.

Corresponding charts for the gas bubble (sH ¼ 0.01) are presented in Fig. 17.3A and B. The behavior is essentially the same as the liquid droplet (sH ¼ 0.5) considered above, except that the mobility is larger due to the smaller hydrodynamic drag force as well as the larger electric driving force, which

364 SECTION

D Diffusiophoresis of Colloidal Particles

is due to the faster velocity on the mobile surface as discussed in Chapter 12 for electrophoresis. Apparently, the basic scenario remains the same here. The effect of droplet viscosity is shown in Fig. 17.4A–C, where the droplet mobility is expressed as a function of sH, the viscosity ratio of the droplet to the suspending medium, for various charge levels (fr ranging from 1 to 5) at three different double layer thickness (ka ¼ 0.1, 1, and 10). In general, the larger sH is, the slower the particle moves, regardless of the double layer thickness. Moreover, mobility ratio to the corresponding rigid particle is presented in Fig. 17.5A–C to highlight the physical sense underlying it. Over 15 times faster motion is observed in Fig. 17.5C for a gas bubble (sH ¼ 0.01). Note that this is due to the joint effect of lower hydrodynamic drag force and larger electric driving force, as discussed in Chapter 12 for electrophoresis. Note that for sH ¼ 100, the droplet mobility reduces to the rigid particle situation. Fig. 17.6A presents the particle mobility as a function of surface charge fr for the sample liquid droplet (sH ¼ 0.5) at various double layer thickness (ka ¼ 1, 2, 5, and 10). Rigid particle situation is shown as well for comparison purpose. Other than larger mobility for a droplet, the behavior is essentially the same as the rigid particle system. The higher ka is, the larger the droplet mobility is. Moreover, a highly charged droplet may move slower than a lowly charged one with two local maxima in each profile. The profiles are symmetric with the vertical axis fr ¼ 0. Corresponding profiles of a gas bubble are shown in Fig. 17.6B. We now go on to examine the general case with the involvement of the electrophoresis component, i.e., b 6¼ 0. Figs. 17.7–17.11 show the overall results with the particles suspended in a NaCl solution, i.e., b ¼  0.2. Really, the general behavior is similar to the observation in Chapter 16 for the rigid particle situation, except with larger mobility for the sample liquid system (sH ¼ 0.5) and gas bubble (sH ¼ 0.01). No further comments are needed as these figures are self-explanatory. They are presented here as they provide various original information about the diffusiophoresis phenomenon, which still remains as an unfamiliar novelty to most people, especially the behavior of highly charged liquid droplets and gas bubbles. These figures shed light on the mysterious diffusiophoretic motion of liquid droplet and gas bubble systems. With their help, we now know what an elephant really looks like. The impact of the b factor is shown in Fig. 17.12 for a representative liquid droplet (sH ¼ 0.5) and a gas bubble (sH ¼ 0.01), respectively. Again, these figures are self-explanatory with general behavior similar to the rigid particle systems treated in Chapter 16. We now go on to examine the diffusiophoretic motion of liquid droplets and gas bubbles in suspensions. The results are shown in Figs. 17.13–17.16 for either sole chemiphoresis component (b ¼ 0) or with an extra involvement of the electrophoresis component as well (b ¼  0.2). Again, the general behavior is similar to the rigid particle situation in Chapter 16, except with larger mobility. The intriguing phenomenon is still observed that a liquid droplet or a gas bubble may move faster in a concentrated suspension than in a dilute one over

17 365

Diffusiophoresis of Liquid Droplets and Gas Bubbles Chapter 0.15

fr = 1 fr = 2 fr = 3 fr = 4

0.1

m*

fr = 5

0.05

(A)

0 –2 10

10

–1

10

0

sH

10

1

10

2

0.35

fr = 1

0.3

fr = 2 0.25

fr = 3 fr = 4

m*

0.2

fr = 5

0.15 0.1 0.05

(B)

0 –2 10

10

–1

10

0

sH



10

1

10

2

FIG. 17.4 Dimensionless mobility m as a function of sH at various fr (b ¼ 0). (A) ka ¼ 0.1; (B) ka ¼ 1; (C) ka ¼ 10.

