Unstable Spreading of Ionic Liquids on an Aqueous Substrate

Subscriber access provided by PEPPERDINE UNIV

Article

Unstable Spreading of Ionic Liquids on Aqueous Substrate Shigeki Tsuchitani, Taiga Fukutake, Daiki Mukai, Hirofumi Miki, and Kunitomo Kikuchi Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b01799 • Publication Date (Web): 26 Sep 2017 Downloaded from http://pubs.acs.org on September 28, 2017

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

Langmuir is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 23

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Unstable Spreading of Ionic Liquids on Aqueous Substrate Shigeki Tsuchitani,*,† Taiga Fukutake,‡ Daiki Mukai,‡ Hirofumi Miki,† and Kunitomo Kikuchi† †

Wakayama University, Faculty of Systems Engineering, Department of Opto-mechatronics, 930 Sakaedani, Wakayama 640-8510, Japan, and ‡Wakayama University, Graduate School of Systems Engineering, 930 Sakaedani, Wakayama 640-8510, Japan

ABSTRACT The spontaneous spreading of thin liquid films over substrate surfaces are attracting much attention due to their broad applications. Under particular conditions, deposited surfactants on the substrates exhibit unstable spreading. In spite of the large effects of the stability of the spreading on accuracy and efficiency of industrial processes using the spreading, how the stability of the spreading process is governed by the physical and chemical properties of the system is not enough know. Recently, ionic liquids are expected as new kinds of surfactants due to their special properties. Here, we investigate the stability of the spreading of deposited imidazolium-based ionic liquids on an aqueous substrate. We mainly focus on the effects of water solubility of the ionic liquids on the stability. Hydrophobic ionic liquids exhibit the spreadings which have highly periodic and petal-like unstable spreading fronts. While, a

ACS Paragon Plus Environment

1

Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 23

hydrophilic ionic liquid spreads without such regular spreading front and its spreading area shrinks after reaching the maximum. We propose a generation model of the unstable spreading of the hydrophobic ionic liquids, i.e., the unstable spreading front is created by the penetration of oncoming water in front of the spreading tip into the more viscous spreading ionic liquid layer like the viscous fingering in a Hele-Shaw cell. However, the direction of the penetration is the opposite to the moving direction of the interface (the spreading direction), which is contrary to the one in the viscous fingering.

TEXT INTRODUCTION The spontaneous spreading of thin liquid films over substrate surfaces are attracting much attention due to their practical importance in fields such as coatings,1 printing, drug delivery,2 developing better antifoaming agents3 and foam extinguishers, and oil spill tracking. When a surfactant comes into contact with a liquid substrate, the surfactant adsorbs at the airliquid interface creating a concentration gradient of the surfactant which generates surface tension gradient on the liquid surface. This induces Marangoni flow of the liquid due to shear stress at the surfactant-liquid interface and spontaneously advances the surfactant toward higher surface tension regions (Marangoni driven spreading). Under particular conditions, deposited surfactants on thin liquid films ( 100 m thick) exhibit unstable spreading that produces significant film corrugation, fingering and branching, which is referred to as fingering instability.4-7 The fingering phenomena were first observed by Marmur and Lelah.8 Troian et al. provided the first attempt at achieving fundamental understanding of the mechanism underlying the fingering instability.9 Since then, many studies for understanding


2

Page 3 of 23

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

the instability of the monolayer spreading of the surfactants, especially on thin liquid films, have been performed.10 Recently, Mollaei and Darooneh have reported a spreading with a fingering instability followed by a shrinking of a hydrosoluble surfactant deposited on a deep water layer (1 cm thick).11 While, in divergent flows of hydrosoluble surfactants continuously supplied from a localized source on thick water layers, quite different types of instabilities were observed, i.e., azimuthally periodic surface flows with a multivortex structure (solutocapillary convection).12,13 In spite of the large efforts for understanding the stability of the spreading, how the stability of the spreading process is governed by the physical and chemical properties of the system is not enough known. Room-temperature ionic liquids have been expected to become excellent alternatives to conventional solvents, electrolytes, and lubricants due to their special features.14-16 From the viewpoint of interfacial chemistry, almost all ionic liquids, especially those with long hydrocarbon chains, have amphiphilic structures.17 Ionic liquids are also attracting much attention as alternative surfactants to conventional oil dispersants in enhanced oil recovery processes because they are environmentally benign.18 Here, we have investigated effects of water solubility of deposited surface active materials on their spreading over a thick aqueous substrate. As the surface active materials, we used imidazolium-based ionic liquids with different water solubility and different viscosity. We have observed very unique unstable spreadings of slightly water-soluble ionic liquids, i.e., they spread to produce highly periodic and petal-like unstable spreading fronts. We also proposed a generation model of such unstable spreadings of the hydrophobic ionic liquids by taking the fluid pressure behind the leading edge of the spreading ionic liquid layer into consideration.


