Using Astigmatism in Round Capillaries To Study Contact Angles and

Subscriber access provided by Eastern Michigan University | Bruce T. Halle Library

Article

Help from a hindrance: using astigmatism in round capillaries to study contact angles and wetting layers Nelly Hobeika, Patrick Bouriat, Abdelhafid Touil, Daniel Broseta, Ross Brown, and Jean Dubessy Langmuir, Just Accepted Manuscript • Publication Date (Web): 05 May 2017 Downloaded from http://pubs.acs.org on May 8, 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 33

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

Help from a hindrance: using astigmatism in round capillaries to study contact angles and wetting layers Nelly Hobeika,† Patrick Bouriat,† Abdelhafid Touil,† Daniel Broseta,∗,† Ross Brown,∗,‡ and Jean Dubessy¶ †CNRS/Univ. Pau & Pays Adour, Laboratoire des fluides complexes et de leurs réservoirs, UMR5150, 64000 Pau, France ‡CNRS/Univ. Pau & Pays Adour, Institut des sciences analytiques et de physico-chimie pour l’environnement et les matériaux , UMR5254, 64000 Pau, France ¶GéoRessources, UMR CNRS 7359, Université de Lorraine, B.P. 70239, 54506 Vandœuvre-lès-Nancy Cedex, France E-mail: [email protected]; [email protected] Phone: +3 (0)5 59 40 76 85; +3 (0)5 59 40 78 49

1

ACS Paragon Plus Environment

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

Abstract Round glass capillaries are a basic tool in soft-matter science, but often are shunned due to the astigmatism they introduce in micrographs. Here, we show how refraction in a capillary can be a help instead of a hindrance to obtain precise and sensitive information on two important interfacial properties: the contact angle of two immiscible fluids and the presence of thin films on the capillary wall. Understanding optical cusps due to refraction allows direct mesurement of the inner diameter of a capillary at the meniscus, which with the height of the meniscus cap, determines the contact angle. The meniscus can thus be measured without intrusive additives to enhance visibility, such as dyes or calibrated particles, in uniform, curved or even tapered capillaries or under demanding conditions not accessible by conventional methods, such as small volumes (µlitres), high temperatures or high pressures. We further elicit the conditions for strong internal reflection on the inner capillary wall, involving the wall and fluid refractive indices and the wall thickness, and show how to choose the capillary section to detect thin (sub-micron) layers on the wall by the contribution of total internal reflection to the cusps. As examples, we report: (i) CO2 -water or -brine contact angles at glass interfaces, measured at temperatures and pressures up to 200 ◦ C and 600 bar, revealing an effect apparently so far unreported: The decrease in the water-wet character of glass, due to dissolved salts in brine, is strongly reduced at high temperatures, where contact angles converge toward the values in pure water; (ii) A tenuous gas hydrate layer growing from the water-guest contact line on glass, invisible in transmission microscopy but prominent in the cusps due to total internal reflection.

Introduction The observation of fluids and other objects in thin transparent capillary tubes under the transmission microscope is becoming a common practice in many laboratories, driven 2


Page 2 of 33

Page 3 of 33

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

by the current trend towards using smaller volumes in fluid characterization and other applications. It is facilitated by the availability of glass and plastic capillaries at low cost, of cooling or heating stages and of pumps allowing precise control of the temperature and pressure over wide ranges under the optical microscope. 1 In addition, the wettability of standard borosilicate or fused silica glass capillaries can be controlled to a large extent by surface treatment such as silanization. However, astigmatism, the optical distortions and aberrations induced by the presence of the cylindrical container are usually disregarded or inadequately corrected; or the difficulty is (we note only partially) solved at the expense of convenience, by immersing the capillary in a liquid with similar refractive index, 2 or by substituting vessels with optically flat walls. It appears that the only attempts to describe these refraction effects, decades ago 3,4 and in a rather limited context, have been largely overlooked. The present paper aims to show the rich potential of capillary observations by harnessing rather than avoiding refraction. We focus here on situations where the capillary contains one or two fluids. In the latter case, these two fluids are separated by a meniscus, which intersects the inner wall with a certain contact angle, θ, characterising the wettability of the wall with respect to the two fluids, see figure 1 . Similar to the mercury thermometer, the glass appears thinner than reality, or the bore is overestimated when examined under the microscope. Hence the apparent contact angle differs from the true angle. Furthermore, the inner wall commonly appears as a more or less bright streak, a cusp, depending on refractive indices and capillary dimensions. This paper presents the analysis needed to exploit these features, with experimental illustrations. Section is a reminder of how the true internal diameter relates to the contact angle. Section shows how to identify the apparent internal diameter from the cusps and how correct it for refraction. Section discusses the brightness of the cusp, and how it may be used to reveal thin films or layers creeping out of the meniscus on the inner wall. One known example is salt creeping from the meniscus between a 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

supersaturated brine and air or oil. 5–7 After discussing experimental details in section , we provide illustrations in section . We examine the CO2 -water or brine interfaces with glass, under conditions of high temperatures and pressures or strong brines relevant to CO2 geological storage, section . Section is an example of how the presence or absence of a cusp reveals thin layers creeping over the substrate, in this case tenuous gas hydrate ’halos’.

Figure 1: Sketch diametral section through a spherical cap meniscus in a (locally) cylindrical glass capillary with internal and external radii Ri and Re . Equation (1) relates the contact angle, θ, to the cap height, h, from pole, P, to base, BB′ , and the radius at the cap base, Ri .