366 SECTION

D Diffusiophoresis of Colloidal Particles

3

fr = 1 fr = 2

2.5

fr = 3

m*

2

fr = 4 fr = 5

1.5

1

0.5

0 –2 10

10

–1

10

0

10

1

10

2

sH

(C) FIG. 17.4—CONT’D

2

fr = 1

m *(droplet) / m *(rigid)

1.8

fr = 2 fr = 3

1.6

fr = 4 fr = 5

1.4

1.2

1 –2 10

(A)

10

–1

10

0

10

1

10

2

sH

FIG. 17.5 Mobility ratio m (droplet)/m (rigid) as a function of sH at various fr (b ¼ 0). (A) ka ¼ 0.1; (B) ka ¼ 1; (C) ka ¼ 10.

17 367

Diffusiophoresis of Liquid Droplets and Gas Bubbles Chapter

m *(droplet) / m *(rigid)

6 5.5

fr = 1

5

fr = 2

4.5

fr = 3

4

fr = 4

3.5

fr = 5

3 2.5 2 1.5

(B)

1 –2 10

10

–1

10

0

sH

10

1

10

2

16

fr = 1

14

m *(droplet) / m *(rigid)

fr = 2 12

fr = 3

10

fr = 4

8

fr = 5

6 4 2 0 –2 10

(C) FIG. 17.5—CONT’D

10

–1

10

sH

0

10

1

10

2

368 SECTION

D Diffusiophoresis of Colloidal Particles

2.5 ka = 1 ka = 2

2

ka = 5 k a = 10

m*

1.5

1

0.5

0 –6

(A)

–4

–2

0

2

4

6

4

6

fr 3

ka = 1 ka = 2 ka = 5 k a = 10

2.5

m*

2

1.5

1

0.5

0 –6

(B)

–4

–2

0

2

fr

FIG. 17.6 Dimensionless mobility m as a function of fr at various ka (b ¼ 0). (A) sH ¼ 0.5; (B) sH ¼ 0.01.

17 369

Diffusiophoresis of Liquid Droplets and Gas Bubbles Chapter 1

fr = 1 fr = 2 fr = 3

0.5

fr = 4

m*

fr = 5 0

–0.5

(A)

–1 –2 10

10

–1

10

0

ka

10

1

10

2

15

fr = 1 fr = 2

10

fr = 3

m*

fr = 4 fr = 5

5

0

(B)

–5 –2 10

10

–1

10

0

ka

10

1

10

2

FIG. 17.7 Dimensionless mobility m as a function of ka at various fr with sH ¼ 0.5 (b ¼  0.2). (A) Small scale; (B) large scale.

370 SECTION

D Diffusiophoresis of Colloidal Particles

1

fr = 1 fr = 2 0.5

fr = 3 fr = 4

m*

fr = 5 0

–0.5

–1 –2 10

(A)

10

–1

10

0

ka

10

1

10

2

15

fr = 1 10

fr = 2

m*

fr = 3 fr = 4

5

fr = 5

0

–5 –2 10

(B)

10

–1

10

0

ka

10

1

10

2

FIG. 17.8 Dimensionless mobility m as a function of ka at various fr with sH ¼ 0.01 (b ¼  0.2). (A) Small scale; (B) large scale.

17 371

Diffusiophoresis of Liquid Droplets and Gas Bubbles Chapter 0 –0.1 –0.2 –0.3

m*

–0.4 –0.5 –0.6

fr = 1

–0.7

fr = 2 fr = 3

–0.8

fr = 4

–0.9 –1 –2 10

fr = 5 10

–1

10

0

10

1

10

2

1

10

sH

(A) 0

fr = 1 fr = 2 fr = 3

–0.1

fr = 4 fr = 5 m*

–0.2

–0.3

–0.4

–0.5 –2 10

10

–1

10

0

10

2

sH

(B) 

FIG. 17.9 Dimensionless mobility m as a function of sH at various fr (b ¼ 0.2). (A) ka ¼ 0.1; (B) ka ¼ 1; (C) ka ¼ 10.