3

Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 4 of 23

EXPERIMENTAL SECTION Spreading experiments were performed for four imidazolium ionic liquids: 1-butyl-3methylimidazolium tetrafluoroborate ([BMIM][BF4]), 1-butyl-3-methylimidazolium hexafluorophosphate ([BMIM][PF6]), and 1-octyl-3-methylimidazolium hexafluorophosphate ([OMIM][PF6]) from Kanto Chemical Co., Inc., and 1-hexyl-3-methylimidazolium hexafluorophosphate ([HMIM][PF6]) from Tokyo Chemical Industry Co., Ltd. Table 1 lists the properties of the ionic liquids we used in the experiments. [BMIM][BF4] is miscible with water in all range of concentrations,19 while the [PF6]− anion in [BMIM][PF6], [HMIM][PF6] and [OMIM][PF6] is more hydrophobic than [BF4]−. The [PF6]− ionic liquids display a low aqueous solubility that decreases with increasing alkyl chain length. The surface tension and water solubility decrease in the order of [BMIM][PF6], [HMIM][PF6] and [OMIM][PF6].

Table 1. Properties of the ionic liquids used in the experiments Name

[BMIM][BF4]

[BMIM][PF6]

[HMIM][PF6]

[OMIM][PF6]

Alkyl chain length of cation

4

4

6

8

Density [g/cm3]

1.12

1.35

1.29

1.22

Solubility in Water (Mole Fraction)

1.00a

(1.21 ± 0.01) ×10-3,20

(4.34 ± 0.02) ×10-4,20

(1.27 ± 0.03) ×10-4,20

Surface tension [mN/m]

44.81 ± 0.0221

44.10 ± 0.0221

39.02 ± 0.0221

35.16 ± 0.0121

Viscosity 21922 45022 58522 68222 [mPa•s] a [BMIM][BF4] mixes up with water in all range of concentrations at 25.0 ◦C and atmospheric pressure.19


4

Page 5 of 23

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Deionized water was filled into a 145 mm diameter petri dish to a depth of 5 mm. To visualize the spreading of the ionic liquid, mica powder (Yamaguchi Mica Co., Ltd., 25 m diameter, 3.0 mg) was sprinkled uniformly on the aqueous surface. A 5 L droplet of ionic liquid was deposited on the aqueous surface with a microsyringe, and the dispersion state of the mica powder was recorded with a video camera (30 fps). In order to evaluate the effects of water depth on the stability of the spreading especially at the latter stage of the spreading, we performed the same spreading experiments on water layers with depths of 3, 5, 7, and 10 mm using a 300 mm diameter petri dish. RESULTS AND DISCUSSION Time evolutions of spreading state. Figure 1 shows time evolutions of the dispersion state of the mica powder during the spreading of the ionic liquids. The mica powder was initially swept away circularly because the expanding ionic liquid forms an area without the mica powder (spreading area). As the spreading progressed, the periphery of the spreading area (spreading front) became unstable. The projected and depressed portions of the unstable pattern with respect to the spreading direction are referred to as projections and depressions, respectively. Figure 2 shows the growth of the depressions towards the inside of the spreading area for [HMIM][PF6] and [OMIM][PF6]. The spreading front of [BMIM][PF6] produced a periodic unevenness with an amplitude of about 10% of the spreading radius [Fig. 1(a), 0.7 s] for the time period of 0.5 to 0.8 s after deposition. The amplitude of the unevenness then enlarged randomly and the periodicity was finally lost.