Refraction in a glass capillary Contact angles by measuring a meniscus Figure 1 shows an equatorial or diametral section through a cylindrical capillary containing a wetting and a non-wetting fluid. The capillary is mounted on a transmission microscope, with the capillary axis perpendicular to and passing through the optical axis. Köhler illumination is assumed, with the condenser aperture stop closed as far as possible, to illuminate the sample with a nearly parallel beam of light, focused into the equatorial

4


Page 4 of 33

Page 5 of 33

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

plane. The image is in general deformed by refraction of light by both the inner and the outer capillary walls. Thus, a bubble or drop in the capillary does not appear spherical, 8 and the apparent inner diameter of the capillary differs from the true diameter. The contact angle, θ, cannot simply be measured off micrographs of the wedge of the wetting fluid at the contact line. However, provided that the inner diameter of the capillary, 2Ri , is less than the capillary length, 9,10 (σ/g∆ρ)1/2 , where σ is the interfacial tension, ∆ρ the density difference between the two fluids, and g the acceleration due to gravity), the meniscus is a spherical cap with a base radius Ri , equal to that of the capillary tube at the position of the contact line. From simple geometry (derivation in the supplementary information, SI), the contact angle is then given by tan θ =

R2i − h2 2Ri h

,

(1)

determined by the height of the cap, h, from pole to base ( P and B-B’, in figure 1) and the radius Ri . The pole and the base generally are not simultaneously in focus. However there is no axial aberration, so provided the capillarity is carefully levelled, there is no difficulty measuring h as the difference of the abscissae of the pole and the base of the cap. Similarly, the outer diameter of the capillary, 2Re , can be measured in air by focusing on the equatorial plane. But astigmatism due to the curved intefaces makes the bore, 2Ri , harder to determine. The simple solution is immersion in an index matching fluid improves the situation by suppressing refraction at the outer surface. 2 Even then, some refraction persists at the inner surface, distorting images of the contents, except for the exceptional case that the index of the contents matches that of the glass. Further, this method is not always available nor even suitable. For example, immersion oils may not be compatible with measurements over the range of temperatures available to temperature controlled stages, due either to congealing or to frying. Another method is to photograph calibrated beads in the capillary. 8 However, these tricks do not apply when measurements are to be made "on the fly" in capillaries 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

with unknown or varying inner diameter, at an unpredetermined position of the meniscus, e.g. when the meniscus creeps along the capillary axis. Direct optical determination of the inner diameter would therefore be useful.

Using a cusp to determine the true internal diameter The difficulty above is that refraction produces longitudinal shadows and bright regions (cusps, see e.g. figure 2), that bewilderingly widen and narrow as the focus is swept over the thickness of the capillary tube, making it hard to decide what to measure, at which depth of focus and how to correct for refraction.

Figure 2: Transmission micrographs of the same meniscus (between pure water, left, and CO2 , right, at 500 bar, 40 ◦ C) with the focus on the pole P (a), and on the base BB’ (b). The prominent cusps on the outer (OC) and inner walls (IC), are due to rays such as those shown in the transverse sections (c), which come into focus in order, on focusing towards the objective, starting beyond the capillary. The capillary inner and outer diameters are here 200 and 330 µm. Scale bar in (b): 100 µm. Now cusps in general signal an extremum in the angular deviation of a bundle of rays impinging on a refracting object, in practice usually a minimum deviation. Rainbows are the most familiar example. 11 We now describe how to identify a particular cusp, that furthermore presents a maximum separation from the capillary axis at a particular depth 6


Page 6 of 33

Page 7 of 33

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

of focus in the capillary. The double extremum condition favours accurate estimation of an apparent internal diameter 2R a , only weakly sensitive to errors in focusing. We first performed Monte Carlo ray tracing simulations to understand the observed sequence of cusps. The conclusions are as follows (for more details, see the SI). When the focus is swept through the capillary, starting on the side opposite the objective, two cusps are particularly prominent. The first, outer cusp, OC in figure 2, appears brightest and sharpest when the focus reaches the equatorial plane of the capillary, thus providing the outer diameter 2Re . It is formed by reflection off the outside of the capillary wall. Note that at this point, the axis of the capillary and in particular the top of the meniscus, are out of focus, due to refraction. Attention should next be focused on the inner cusp, IC in figure 2. This cusp is formed by rays that do not enter the capillary cavity, but are reflected off the inner surface. With the condenser carefully adjusted to focus Köhler illumination into the equatorial plane of the capillary, cusp IC is sharpest at a focus somewhat within the focus for cusp OC. Cusp IC may be weakened by refraction of light into the capillary cavity, depending on the refractive index of the fluid or material lying against the wall. Nonetheless the high dynamic range of even cheap digital cameras makes jumps in the brightness of cusp IC a sensitive probe of inhomogeneities of the solids or fluids in contact with the capillary wall. At the other extreme, total internal reflection (TIR) makes cusp IC very bright at places where the refractive index of the fluid or material lying against the capillary wall, n f , is low enough compared to that of the glass, n g . The precise conditions are derived and discussed below. Dimming of cusp IC under nominal conditions of TIR, due to tunneling losses through the film in contact with the glass, make this cusp very sensitive to the thickness of wetting films or some other material extending on the capillary wall into the other fluid, see section . Examples will be given in section . Cusp IC broadens or narrows and moves perpendicular to the capillary axis as the focus is adjusted. This effect is due to some rays grazing into and out of the capillary

7


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

cavity. Because the fluids on each side of the meniscus generally have different refractive indices, the cusps do not in general line up to the left and right of the meniscus. But at a particular focus, both sides align, as rays are refracted into the capillary wall, reflected on its inner face, and refracted out of the outer surface either totally, i.e. without entering the cavity (see figures 2(b) and 3), or partially. At this special position, cusp IC arises from rays propagating solely in the capillary wall. The position, but not the brightness, is therefore independent of the contents of the capillary at the point of observation. The cusp is also sharpest and brightest and at a maximum distance from the capillary axis: this distance is the apparent radius, R a . Together with the corresponding cusp on the other side of the capillary, cusp IC determines an apparent inner capillary diameter 2R a .

Figure 3: Schematic illustration of the formation of an image of the inside capillary wall by reflection, corresponding to cusp IC when ie + φ = π/2, i.e. vanishing, hence minimum deviation, and a ray entering and exiting the capillary parallel to the optical axis, at a distance R a off it.