372 SECTION

D Diffusiophoresis of Colloidal Particles

1.5

fr = 1 fr = 2 fr = 3

1

fr = 4 fr = 5 m*

0.5

0

–0.5 –2 10

10

–1

10

0

10

1

10

2

sH

(C) FIG. 17.9—CONT’D

1.6

fr = 1

m *(droplet) / m *(rigid)

1.5

fr = 2 1.4

fr = 3 fr = 4

1.3

fr = 5 1.2

1.1

1 –2 10

10

–1

10

0

10

1

10

2

sH

(A) 



FIG. 17.10 Mobility ratio m (droplet)/m (rigid) as a function of sH at various fr (b ¼ 0.2). (A) ka ¼ 0.1; (B) ka ¼ 1; (C) ka ¼ 10.

17 373

Diffusiophoresis of Liquid Droplets and Gas Bubbles Chapter 2

fr = 1

m *(droplet) / m *(rigid)

fr = 2 fr = 3

1.5

fr = 4 fr = 5

1

0.5 –2 10

10

–1

10

0

10

1

10

2

sH

(B) 4 2

m *(droplet) / m *(rigid)

0 –2 –4

fr = 1

–6

fr = 2

–8

fr = 3

–10

fr = 4

–12 –14 –2 10

(C) FIG. 17.10—CONT’D

fr = 5 10

–1

10

0

sH

10

1

10

2

374 SECTION

D Diffusiophoresis of Colloidal Particles

1

m*

0.5

0

s H = 0.01 s H = 0.1 sH = 1

–0.5

s H = 100 Rigid –1

–5

0

5

fr

FIG. 17.11 Dimensionless mobility m as a function of fr at various sH with ka ¼ 1 (b ¼ 0.2).

10

NaOH ( b = – 0.596) KOH (b = – 0.459) NaCl (b = – 0.2) KCl ( b = 0)

5

HCl ( b = 0.65)

m*

H 2CO 3 ( b = 0.789)

0

(A)

–5 –2 10

10

–1

10

0

ka

10

1

10

2

FIG. 17.12 Dimensionless mobility m as a function of ka at various b with fr ¼ 3. (A) sH ¼ 0.5; (B) sH ¼ 0.01.

17 375

Diffusiophoresis of Liquid Droplets and Gas Bubbles Chapter 10

NaOH ( b = – 0.596) KOH (b = – 0.459) NaCl (b = – 0.2) KCl ( b = 0) 5

HCl ( b = 0.65)

m*

H2 CO3 ( b = 0.789)

0

–5 –2 10

10

–1

10

0

10

1

10

2

ka

(B) FIG. 17.12—CONT’D 0.5 Single 0.4

H = 10–6 H = 10

m*

0.3

–3

H = 0.01 H = 0.1 H = 0.4

0.2

0.1

(A)

0 –2 10

10

–1

ka

10

0

10

1

FIG. 17.13 Dimensionless mobility m as a function of ka at various H with sH ¼ 0.5 (b ¼ 0). (A) fr ¼ 1 (linear scale); (B) fr ¼ 1 (log scale); (C) fr ¼ 3 (linear scale); (D) fr ¼ 3 (log scale); (E) fr ¼ 5 (linear scale); (F) fr ¼ 5 (log scale).