5

Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

0.3 s

0.7 s

Page 6 of 23

1.0 s

1.5 s

(a)

(b)

(c)

(d)

Figure 1. Time evolution of the dispersion state of mica powder on an aqueous surface, showing the spreading process for ionic liquids of (a) [BMIM][BF4], (b) [BMIM][PF6], (c) [HMIM][PF6], and (d) [OMIM][PF6]. The scale bar under the photographs indicates a length of 30 mm.


6

Page 7 of 23

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

(a)

t=0.5 s

(b)

t=0.5 s

t=0.6 s

t=0.6 s

t=0.7 s

t=0.7 s

t=0.8 s

t=0.8 s

t=0.9 s

t=0.9 s

t=1.0 s

t=1.0 s

Figure 2. Growth of the depressions in the unstable spreading front towards the inside of the spreading area for (a) [HMIM][PF6] and (b) [OMIM][PF6].

In the case of [HMIM][PF6], a petal-like periodic unevenness was created during the initial time from deposition (about 0.16 s), and the periodicity of the unevenness was maintained for more than 2 s. The depressions grew into the inside of the spreading area in both the radial and circumferential directions, and went around to the backside of the neighboring projections, which indicates the generation of vortices [Fig. 2(a)]. In the spreading of [OMIM][PF6], which has the lowest surface tension and water solubility and the highest viscosity (see Table 1) of the ionic liquids studied here, the creation of depressions with sharp tips began at about 0.6 s. The depressions then penetrated into the


7

Langmuir

spreading area, like the root of a tree, to form a periodic unevenness. As the spreading progressed, the root-like depressions grew longer, while some went around to the backside of the neighboring projections [Fig. 2(b)]. Finally, some depressions vanished. Figure 3(a) shows the time dependence of the average wavelength of the unstable spreading front for [BMIM][PF6], [HMIM][PF6] and [OMIM][PF6]. The average wavelength increases proportionally with

(t: time, : exponent) and with a decrease in the alkyl chain length of the

Average wavelength (mm)

cation. During the late stage of the spreading of [HMIM][PF6] and [OMIM][PF6], some

[BMIM][PF6] [HMIM][PF6] [OMIM][PF6]

(a)

10 8 6 4 0.2

0.4 [BMIM][PF6] [HMIM][PF6] [OMIM][PF6]

Amplitude (mm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 23

0.6 0.8 1 Time (s)

(b)

10

1

0.2

0.4

0.6 0.8 1 Time (s)

Figure 3. Time dependence of (a) average wavelength and (b) amplitude of the unstable spreading front for the three hydrophobic ionic liquids.


8

Page 9 of 23

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

projections were broken and some neighboring projections fused with each other, which resulted in a reduction in the number of projections. The spreading front of highly water-soluble [BMIM][BF4] behaved quite differently from that of the three slightly water-soluble ionic liquids; the amplitude of the unstable spreading front was far smaller during the latter stage. The spreading front had no periodicity at any time during the spreading process. After reaching the maximum spreading area at about 2 s, the spreading front shrank with time to formed sharp projections. Such shrinking of the spreading area has also been observed in the spreading of a deposited hydrosoluble surfactant and the axisymmetric continuous Marangoni flows induced by hydrosoluble surfactants both on thick water layers, 11,13 which are caused by an increase in the surfactant concentration in the water layer, i.e., dissolution of the surfactants into the water.13 Time dependence of spreading radius. Two spreading radii are defined, the inner and outer spreading radii, which are the radii of the inscribed and circumscribed circles of the spreading front, respectively. Figures 4(a) and (b) show the time dependence of the inner and outer spreading radii. Both radii r, exhibited a power-law behavior,

(: spreading exponent),

which is commonly observed in most experiments on surfactant spreading.23-28 The inner spreading radius for all ionic liquids and the outer radius for [BMIM][BF4] deviated from the power-law curves toward smaller values at the latter stage; therefore, the power curves were produced based on the data in the region of

s. The exponent  in the outer spreading radius

curves for [BMIM][PF6], [HMIM][PF6] and [OMIM][PF6] is 0.57, 0.56 and 0.47, respectively. The theoretical exponent in a monolayer spreading fed from a stationary source of constant surfactant concentration is 0.75,23-25 which has been verified experimentally by many