8


Page 8 of 33

Page 9 of 33

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

Under the adjustments described above, rays giving rise to cusp IC in practice are reflected off the inner capillary surface at points close to its diametral plane. Figure 3 shows a ray reflected exactly off the equator at point P on the inner surface. It is incident from the top, in the plane perpendicular to the capillary axis, at a point Q defined by the hour angle φ (determined in the SI). Let ie and re be the angles of incidence and refraction at the outer surface, and ii and ri those at the inner surface. In order to determine the relation between the true and the apparent inner diameters, we consider the particular rays that enter and exit the capillary parallel to the optical axis, i.e. such that φ + ie = π/2, see figure 3. They therefore correspond to a minimum (because vanishing) deviation and are at the heart of the cusp IC. See the SI for a proof that a there is always a ray satisfying these constraints. The cusp will be bright provided indeed the conditions for significant reflection on the inner surface of the capillary are met, rather than loss by refraction into the capillary cavity, see below. For the moment, the incoming ray is first refracted at the outer surface at point Q, then reflected at the inner wall at point P in the diametral plane, and finally refracted again at point Q’ on the other side of the outer surface. Q’ and Q are symmetrical with respect to the diametral plane. The apparent radius R a is the distance between the outgoing ray and the optical axis, or half the distance between the cusps IC on both sides of the capillary. We may now derive the relation between the apparent and the true radii. Applying Snell’s second law of refraction at the outer capillary wall,

n g sin re = n0 sin ie

,

(2)

where we assume for generality that the capillary is immersed in a medium of refractive index n0 . Usually, n0 = 1 for a capillary in air.

9


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 10 of 33

The law of sines in triangle OPQ reads

sin re /Ri = sin(π − (re + φ))/Re = sin(re + φ)/Re

,

(3)

whence Ri /Re =

sin re sin re = sin(re + φ) sin re cos φ + cos re sin φ

.

(4)

Now, in triangle ODQ, cos φ = R a /Re (and sin φ = [1 − ( R a /Re )2 ]1/2 ). Equation (2) also reads sin re = n0 sin ie /n g

.

(5)

Furthermore, from the condition φ + ie = π/2 in eqn. (3), sin ie = sin (π/2 − φ) = cos φ. Thus, we have

sin re = n0 sin ie /n g = n0 cos φ/n g =

from which one derives cos re (expressed as

p

n0 R a n g Re

,

(6)

1 − sin re2 )and a little algebra leads to the

final relation: R /R p a e Ri /Re = p 2 2 n 1 − R a /Re 1 − R2a /n2 R2e + R2a /R2e

,

(7)

where for generality n = n g /n0 . Equation (6) shows that the inner radius Ri , needed in eqn. (1) to determine the contact angle θ, can be directly inferred from the measured quantities Re , the capillary outer radius, and R a , the apparent radius of the cusp, or half of the distance between the two cusps IC. As expected, the fluid in the capillary has no impact on the value of R a , though some impact on the brightness of cusp IC is expected, as we soon shall see. This result was derived a quarter of a century ago, 4 in a very limited context, but remained unnoticed. Ongoing progress in capillary manufacture, capillary pullers, cameras and microscopes, as well as in accessories for use of microcapillaries at controlled temperature and pressure,

10


Page 11 of 33

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

make the method generally attractive today. It allows in particular the simple and precise determination of volumes in microcapillaries, provided there is a symmetry of revolution around the capillary axis.

Figure 4: Relation between the apparent (R a ) and the true internal radius (Ri ) of a capillary, from eqn. (7), for three values of n g : 1.44,1.46 & 1.48 (arrow). The inset, showing a waterCO2 meniscus (150 bar, 25 ◦ C), illustrates the apparent wall thinning for a capillary with internal and external diameters 300 and 400 µm (tie-line in main figure), scale bar 100 µm. The cusps IC (white arrows) render the apparent inner wall readily visible on the CO2 side of the meniscus, despite the presence of water droplets formed on the glass on the right during an earlier stage of the experiment. The cusps are not visible on the water side for reasons explained in section . The ratios Ri /Re and R a /Re are central in the discussion below. We call them the true and the apparent aspect ratios of the capillary. The ratio Ri /Re → 0 (resp. 1) characterises thick (resp. thin) walled vessels. Using eqn. (7), figure 4 shows the true vs. the apparent aspect ratio for the typical value n g = 1.46 (fused silica glass). The cavity appears enlarged (R a > Ri ), particularly for thin-walled capillaries. Note also the very small error introduced 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 33

by an uncertainty δn g = ±0.02 in n g . The relative error is by numerical inspection δRi /Ri < δn g /2n g for realistic capillary aspect ratios Ri /Re . Equation (7) and this all-optical method for determining the capillary inner diameter Ri and dependent quantities such as the contact angle, are particularly attractive for homemade capillaries, e.g. drawn capillaries. The method requires neither dyes 12 nor calibrated beads, 8 which may be intrusive in some experiments. Recall for example that many dyes are ionic and may be surface-active.

Taking advantage of total internal reflection (TIR) Case 1: Single fluid lying against the inner wall Up to now, we showed that the cusp IC is due to reflection off the inner wall, back into the glass, but did not consider its brightness. As shown in the SI, the cusp must always be present. Furthermore, according to the Fresnel relations, 13 the intensity of the reflection at general angle of incidence increases with the contrast in the refractive index between the glass and the fluid, n g − n f , where n g and n f are the indices of the glass and the fluid in the vessel. But by far the most common case, e.g. aqueous media, even strong brines, is n f < n g , opening the possibility for TIR at the inner wall and a particularly brilliant cusp. Quite generally, TIR occurs when the angle of incidence i exceeds the critical angle, ic defined by: n g sin ic = n f sin π/2 = n f

,

(8)

Under the conditions of TIR, light cannot propagate into the fluid, except in the form of an evanescent or tunneling field, with intensity decaying away from the interface with a characteristic length scale, the penetration depth, d, dependent on the angle of incidence, i, and the critical angle, ic , as: 13

d=

λ 4πn f sin2 i/ sin2 ic − 1

1/2 = 12

λ 4πn g sin2 i − (n f /n g )2


1/2

,

(9)

Page 13 of 33

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

where λ is the wavelength. The penetration depth is appreciable only for i ∼ ic .

We next derive a surpisingly simple relation between the capillary section and the limit refractive index for TIR, n f l . It will be noticed that for cusp IC, the angle of incidence at the inner wall is i = ii = φ + re (see figure 3), where, as shown in the SI, the cusp condition completely predetermines both φ and re as functions of the index of the glass and the aspect ratio of the capillary. Therefore, setting ic = φ + re in eqn. (8), the cusp will be particularly bright due to TIR, for fluids with indices up to a limit, n f l , defined by n f ≤ n f l = n g sin(φ + re )

.