376 SECTION 10

D Diffusiophoresis of Colloidal Particles

1

100 –1

10

–2

m*

10

10 10

–3

Single H = 10–6 H = 10

–4

H = 0.01 H = 0.1

10–5 10

–3

H = 0.4

–6

10

–2

10

–1

10

0

10

1

10

2

ka

(B) 3

Single

2

H = 10

–6

H = 10

–3

m*

H = 0.01 H = 0.1 1

(C)

0 –2 10

FIG. 17.13—CONT’D

H = 0.4

10

–1

ka

10

0

10

1

17 377

m*

Diffusiophoresis of Liquid Droplets and Gas Bubbles Chapter

10

2

10

1

10

0

10

–1

10

–2

Single

10 10

H = 10–6

–3

H = 10

–3

H = 0.01

–4

H = 0.1 10 10

–5

H = 0.4

–6

10

–2

10

–1

10

0

10

1

10

ka

(D) 3

Single

2

H = 10

–6

H = 10

–3

m*

H = 0.01 H = 0.1 1

(E)

0 –2 10

FIG. 17.13—CONT’D

H = 0.4

10

–1

ka

10

0

10

1

2

m*

378 SECTION 10

2

10

1

10

0

10

–1

10

–2

Single

10 10

(F)

H = 10–6

–3

H = 10

–3

H = 0.01

–4

H = 0.1

10 10

D Diffusiophoresis of Colloidal Particles

H = 0.4

–5

–6

10

–2

10

–1

10

0

ka

10

1

10

2

10

0

FIG. 17.13—CONT’D

0.1

fr = 1

0.08

fr = 2 0.06

m*

fr = 3 fr = 4

0.04

fr = 5

0.02

0 –4 10

10

–3

10

(A)

–2

10

–1

H 

FIG. 17.14 Dimensionless mobility m as a function of H at various fr with sH ¼ 0.5 (b ¼ 0). (A) ka ¼ 0.1; (B) ka ¼ 1; (C) ka ¼ 10.

17 379

Diffusiophoresis of Liquid Droplets and Gas Bubbles Chapter 0.4

fr = 1 0.35

fr = 2 fr = 3

0.3

fr = 4 fr = 5

m*

0.25 0.2 0.15 0.1 0.05 0 –4 10

10

–3

10

(B)

–2

10

–1

10

H 4

fr = 1 fr = 2 fr = 3

3

fr = 4

m*

fr = 5 2

1

0 –4 10

(C) FIG. 17.14—CONT’D

10

–3

10

–2

H

10

–1

10

0

0

380 SECTION

D Diffusiophoresis of Colloidal Particles

1.5

Single H = 10–6 1

H = 10–3

m*

H = 0.01 H = 0.1

0.5

H = 0.4

0

–0.5 –2 10

10

–1

0

10

0

10

10

1

ka

(A) 3.5

Single

3

H = 10–6

2.5

H = 10

m*

2

–3

H = 0.01

1.5

H = 0.1

1

H = 0.4

0.5 0 –0.5

(B)

–1 –2 10

10

–1

ka

10

1

FIG. 17.15 Dimensionless mobility m as a function of ka at various H with sH ¼ 0.5 (b ¼  0.2). (A) fr ¼  1. Solid lines: positive fr. Dashed lines: negative fr. (B) fr ¼ 3. Solid lines: positive fr. Dashed lines: negative fr. (C) fr ¼ 5. Solid lines: positive fr. Dashed lines: negative fr.

17 381

Diffusiophoresis of Liquid Droplets and Gas Bubbles Chapter 3 Single H = 10–6 H = 10

2

–3

H = 0.01 H = 0.1

m*

H = 0.4 1

0

–1 –2 10

10

(C)

–1

ka

10

0

10

1

FIG. 17.15—CONT’D

1

m*

0.5

0

fr = ± 1 fr = ± 2 fr = ± 3

–0.5

fr = ± 4 fr = ± 5 –1 –4 10

10

–3

10

(A)

–2

10

–1

10

0

H 

FIG. 17.16 Dimensionless mobility m as a function of H at various fr with sH ¼ 0.5 (b ¼ 0.2). (A) ka ¼ 0.1. Solid lines: positive fr. Dashed lines: negative fr (B) ka ¼ 1. Solid lines: positive fr. Dashed lines: negative fr. (C) ka ¼ 10. Solid lines: positive fr. Dashed lines: negative fr.