9

Langmuir

researchers.23,24,26-28 If the surfactant source becomes depleted at the latter time, then the spreading exponent is predicted to be reduced and approach 3/8.29 A deposited droplet of [OMIM][PF6] in the center of a spreading area was observed until the last stage [Fig. 1(d)] and behaved as an infinite reservoir. In the spreading of a dilute mixture of anionic surfactants with a common cationic surfactant,

Inner spreading radius (mm)

the spreading exponent was determined to be 0.575,24 which is almost equal to the exponents

70 50 30

[BMIM][BF 4] [BMIM][PF 6] [HMIM][PF6] [OMIM][PF6]

∝t

(a)

0.45

∝t 0.56 ∝t 0.51 ∝t 0.47

10 8 6 0.1

Outer spreading radius (mm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 23

70 50 30

[BMIM][BF 4] [BMIM][PF 6] [HMIM][PF6] [OMIM][PF6]

∝t

1

Time (s)

(b) ∝t 0.57

0.47

∝t 0.56 ∝t 0.47

10 8 6 0.1

Time (s)

1

Figure 4. Time dependence of the (a) inner and (b) outer spreading radii. Curve fitting was performed using data points in the range of

s.


10

Page 11 of 23

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

obtained here. Joos and Hunsel speculated that the reason for this disagreement with the theoretical value is that the spreading coefficient is dependent on time.24 Although little is known regarding the dynamics of dissociation, diffusion and adsorption of surface-active ionic liquids in an aqueous phase, from studies on the dynamic surface tension of aqueous solutions of ionic surfactants,30 we infer that the time scale for the establishment of equilibrium interfacial and surface tension during the spreading of ionic liquids is larger than the time scale of the spreading due to the electrostatic interactions between already adsorbed cations on aqueous surface and subsequently adsorbing cations. Generation model of the unstable spreading front. The time variations of the outer spreading radius for the ionic liquids with the [PF6]－ anion obeyed a power law until the last stage of the spreading process [Fig. 4(b)], whereas the inner spreading radius deviated from this behavior toward the smaller spreading radius at the latter stage. These results and the observation presented in Fig. 2 suggest that the unstable spreading patterns are created by a slowdown of the velocity of the depressions rather than advancement of the projections. The strong hydrophobicity of [PF6]−,31 and the hydrogen bonding interactions between fluorine atoms in [PF6]− and the C2 hydrogen on the imidazolium ring, which releases hydrated water of the cation and [PF6]−,32 cause the structure of the spreading layers of [BMIM][PF6], [HMIM][PF6] and [OMIM][PF6] on the aqueous surface to be almost the same as those on neat ionic liquid surfaces.33 Therefore, such spreading layers have much higher viscosity than the aqueous phase (0.89 mPa•s at 25°C) outside of the spreading area (see Table 1). The leading edge of a localized, insoluble surfactant monolayer spreading over the free surface of a thin fluid layer behaves locally like an advancing rigid plate. In the vicinity of such leading edge, two qualitatively distinct surface regions with different distributions of fluid pressure exist:


11

Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 23

the spreading tip which has local maxima of Marangoni stress and fluid pressure due to collisions with the oncoming fluid and the region behind the spreading tip which has the viscous boundary layer beneath it.34,35 The stress and pressure peaks at the spreading tip are sensitive to surface active contaminant in the liquid substrate and surface diffusion of the spreading surfactant (when the surfactant is slightly soluble), both of which decrease the peak height or eliminate the peak, and moderate the pressure gradient around the spreading tip. The viscous boundary layer has a thickness on the order of

. The fluid pressure in the

boundary layer, which is independent of the distance from the liquid surface (spreading monolyer),36 monotonically decreases with the distance x from the spreading tip towards the inside of the spreading area, such that