(10)

Thus, by eqn. 3, nfl ng

= sin (φ + re ) R e n0 sin ie (by eqn. (2)), Ri n g R e n0 sin(π/2 − φ) (see figure 3), = Ri n g R e n0 = cos φ . Ri n g

=

(11)

Observing that cos φ = R a /Re (cf. figure 3) , we have the final simple relation between n f l and the true and apparent aspect ratios: nfl Ra R a /Re = = ng nRi n( Ri /Re )

.

(12)

In the next paragraph, we make use of the fact that it is largely possible to tune the aspect ratio of the capillary to a particular value of n f l . This choice requires expressing n f l as a function of the true aspect ratio. One route is to solve for R a in a cubic equation easily obtained from eq. (7). An alternative used here, again with a cubic equation, is to 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 33

determine φ and re appearing in eq. (10), as functions of n g and Ri /Re , see the SI. Thus, n f l is an intrinsic property of the capillary, determined (via φ and re ) by Ri /Re and the refractive index n g (strictly n = n g /n0 ). Figure 5 shows n f l /n g thus determined as a function of the true aspect ratio, for silica capillaries in air. The penetration depth, d, can then be rewritten as follows

d=

λ

4πn g (n f l /n g )2 − (n f /n g )2

1/2

,

(13)

or, for fluid indices n f slightly below the critical value, n f l ,

d∼

λ 4π (2n f l

)1/2 (n

fl

− n f )1/2

,

(14)

Fluids with refractive index n f > n f l give rise to a partial reflection determined by the Fresnel relations. The reflection decays very fast with incresing n f , see section 2 in the SI, which shows the reflectivity calculated as a function of n f for the two capillaries used in this study. Figure 5 highlights the sensitivity of the intensity of the cusp to the aspect ratio and the refractive indices. The limit refractive indices for the silica capillaries used here (n g = 1.46), with aspect ratios 100 µm/165 µm and 150 µm/200 µm, are for example n f l ∼ 1.36 and

∼ 1.26. TIR occurs (bright inner cusp IC), if the material in contact with the inner wall has a refractive index below this limit index, n f < n f l : this is for instance the case for water (n f =1.33) and supercritical CO2 (n f =1.24) in a capillary with radii 100 and 165 µm (see Figure 2), and with supercritical CO2 but not water in a capillary with radii 150 and 300 µm (see Figure 4). On the other hand, in a 200/330 µm capillary, figure 6 (and incidentally in the Monte Carlo simulation in figure 4 of the SI), the cusp is bright for both water and CO2 , as expected from figure 5. For the same reasons, many oils, with a refractive index n f ∼ 1.4, are expected to give weak or very weak cusps in both the capillaries used here. Anticipating, cyclopentane in 14


Page 15 of 33

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

figure 9 (nCP = 1.41),is an example.

Figure 5: How to tune the capillary dimensions to exhibit a fluid by total internal reflection (TIR). The curve shows the limit refractive index of the fluid for TIR on the inner wall, n f l (plotted as n f l /n g ), as a function of Ri /Re , for a silica capillary (n g = 1.46) in air. The vertical tie-lines show capillaries used here, with aspect ratios Ri /Re = 100/165 ∼ 0.61 and 150 µm/200 µm = 0.75. Fluids with indices n f below the curve give rise to a brilliant cusp IC, by TIR; those above the line do not (e.g. figure 4), see the text. Case 2: Detection of a wetting layer along the capillary wall Consider now what happens when extraneous matter intrudes between a core fluid and the capillary wall. As we now show, the wide range of aspect ratios of commercial capillaries means that one can often be chosen to detect a solid or liquid intrusion, by arranging that nintrusion < n f l < ncore fluid . The preceding discussion on indices also applies to the intruding material, whose leading edge will always be visible as a discontinuity in the brightness of the cusp. The jump in intensity is particularly spectacular when only one of the fluids meets the condition for TIR and is thicker than the tunneling length, see section . Consider for instance an oil, with typical refractive index n f =1.4, that is displaced by water or hydrate (both with refractive indices in the range of 1.33-1.35) forming a layer on the capillary wall: a bright inner cusp is expected from this replacement if the capillary has diameters 200 and 330 µm, but only a faint or invisible cusp is expected in a capillary 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 33

with diameters 300 and 400 µm. The example given in section below, shows how sensitive this method can be, provided the capillary dimensions are appropriately chosen. In this example co-crystallization of the two fluids occurs on the capillary wall: water and an immiscible hydrate–former, here a light oil, readily give rise to a thin ’halo’ of hydrate propagating over the hydrophilic substrate, on the guest side of the meniscus. 14–16 Salt or salt hydrate films are other candidates for this effect. 5–7

Experimental materials and methods Materials: We used 10 cm fused silica capillary tubes (clear fused quartz, VitrotubesTM ). The fluids were compressed CO2 (Linde, purity 4.5) and deionised water (resistivity

> 18 MΩcm, PureLab Classic from ELGA Labwater). Dry cyclohexane (99.9 %) and the dichloro-dimethyl-silane (DCDMS) were purchased from Aldrich for hydrophobizing the glass. Absolute ethanol (analytical grade) and lithium chloride, LiCl were also supplied by Aldrich. Methods: Some capillaries were rendered mildly hydrophobic by silane-treating the glass with a procedure adapted from Dickson et al. 17 A solution of 10−2 M DCDMS in dry cyclohexane was introduced by capillary rise into the capillary tube and left for one hour under inert N2 atmosphere. Unreacted silane was removed by washing the capillaries several times with pure dry cyclohexane. Finally they were washed in absolute ethanol and dried at 110 ◦ C for 30 min. According to Dickson et al. the proportion of unreacted silanol (SiOH) groups on the surface of the silane-treated glass is about 12 %, making the glass ’intermediate-wet’ or mildly hydrophobic as assessed by the contact angle measured at atmospheric pressure, 98 ± 2 ◦ . The treated glass became CO2 -wet when the pressure was increased, with contact angles in water approaching 160 ◦ with dense (liquid) CO2 . Instrumentation and procedure: We loaded the tubes by capillary rise of the aqueous phase and flame-sealed one end with a microtorch (Prodont Holliger). Centrifugation