382 SECTION

D Diffusiophoresis of Colloidal Particles

1

fr = ± 1 fr = ± 2 fr = ± 3 fr = ± 4 fr = ± 5

m*

0.5

0

–0.5 –4 10

10

–3

(B)

10

–2

10

–1

10

10

–1

10

0

H 4

fr = ± 1 fr = ± 2 fr = ± 3 fr = ± 4 fr = ± 5

3.5 3 2.5

m*

2 1.5 1 0.5 0 –0.5 –4 10

(C) FIG. 17.16—CONT’D

10

–3

10

–2

H

0

Diffusiophoresis of Liquid Droplets and Gas Bubbles Chapter

17 383

ka range around unity. This is again attributed to the double layer suppression effect due to the boundary confinement of neighboring particles, which gets more profound in concentrated suspensions. This concludes the discussion in Chapter 17.

REFERENCES [1] Lee E, Min WL, Hsu JP. Dynamic electrophoresis of a droplet in a spherical cavity. Langmuir 2006;22(8):3920–8. [2] Lou J, Lee E. Dynamic electrophoresis of concentrated droplet dispersions at arbitrary surface potentials. Chem Eng Sci 2007;62(22):6234–45. [3] Liao C, et al. Electrophoretic motion of a liquid droplet and a bubble normal to an air–water interface. Colloids Surf A Physicochem Eng Asp 2016;507:124–33. [4] Huang CH, Lee E. Electrophoretic motion of a liquid droplet in a cylindrical pore. J Phys Chem C 2012;116(28):15058–67. [5] Im DJ, et al. Influences of electric field on living cells in a charged water-in-oil droplet under electrophoretic actuation. Biomicrofluidics 2011;5(4):044112. [6] Schnitzer O, Frankel I, Yariv E. Electrophoresis of bubbles. J Fluid Mech 2014;753:49–79. [7] Vitale SA, Katz JL. Liquid droplet dispersions formed by homogeneous liquid–liquid nucleation: “The ouzo effect” Langmuir 2003;19(10):4105–10. [8] Bouchemal K, et al. Nano-emulsion formulation using spontaneous emulsification: solvent, oil and surfactant optimisation. Int J Pharm 2004;280(1-2):241–51. [9] Hartman SV, Bozˇicˇ B, Derganc J. Migration of blood cells and phospholipid vesicles induced by concentration gradients in microcavities. New Biotechnol 2018, in press. [10] Shin S, et al. Size-dependent control of colloid transport via solute gradients in dead-end channels. Proc Natl Acad Sci 2016;113(2):257–61. [11] Kar A, et al. Enhanced transport into and out of dead-end pores. ACS Nano 2015;9(1):746–53. [12] Stubenrauch C. Microemulsions background, new concepts, applications, perspectives 2009, Wiley-Blackwell. [13] Bear J. Dynamics of fluids in porous media. Dover Publication; New York; 2013. [14] Fuerstman MJ, et al. Solving mazes using microfluidic networks. Langmuir 2003;19(11): 4714–22. [15] Goodknight RC, Klikoff Jr WA, Fatt I. Non-steady-state fluid flow and diffusion in porous media containing dead-end pore volume 1. J Phys Chem 1960;64(9):1162–8. [16] Dagdug L, et al. Transient diffusion in a tube with dead ends. J Chem Phys 2007;127(22):224712. [17] Chhabra G, et al. Design and development of nanoemulsion drug delivery system of amlodipine besilate for improvement of oral bioavailability. Drug Dev Ind Pharm 2011;37(8): 907–16. [18] Lawrence MJ, Rees GD. Microemulsion-based media as novel drug delivery systems. Adv Drug Deliv Rev 2012;64:175–93. [19] Bhargava H, Narurkar A, Lieb L. Using microemulsions for drug delivery. Pharm Technol 1987;11(3):46–52. [20] Kreuter J. Colloidal drug delivery systems. vol. 66. Marcel Dekker; New York; 2014. [21] Lawrence MJ. Surfactant systems: microemulsions and vesicles as vehicles for drug delivery. Eur J Drug Metab Pharmacokinet 1994;19(3):257–69.

384 SECTION

D Diffusiophoresis of Colloidal Particles

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