, where R = HV/ is the Reynolds number,

and  and  are the density and viscosity of the fluid layer, respectively, H is the fluid depth, and V is the velocity of the monolayer tip.34,35 Therefore, the spreading of the slightly water-soluble ionic liquids is modeled as an expanding thin viscous ionic liquid layer, of which the spreading front is pushed by the oncoming less viscous water and has a negative pressure gradient in the direction opposite to the spreading at the fluid surface. This situation is similar to the viscous fingering in a Hele-Shaw cell.37 When a less viscous fluid pushes a more viscous fluid in the confined geometry of a Hele-Shaw cell, the interface between the fluids develops instability and leads to the formation of finger-like patterns. Troian et al. first pointed out the similarity between patterns produced by surfactants spreading over thin liquid films (

1 m thick) and those in a Hele-Shaw cell, in addition to the

mathematical similarity in their mechanisms.4,9 In the present cases, the thickness of the liquid substrate is much larger; therefore, the conventional theories on the fingering instability5,9 are not available.


12

Page 13 of 23

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

We consider the flow of a thin surface layer with a thickness than the boundary layer thickness (

, which is sufficiently smaller

). The thin layer includes the spreading ionic liquid

layer (cations adsorbed on the aqueous surface and anions electrostatically interacting with cations) and the water layer that penetrates into the spreading area (Fig. 2). The force balance on the surface layer is expressed as: ,

(1)

where  is the shear stress arising from substratum water flow, is the surface tension of the fluid, and p is the fluid pressure in the surface layer. Using the solution of the Rayleigh problem (Stokes first problem),36 which gives the development of the fluid motion in the half space on a rigid plate that suddenly moves in the tangential direction with constant velocity at t = 0, the fluid velocity beneath the spreading layer in the spreading direction is , where

(2)

is the error function, x is the distance from the spreading tip, y

is the depth from the spreading layer, and  is the kinetic viscosity of the fluid. The shear stress  at the spreading layer-water interface is approximated as: (3) for

, where and  are the density and coefficient of viscosity (

) of water,

respectively. Hence, the surface flow velocity is proportional to the gradients in the surface tension of the fluid and the fluid pressure:

. Since

is the spreading velocity, the velocity of the penetrated water layer relative to the spreading tip is given by: .

(4)


13

Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 23

This equation is similar to Darcy’s law governing flow velocity in a Hele-Shaw cell;37 the gradient in the fluid pressure in the surface layer at the spreading front is the main cause for the formation of the unstable spreading front. As in the case of the viscous fingering, the viscosity of the spreading ionic liquid layer has to be enough larger than that of water. Using the spreading exponent of 0.5 obtained in the present experiments, the spreading velocity V is proportional to

. When the fluid pressure in the surface layer at the spreading ,35 the pressure gradient towards the inside of the spreading

front varies, such as area is

; the magnitude increases with the water

depth H and decreases with time. The effects of water depth on the stability of the unstable patterns were investigated. Figure 5 shows dispersion state of mica powder on aqueous surface at 2 s after deposition of [BMIM][PF6], [HMIM][PF6], and [OMIM][PF6] on water layers with depths of 3, 5, 7, and 10 mm. A decrease in the water depth promoted the collapse of the periodic pattern at the latter stage of spreading. In other words, an increase in the water depth stabilized the maintenance of the periodic pattern for longer time. This result strongly supports our proposed mechanism that the pressure gradient at the spreading front generated by the spreading of the hydrophobic ionic liquids is the main cause for the formation and maintenance of regular and periodic unstable patterns, similar to the viscous fingering in the Hele-Shaw cell. Thus, a larger pressure maximum, which also increases with the Reynolds number,35 and pressure gradient stabilize the regularity at the unstable spreading front.


14

Page 15 of 23

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

3 mm

5 mm

7 mm

10 mm

(a)

(b)

(c)

Figure 5. Effects depth of water layer on spreading state. Photographs show dispersion state of mica powder on aqueous surface at 2 s after deposition of ionic liquids of (a) [BMIM][PF6], (b) [HMIM][PF6], and (c) [OMIM][PF6] on water layers with depths of 3, 5, 7, and 10 mm.