16


Page 17 of 33

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

(5000 rpm for about 1/2 h) drove the aqueous phase to the sealed end of the capillary. The meniscus was typically located about 10–20 mm from the closed end. Capllaries were photographed with a Ueye SE1240 camera on an Olympus B50 upright microscope equipped with a CAP500 temperature-controlled stage (Linkam), which provides temperature control to within 0.1-0.2 ◦ C. The capillaries were set in the 1 mm x 0.6 mm rectangular channel of the silver block of the stage. The stage allows recentering the capillary when the meniscus responds to changing pressure (the aqueous phase is slightly compressible) or temperature (here a bigger effect). The open end of the capillary was glued with cyanoacrylate glue into a stainless steel tube (OD = 1/16”, ID = 500 µm), connected via a three-way valve to an ISCO piston pump (65DM) filled with CO2 , allowing pressure control up to 700 bar. Prior to carrying out the measurements, the system was purged 3–4 times at a pressure in the range 30-40 bar. The microscope operated in transmission mode with Köhler illumination and a x10 long working distance objective. Care was taken to set the capillary axis on, and perpendicular to the optical axis, so that the height of the meniscus could be accurately determined from micrographs focused successively on the pole and the contact line. Contact angle isotherms were measured as follows, between 22 and 205 ◦ C, over a pressure interval extending up to 600 bar: Pressure was increased by steps to the maximum value, and then decreased stepwise back to the minimum pressure, usually 50 bar; then T was changed (usually increased) to the next isotherm. Photographs of the meniscus were taken after waiting a few minutes at each step to equilibrate the system. We emphasize that static contact angles can take any value between two limits: the advancing and receding angles. 18 Such hysteresis relates to various factors such as the existence of pinning defects on the substrate, or the adsorption on the substrate of compounds from the displaced fluid. Compression induces a contraction, very limited in the case of water because of its very low compressibility. The contact angles recorded when increasing pressure along an isotherm should thus be close to the water-receding, or CO2 -advancing

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 33

limit, and vice versa while releasing the pressure. Likewise, measurements along an isobar while increasing the temperature correspond to water-advancing angles. We did not notice any significant difference between the contact angles obtained upon increasing and releasing the pressure, except in the measurements carried out with a strong brine as the aqueous phase (8 M LiCl). Possible reasons are discussed below. Unless otherwise specified, the contact angles displayed in the graphs below are recorded at increasing pressure. It should further be borne in mind that silica surfaces display variable types and density of hydroxyl groups (silanols), depending on the underlying structure (crystalline or amorphous) and substrate preparation or history, with an impact on wettability and contact angles. 19 Error bars shown below (±2 ◦ ) were deduced from random perturbation of the experimental data based on the estimated 4-pixel error on all measurements. An extension of the analysis carried out by Cheong et al. 12 shows that the error on the contact angle, ∆θ, is related to that on the height ∆h, and that on the inner radius, ∆Ri , as follows: ∂θ ∂θ ∆Ri δθ = ∆h + ∂h ∂Ri ∆Ri 1 + sin θ ∆h + cos θ = Ri Ri

(15)

Cheong et al. 12 neglected errors in Ri . Eqn. (15) shows that for low contact angles 10 % error in Ri contributes 6 ◦ error in θ, underlining the importance of an accurate determination of the capillary inner diameter.

18


Page 19 of 33

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

Experimental illustrations CO2 -water and CO2 -brine contact angles at high temperature or pressure Contact angles of pure water and CO2 on hydrophilic and mildly hydrophobic glass

Figure 6: Micrographs of the water-CO2 meniscus (water on the left) in a silane-treated capillary at increasing pressures at room temperature (22 ◦ C). Scale bar: 100 µm (in the first vignette). We start with the results obtained with the mildly hydrophobic (silane-treated) glass at room temperature (22 ◦ C), because they can be compared readily to those of Dickson et al., 17 obtained by means of the conventional sessile drop technique. The micrographs in figure 6 show the strong pressure dependence of substrate wettability: it is intermediatewet at low pressure, with contact angle slightly above 90 ◦ , and becomes CO2 -wet at high 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 33

pressure (or CO2 density). Figure 7 shows the contact angles extracted by the method of sections and , together with those measured by Dickson et al. 17 The two sets of results are in very good agreement: contact angles increase to about 160 ◦ under CO2 at 200 bar, with a surge near the vapour pressure of CO2 at the temperature of the experiment, ∼ 60 bar at T=22 ◦ C. Figure 7(b) shows the pure water-CO2 contact angles measured in the untreated (bare) capillaries along four isotherms from 40 to 205 ◦ C, for a pressure range extending from 50 to 600 bar. The angles are low, in the range of 5 to 9 ◦ , and show negligible pressure dependence. The figure also shows a marginal increase of the contact angle with increasing temperature, consistent with the analysis of literature results presented in ref. 20

Contact angles of a strong brine and CO2 on glass The strong brine is an 8 M solution of LiCl, chosen because it is highly soluble in water. Figure 8 displays the contact angles measured along the same isotherms as above and for a similar range of pressure (cf. figure 7(b)). The data are somewhat more dispersed and hysteresis is larger than for pure water, possibly because contact line pinning was occasionally observed, an effect most likely due to small salt crystallites observed on the capillary wall. They arise by evaporation occurring in the repeated CO2 injections and purges at the beginning of the experiment. Some authors have pointed out the difficulty of measuring these angles, specially the receding angle. 21 The relatively high angles observed at low pressure, 50–100 bar, are likely to be advancing angles, as they are obtained after heating from the previous isotherm, which induces expansion of the brine. Compression, on the other hand, induces contraction and retreat of the contact line. This effect was noticeable only if the pressure was significantly increased, because the compressibility of water, specially brine, is extremely small. Comparing figures 7(b) and 8 shows that, at least for the lowest temperature investigated, 40 ◦ C, contact angles are significantly higher, ∼ 25 ◦ , when the aqueous phase is an 8 M LiCl brine than when it is pure water, ∼ 6 ◦ . This trend is in line with what has been 20


Page 21 of 33

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

Figure 7: Pressure dependence of the contact angle of water-CO2 in (a) a hydrophobic, silane-treated capillary at 22 ◦ C (filled and open data from ref. 17 and this work, respectively) and (b) a hydrophilic, untreated capillary at different temperatures: 40 ◦ C (circles), 100 ◦ C (triangles), 150 ◦ C (squares), 205 ◦ C (diamonds). Error bars are shown only for the latter isotherm.