We consider the effects of water solubility of the ionic liquids (see Table 1) on the unstable spreading. Figure 3(b) shows the time variation of the amplitude for an unstable pattern, which is defined as the difference between the inner and outer spreading radii for the spreading of hydrophobic ionic liquids. At the latter stage of the spreading process, the amplitude is larger and in the order of [BMIM][PF6], [HMIM][PF6] and [OMIM][PF6]; the ionic liquid with higher water solubility has a larger amplitude. As described previously, surface diffusion of the spreading surfactant decreases or eliminates the local stress and pressure maxima at the spreading tip. Therefore, a more water-soluble ionic liquid has a lower pressure peak and a smaller pressure gradient at the spreading front. We consider this to be the main cause for


15

Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 23

unstable spreading with a larger amplitude of the ionic liquid having a cation with a shorter alkyl chain and a [PF6]− anion, i.e., it is easier for collapse to occur at the latter stage of the spreading process, especially in the spreading over water layers with small depths. In the Saffman-Taylor theory of viscous fingering, the estimated wavelength  of the lateral perturbation in the shape of the interface is determined by a balance between the pressure gradient dp/dx and the interfacial tension  :38 .

(5)

Therefore, one reason for the increases in the wavelength of unstable spreading with time and with the decrease in the alkyl chain length of the cation [Fig. 3(a)] is the decreases in the pressure gradient at the spreading front due to a reduction in the Reynolds number by the decrease in the spreading velocity with time, and with the increasing water solubility of the ionic liquid with the decrease in alkyl chain length. The wavelength is also affected by the interfacial tension  between the spreading ionic liquid layer and aqueous surface, which is a kind of line tension. In Fig. 3(a), average wavelength of [HMIM][PF6] is almost equal to that of [OMIM[[PF6] despite the former has a three times larger water solubility than that of the latter. In order to discuss this result in detail, we have to take the effects of the interfacial tension into consideration. However, in the present stage, we don’t have enough information about the interfacial tension between ionic liquid layer and aqueous surface.

CONCLUSIONS Hydrophobic ionic liquids exhibited the spreadings which had highly periodic and petal-like unstable spreading fronts. Such unstable spreadings with highly regular spreading front have not been observed in the previous spreading experiments of deposited surfactants on thick liquid


16

Page 17 of 23

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

layers. Flow instabilities arising from the viscous response of the materials are observed in a wide range of situations.38,39 Saffman-Taylor instability is the most well-known example of such flow instability.37 A common feature in all of the situations examined is that the magnitude of the negative hydrostatic stress in front of an advancing interface increases in the direction of interfacial motion. In this study, we have shown that such a fluid instability is generated in the opposite situation, i.e., the instability of the spreading hydrophobic ionic liquids is created by the negative fluid pressure behind the spreading tip, which increases in the direction opposite to the spreading. In this case, the interface (spreading tip) advances not by the fluid pressure but by Marangoni force.

AUTHOR INFORMATION Corresponding Author * Author to whom correspondence should be addressed. Telephone: +81-73-457-8146. Fax: +8173-457-8201. E-mail: [email protected]. Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT The authors thank T. Inoue and T. Ikeda for helpful discussions. This work was supported by Grants-in-Aid for Scientific Research (Nos. 24560294 and 15K05897) from Japan Society for the Promotion of Research.


17

Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 23

REFERENCES (1) Weinstein, S. J.; Ruschak, K. J. Coating Flows. Annu. Rev. Fluid Mech. 2004, 36, 29–53. (2) Haitsma, J. J.; Lachmann, U.; Lachmann, B. Exogenous surfactant as a drug delivery agent. Adv. Drug Deliv. Rev. 2001, 47, 197–207. (3) Cantat, I.; Cohen-Addad, S.; Elias, F.; Graner, F.; Höhler, R.; Pitois, O.; Rouyer, F.; SaintJalmes, A. Foams: Structure and Dynamics; Oxford University Press: Oxford, U.K. 2013. (4) Troian, S. M.; Wu, X. L.; Safran, S. A. Fingering instability in thin wetting films. Phys. Rev. Lett. 1989, 62, 1496–1499. (5) Matar, O. K.; Troian, S. M. Spreading of a surfactant monolayer on a thin liquid film: Onset and evolution of digitated structures. Chaos 1999, 9, 141–153. (6) Afsar-Siddiqui, A. B.; Luckham, P. F.; Matar, O. K. Unstable Spreading of Aqueous Anionic Surfactant Solutions on Liquid Films. Part 1. Sparingly Soluble Surfactant. Langmuir 2003, 19, 696– 702. (7) Afsar-Siddiqui, A. B.; Luckham, P. F.; Matar, O. K. Unstable Spreading of Aqueous Anionic Surfactant Solutions on Liquid Films. 2. Highly Soluble Surfactant. Langmuir 2003, 19, 703–708. (8) Marmur, A.; Lelah, M. D. The Spreading of Aqueous Surfactant Solutions on Glass. Chem. Eng. Commun. 1981, 13, 133–143. (9) Troian, S. M.; Herbolzheimer, E.; Safran, S. A. Model for the fingering instability of spreading surfactant drops. Phys. Rev. Lett. 1990, 65, 333–336.


18

Page 19 of 23

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

(10) Craster, R. V.; Matar, O. K. Dynamics and stability of thin liquid films. Rev. Mod. Phys. 2009, 81, 1131–1198. (11) Mollaei, S.; Darooneh, A. H. Spreading, Fingering Instability and Shrinking of a Hydrosoluble Surfactant on Water. Exp. Therm. Fluid Sci. 2017, 86, 98–101. (12) Mizev, A. Influence of an Adsorption Layer on the Structure and Stability of Surface Tension Driven Flows. Phys. Fluids 2005, 17, 122107-1–122107-5. (13) Roché, M.; Li, Z.; Griffiths, I. M.; Le Roux, S.; Cantat, I.; Saint-Jalmes, A.; Stone, H. A. Marangoni Flow of Soluble Amphiphiles. Phys. Rev. Lett. 2014, 112, 208302-1–208302-5. (14) Welton, T. Room-Temperature Ionic Liquids. Solvents for Synthesis and Catalysis. Chem. Rev. 1999, 99, 2071– 2084. (15) Armand, M.; Endres, F.; MacFarlane, D. R.; Ohno, H.; Scrosati, B. Ionic-liquid materials for the electrochemical challenges of the future. Nature mater. 2009, 8, 621– 629. (16) Zhou, F.; Liang, Y.; W. Liu, Ionic liquid lubricants: designed chemistry for engineering applications. Chem. Soc. Rev. 2009, 38, 2590– 2599. (17) Aratono, M.; Shimamoto, K.; Onohara, A.; Murakami, D.; Tanida, H.; Watanabe, I.; Ozeki, T.; Matsubara, H.; Takiue, T. Adsorption of 1-Decyl-3-methylimidazolium Bromide and Solvation Structure of Bromide at the Air/Water Interface. Analytical Sciences 2008, 24, 1279– 1283.


19

Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 23

(18) Bin-Dahbag, M. S.; Al Quraishi, A. A.; Benzagouta, M. S.; Kinawy, M. M.; Al Nashef, I. M.; Al Mushaegeh, E. Experimental Study of Use of Ionic Liquids in Enhanced Oil Recovery. J. Pet. Environ. Biotechnol. 2014, 4, 1000165-1–1000165-7. (19) Rilo, E.; Pico, J.; G.-Garabal, S.; Varela, L. M.; Cabeza, O. Density and surface tension in binary mixtures of CnMIM-BF4 ionic liquids with water and ethanol. Fluid Phase Equilibria, 2009, 285, 83–89. (20) Freire, M. G.; Neves, C. M. S. S.; Carvalho, P. J.; Gardas, R. L.; Fernandes, A. M.; Marrucho, I. M.; Santos, L. M. N. B. F.; Coutinho, J. A. P. Mutual Solubilities of Water and Hydrophobic Ionic Liquids. J. Phys. Chem. B 2007, 111, 13082–13089. (21) Freire, M. G.; Carvalho, P. J.; Fernandes, A. M.; Marrucho, I. M.; Queimada, A. J.; Coutinho, J. A. P. Surface tensions of imidazolium based ionic liquids: Anion, cation, temperature and water effect. J. Colloid Interface Sci. 2007, 314, 621– 630. (22) J. G. Huddleston, A. E. Visser, W. M. Reichert, H. D. Willauer, G. A. Broker, and R. D. Rogers, Characterization and comparison of hydrophilic and hydrophobic room temperature ionic liquids incorporating the imidazolium cation. Green Chem. 2001, 3, 156–164. (23) Joos, P.; Pintens, P. Spreading Kinetics of Liquids on Liquids. J. Colloid Interface Sci. 1977, 60, 507– 513. (24) Joos, P.; Hunsel, J. V. Spreading of Aqueous Surfactant Solutions on Organic Liquids. J. Colloid Interface Sci. 1985, 106, 161–167.