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 33

Figure 8: Pressure dependence of a ∼ 8 M LiCl brine-CO2 contact angle on untreated glass at : 40 ◦ C (circles), 100 ◦ C (triangles), 150 ◦ C (squares), 205 ◦ C (diamonds). Full symbols correspond to water-advancing angles (see text). observed with other brines (mainly NaCl brines, but CaCl2 and MgCl2 brines as well), by conventional drop methods, for temperatures not exceeding 80 ◦ C and in a narrower pressure range, ≤ 150 bar. 20,22–25 Higher contact angles with brine than with water are also observed at ambient temperature and pressure, i.e. in the absence of a gas, so that the brine is in equilibrium with its vapour. For example, Sghaier et al. 26 observed a significant increase of the contact angle of nearly-saturated NaCl brines at 20 ◦ C, in the range 10–35 ◦ , depending on the glass substrate, consistent with our observations with a concentrated LiCl brine on silica at 40 ◦ C in a wide range of CO2 pressures (figure 8). These authors accounted qualitatively for this variation by considering the salt-induced increase of the denominator,γlv , (the water surface tension) in the Young equation: cos θ = (γsv − γsl )/γlv

,

(16)

where γsv and γsl are the substrate-vapour and substrate-liquid water interfacial tensions 22


Page 23 of 33

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

(IFT’s). A similar argument has been invoked by Espinoza and Santamarina 23 and by Jung and Wan 25 to account for the effects of pressure and brine salinity on θ. Of the three interfacial tensions involved in eqn. (16), only the brine-CO2 IFT, γlv , can be measured and is well characterized as a function of brine salinity and CO2 pressure. These two parameters act independently, 27 i.e.

γlv ( p, salinity) = γW,CO2 ( p) + δ(salinity)

,

(17)

where γW,CO2 ( p) is the pure water-CO2 IFT, which decreases from ∼ 70 mN/m at 40 ◦ C at low pressure to a plateau of ∼ 25 mN/m when p exceeds 100–150 bar. 22 The pressureindependent increase in tension due to dissolved salts, δ, is ∼ 13 mN/m for a 8 M LiCl brine at 40 ◦ C. 28 Now, the Young equation can be used to relate the contact angle θ to that under reference conditions, e.g. low pressure p and/or pure water, (subscript 0):

cos θ = cos θ0

(γsv − γsl ) γlv0 (γsv − γsl )0 γlv

(18)

The dependence of γsv − γsl with pressure and brine salinity is poorly known. However, γsv decreases with increasing pressure, since CO2 adsorbs on silica, and is not influenced by brine salinity. Furthermore, we observe experimentally that cos θ remains approximately constant when pressure increases above ∼ 100 bar. Therefore, γsv − γsl must decrease in such a way that it balances the decrease of γlv . We also observe that, at T=40 ◦ C, θ increases from θ0 ∼ 5 ◦ to θ ∼ 25 ◦ when salinity increases from 0 to 8 M LiCl, which is roughly consistent with cos θ ∼ cos θ0 γlv0 /γlv ∼ cos θ0 × 70/(70 + 13), meaning that γsv − γsl is barely influenced by the presence of salt. The present data suggest however that the full story is more complicated, as we now show. Figure 8 also shows that as the temperature is raised above 100 ◦ C, the presence of dissolved salt (8 M LiCl) diminishes the contact angle θ, which for the highest T inves23


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 24 of 33

tigated (150 and 205 ◦ C) comes close to the values observed with pure water at similar T and P (see Figure 7(b)). To our knowledge this is the first observation of this effect. This behaviour might be rationalized by the fact that increased thermal agitation at high temperature possibly annihilates the disturbance of the water hydrogen bond network by dissolved ionic species, with an effect on γsl and γlv . Molecular dynamics simulations similar to those in ref. 19 might be used to test this conjecture.

Thin layers revealed by the capillary inner cusp As pointed out in section , thin liquid or solid films intruding along the inner capillary wall give rise to a discontinuity in the brightness of cusp IC. The jump may be particularly pronounced if the aspect ratio is chosen such that the conditions for total internal reflection are met by the intruding fluid or layer on the wall, but not by the bulk fluid in the cavity. Only if the index of the latter fluid is close to the critical value, n f l , will the cusp be significant on the bulk fluid side of the meniscus, see figure 3 in the SI. As an illustration, consider a water-cyclopentane interface in presence of a glass substrate. Under appropriate conditions, 29 a layer of cyclopentane hydrate can be induced to grow over the water-oil or ice-oil interface, here the meniscus. When the interface is completely covered, a tenuous layer of hydrate, called a ’halo’, 14 extends over the glass substrate, here the capillary wall. Viewed growing over a flat substrate, the halo is hardly visible in standard transmission microscopy, but requires more complicated methods such as phase contrast or fluorescence microscopy. 15 In figure 9(a), the lateral extension of total internal reflection in the cusps IC coincides with the halo, which is readily visible. The jump in brightness is conspicuous because the refractive index of cyclopentane, 1.41, is higher than the critical index for total internal reflection in this particular capillary (Ri /Re = 100/165, n g = 1.46, n f l = 1.361 cf. the left tie-line in figure 5), while that of the hydrate, nh = 1.35, 30 is below it. Hence the progress of the growing halo is highlighted by a bright cusp creeping over the much dimmer one 24


Page 25 of 33

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

on the oil-filled side of the meniscus. Furthermore, the intensity of the reflection in figure 9(a) drops sharply at the halo tip, which is therefore blunt. Note that the halo is manifest all over the glass in transmission images. Later, figure 9(b-c), the halo edge is so thin that it is not detectable directly in transmission images. It is nonetheless revealed by the cusps IC. Moreoever, the progressive dimming of the cusp towards the direction of growth shows that the thickness tapers towards the front. The vanishing of the cusp corresponds to a thickness comparable to the penetration length d in eqn. (9). Using the refractive indices of the glass (1.46) and the hydrate (1.35), we estimate d ∼ 140 nm, in good agreement with an earlier estimate of the thickness of the halo front, deduced from a combination of techniques including confocal reflectance. 15 The results derived in section and illustrated here are not only anecdotal. Even without the effect of total internal reflection, the sensitivity and high dynamic range of modern digital cameras make it easy to detect the jump or even subtle variations in the brightness of the cusp. Furthermore, for aqueous media, the aspect ratio of the capillary can in general be chosen in advance to fulfill the TIR switching condition. For example, the aspect ratios of the current standard silica capillaries from VitrotubeTM are in the interval 0.588 ≤ Ri /Re ≤ 0.8, or 1.17 ≤ n f l ≤ 1.37. This range of refractive indices covers strong brines and dense (supercritical or liquid) CO2 .