20

Page 21 of 23

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

(25) Dussaud, A. D.; Troian, S. M. Dynamics of spontaneous spreading with evaporation on a deep fluid layer. Phys. Fluids 1998, 10, 23– 38. (26) Foda, M.; Cox, R. G. The spreading of thin liquid films on a water-air interface. J. Fluid Mech. 1980, 101, 33–51. (27) Huh, C.; Inoue, M.; Mason, S. G. Uni-directional spreading of one liquid on the surface of another. Can. J. Chem. Eng. 1975, 53, 367– 371. (28) Camp, D. W.; Berg, J. C. The spreading of oil on water in the surface tension regime. J. Fluid Mech. 1987, 184, 445– 462. (29) Jensen, O. E. The spreading of insoluble surfactant at the free surface of a deep fluid layer. J. Fluid Mech. 1995, 293, 349– 378. (30) Ritacco, H.; Langevin, D.; Diamant, H.; Andelman, D. Dynamic Surface Tension of Aqueous Solutions of Ionic Surfactants: Role of Electrostatics. Langmuir 2011, 27, 1009– 1014. (31) Freire, M. G.; Santos, L. M. N. B. F.; Fernandes, A. M.; Coutinho, J. A. P.; Marrucho, I. M. An overview of the mutual solubilities of water–imidazolium-based ionic liquids systems. Fluid Phase Equilibria 2007, 261, 449–454. (32) Talaty, E. R.; Raja, S.; Storhaug, V. J.; Dölle, A.; Carper, W. R. Raman and Infrared Spectra and ab Initio Calculations of C2-4MIM Imidazolium Hexafluorophosphate Ionic Liquids. J. Phys. Chem. B 2004, 108, 13177–13184.


21

Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 23

(33) Matsubara, H.; Onohara, A.; Imai, Y.; Shimamoto, K.; Takiue, T.; Aratono, M. Effect of temperature and counterion on adsorption of imidazolium ionic liquids at air–water interface. Colloids and Surfaces A 2010, 370, 113–119. (34) Jensen O. E.; Halpern, D. The stress singularity in surfactant-driven thin-film flows. Part 1. Viscous effects. J. Fluid Mech. 1998, 372, 273–300. (35) Jensen, O. E. The stress singularity in surfactant-driven thin-film flows. Part 2. Inertial effects. J. Fluid Mech. 1998, 372, 301–322. (36) Currie, I. G. Fundamental Mechanics of Fluids, Third Edition; Marcel Dekker, Inc.: New York, U.S.A. 2003, 262–266. (37) Saffman, P. G.; G. I. Taylor, G. I. The Penetration of a Fluid into a Porous Medium or HeleShaw Cell Containing a More Viscous Liquid. Proc. R. Soc. London, Ser. A 1958, 245, 312–329. (38) Shull, K. R.; Flanigan, C. M.; Crosby, A. J. Fingering Instabilities of Confined Elastic Layers in Tension. Phys. Rev. Lett. 2000, 84, 3057–3060. (39) Argon A. S.; Salama, M. The mechanism of fracture in glassy materials capable of some inelastic deformation. Mater. Sci. Eng. 1976, 23, 219–230.


22

Page 23 of 23

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Table of contents only

[HMIM][PF6]

[OMIM][PF6]


23

Unstable Spreading of Ionic Liquids on an Aqueous Substrate

Recommend Documents