Conclusion and outlook Studies of contact angles and wetting by capillary rise have a venerable history, stretching back at least as far as the work of Jurin. 31,32 Lately, instruments such as contact-angle goniometers have superseded the capillary, which largely has been relegated to the elementary classroom. Today, however, both the modest glass capillary, 2 and more sophisticated versions such as pulled pipettes 33,34 are commonly used in investigation of fundamental

25


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

Figure 9: Using the contrast of cusp IC to highlight growth of thin films: (a) Growth of a thin but visible film of polycristalline cyclopentane hydrate, initiated at the water-cyclopentane meniscus on the left at −4 ◦ C; (b-c) Views 60 and 102 s later (capilllary recentred). Although the halo is tenuous to the point of invisibility in the transmission image, the cusps IC clearly show up its progression to the right and thickening. Scale bar in (a): 200 µm.

26


Page 26 of 33

Page 27 of 33

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

aspects of wetting phenomena and flow transpmort in porous media. Indeed, the capillary is the simplest example of a microfluidic device and a pore model. Even modest research microscopes and digital cameras provide high resolution images of round capillaries that can be used to measure contact angles to a high degree of accuracy, provided one understands the distorsion introduced by the curved surfaces. Our aim here was to provide and illustrate the necessary perspective. The central point is to understand the conditions of formation of the cusp due to reflection of light off the inner capillary wall. Variations of the brightness of the cusp parallel to the capillary axis are explained here and turned to advantage to highlight thin liquid or solid films growing or disappearing on the inner glass wall. The variation is spectacular when the capillary aspect ratio is chosen so that only one of the media in contact with the glass fulfills the conditions for total internal reflection. This condition is readily met thanks to the wide range of capillary aspect ratios available commercially. The method is just as well applicable to capillaries with variable diameter, and can be extended to higher pressures and temperatures as pumps and heating plates operating in these ranges are becoming commercially available. As an illustration, the wettability of silica at the water- or brine-CO2 interface is of practical importance for geological storage of CO2 . Our measurements in bare or silanetreated glass capillaries range from 20 to ∼ 200 ◦ C, at pressures up to 600 bar and salinity up to 8 M LiCl, representative of conditions encountered in geological storage of CO2 . They confirm confirm and extend the range of earlier data: A strong effect of CO2 pressure or density on contact angle is observed with silane- treated glass, but not with bare glass. Increasing the temperature slightly increases contact angles on glass. We observed a new effect in hot brine: Salinity does increase contact angles on glass, but this effect is attenuated at high temperatures (T > 100 ◦ C), where glass thus remains strongly water-wet. In conclusion, understanding and exploiting refraction in capillaries is for several reasons appealing to study wetting and to determine contact angles from the geometry of a capillary meniscus: ease of use and availability of the equipment; need for insignificant

27


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 28 of 33

amounts of the fluids; adaptability to demanding conditions such as high pressures or extreme temperatures. A further advantage of the present method is that it does not require additives to enhance meniscus visibility, that might perturb the contact angle. Here, both the fluids were transparent, but it suffices that just the wetting fluid should be clear.

Acknowledgement L’Agence Nationale pour la Recherche partially funded this work, projects ’CGS-µLab’, ANR-12-SEED-0001 and ’Hydre’, ANR 15-CE-06-000.

Supporting Information Available Derivation of eqn. (1); details of the Monte Carlo ray tracing simulations; analytical proof that the cusp IC is always expected and expressions for the various angles characterising its formation. This material is available free of charge via the Internet at http://pubs.acs.org/.

Bibliography (1) Chou, I.-M.; Pan, Z. In Near-critical and supercritical water and their applications for Biorefineries; Fang, Z., Xu, C., Eds.; Springer: Dordrecht, 2014; Chapter 6. (2) Heshmati, M.; Piri, M. Experimental Investigation of Dynamic Contact Angle and Capillary Rise in Tubes with Circular and Noncircular Cross Sections. Langmuir 2014, 30, 14151–14162, DOI: 10.1021/la501724y, PMID: 25323811. (3) Coucoulas, L. M.; Dawe, R. A.; Mahers, E. G. The refraction correction for the spinning drop interfacial tensiometer. Journal of Colloid and Interface Science 1983, 93, 281 – 284, DOI: http://dx.doi.org/10.1016/0021-9797(83)90408-3. 28


Page 29 of 33

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

(4) Chen, E. Q.; Lam, C. F.; Periasamy, A. Effect of refraction on optical microscopic measurement of internal blood-vessel diameter and its correction. Journal of Microscopy 1991, 164, 239–245, DOI: 10.1111/j.1365-2818.1991.tb03210.x. (5) Shahidzadeh-Bonn, N.; Rafaï, S.; Bonn, D.; Wegdam, G. Salt Crystallization during Evaporation: Impact of Interfacial Properties. Langmuir 2008, 24, 8599–8605, DOI: 10.1021/la8005629, PMID: 18652495. (6) Bouzid, M.; Mercury, L.; Lassin, A.; Matray, J.-M. Salt precipitation and trapped liquid cavitation in micrometric capillary tubes. Journal of Colloid and Interface Science 2011, 360, 768 – 776, DOI: http://dx.doi.org/10.1016/j.jcis.2011.04.095. (7) Naillon, A.; Duru, P.; Marcoux, M.; Prat, M. Evaporation with sodium chloride crystallization in a capillary tube. Journal of Crystal Growth 2015, 422, 52 – 61, DOI: http://dx.doi.org/10.1016/j.jcrysgro.2015.04.010. (8) Liu, Z.; Muldrew, K.; Wan, R. G.; Elliott, J. A. W. Measurement of freezing point depression of water in glass capillaries and the associated ice front shape. Phys. Rev. E 2003, 67, 061602, DOI: 10.1103/PhysRevE.67.061602. (9) de Gennes, P. G.; Brochard-Wyart, F.; Quéré, D. Capillarity and Wetting Phenomena; Springer: Berlin, 2003. (10) Erbil, H. Y. Surface Chemistry of Solid and Liquid Interfaces; Blackwell: Oxford, 2006. (11) Minnaert, M. Light and color in the outdoors, 5th ed.; Springer: New York, 1993. (12) Cheong, B. H.-P.; Ng, T. W.; Yu, Y.; Liew, O. W. Using the Meniscus in a Capillary for Small Volume Contact Angle Measurement in Biochemical Applications. Langmuir 2011, 27, 11925–11929, DOI: 10.1021/la202800s, PMID: 21859131. (13) Jackson, J. D. Classical Electrodynamics, Third Edition; J. Wiley: Hoboken, NJ, 1999.

29


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 30 of 33

(14) Beltrán, J. G.; Servio, P. Morphological Investigations of Methane-Hydrate Films Formed on a Glass Surface. Cryst. Growth Des. 2010, 10, 4339–4347, DOI: 10.1021/cg1003098. (15) Martínez de Baños, M. L.; Hobeika, N.; Bouriat, P.; Broseta, D.; Enciso, E.; Clément, F.; Brown, R. How Do Gas Hydrates Spread on a Substrate? Crystal Growth & Design 2016, 16, 4360–4373, DOI: 10.1021/acs.cgd.6b00471. (16) Touil, A.; Hobeika, N.; Broseta, D.; Brown, R. 2017, in preparation. (17) Dickson, J. L.; Gupta, G.; Horozov, T. S.; Binks, B. P.; Johnston, K. P. Wetting Phenomena at the CO2/Water/Glass Interface. Langmuir 2006, 22, 2161–2170, DOI: 10.1021/la0527238, PMID: 16489803. (18) Carrier, O.; Bonn, D. In Droplet wetting and evaporation; Brutin, D., Ed.; Elsevier: Dordrecht, Holland, 2015; Chapter 2. (19) Chen, C.; Zhang, N.; Li, W.; Song, Y. Water Contact Angle Dependence with Hydroxyl Functional Groups on Silica Surfaces under CO2 Sequestration Conditions. Environmental Science & Technology 2015, 49, 14680–14687, DOI: 10.1021/acs.est.5b03646, PMID: 26509282. (20) Palamara, D.; Neeman, T.; Golab, A.; Sheppard, A. A statistical analysis of the effects of pressure, temperature and salinity on contact angles in CO2–brine–quartz systems. International Journal of Greenhouse Gas Control 2015, 42, 516 – 524, DOI: https://doi.org/10.1016/j.ijggc.2015.09.007. (21) Bormashenko, E. Wetting of real solid surfaces: new glance on well-known problems. Colloid and Polymer Science 2013, 291, 339–342, DOI: 10.1007/s00396-012-2778-8. (22) Chiquet, P.; Broseta, D.; Thibeau, S. Wettability alteration of caprock minerals by carbon dioxide. Geofluids 2007, 7, 112–122, DOI: 10.1111/j.1468-8123.2007.00168.x. 30


Page 31 of 33

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

(23) Espinoza, D. N.; Santamarina, J. C. Water-CO2-mineral systems: Interfacial tension, contact angle, and diffusion—Implications to CO2 geological storage. Water Resources Research 2010, 46, n/a–n/a, DOI: 10.1029/2009WR008634, W07537. (24) Saraji, S.; Piri, M.; Goual, L. The effects of {SO2} contamination, brine salinity, pressure, and temperature on dynamic contact angles and interfacial tension of supercritical CO2/brine/quartz systems. International Journal of Greenhouse Gas Control 2014, 28, 147 – 155, DOI: http://dx.doi.org/10.1016/j.ijggc.2014.06.024. (25) Jung, J.-W.; Wan, J. Supercritical CO2 and Ionic Strength Effects on Wettability of Silica Surfaces: Equilibrium Contact Angle Measurements. Energy & Fuels 2012, 26, 6053–6059, DOI: 10.1021/ef300913t. (26) Sghaier, N.; Prat, M.; Nasrallah, S. B. On the influence of sodium chloride concentration on equilibrium contact angle. Chemical Engineering Journal 2006, 122, 47 – 53, DOI: http://dx.doi.org/10.1016/j.cej.2006.02.017. (27) Duchateau, C.; Broseta, D. A simple method for determining brine–gas interfacial tensions. Advances in Water Resources 2012, 42, 30 – 36, DOI: http://dx.doi.org/10.1016/j.advwatres.2012.03.008. (28) Abramzon, A. A.; Gaukhberg, R. D. Surface tensions of salt solutions. Russ. J. Appl. Chem. 1993, 66, 1139. (29) Taylor, C. J.; Miller, K. T.; Koh, C. A.; Dendy Sloan Jr., E. Macroscopic investigation of hydrate film growth at the hydrocarbon/water interface. Chem. Eng. Sci. 2007, 62, 6524 – 6533, DOI: http://dx.doi.org/10.1016/j.ces.2007.07.038. (30) Sloan, E. D.; Koh, C. A. Clathrate Hydrates of Natural Gases; CRC Press: Boca Raton, Florida, 2008.

31


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 32 of 33

(31) Jurin, J. An Account of Some Experiments Shown before the Royal Society; With an Enquiry into the Cause of the Ascent and Suspension of Water in Capillary Tubes. Phil. Trans. 1717-1719, 30, 739–747. (32) Extrand, C. W. Origins of Wetting. Langmuir 2016, 32, 7697–7706, DOI: 10.1021/acs.langmuir.6b01935, PMID: 27459085. (33) Gorce, J.-B.; Hewitt, I. J.; Vella, D. Capillary Imbibition into Converging Tubes: Beating Washburn’s Law and the Optimal Imbibition of Liquids. Langmuir 2016, 32, 1560–1567, DOI: 10.1021/acs.langmuir.5b04495, PMID: 26784118. (34) Budaraju, A.; Phirani, J.; Kondaraju, S.; Bahga, S. S. Capillary Displacement of Viscous Liquids in Geometries with Axial Variations. Langmuir 2016, 32, 10513–10521, DOI: 10.1021/acs.langmuir.6b02788, PMID: 27653244.

32


Page 33 of 33

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

Graphical TOC Entry

Optical cusps due to astigmatism in microcapillaries on a standard transmission microscope, help measure contact angles and exhibit tenuous solid or liquid wetting layers.

33


Using Astigmatism in Round Capillaries To Study Contact Angles and

Recommend Documents