Sessile drops of surfactant solutions on nonhorizontal solid surfaces

Sessile Drops of Surfactant Solutions on Nonhorizontal Solid Surfaces SRIRAM PADMANABHAN AND ARIJIT B O S E l Department of Chemical Engineering, University of Rhode Island, Kingston, Rhode Island 02881 Received March 11, 1987; accepted July 16, 1987 The effect of surface active agents on contact angle hysteresis is examined by photographing sessile drops at the point of incipient motion on an inclined solid. For solutions of anionic and cationic fluorocarbon surfactants Zonyl FSA and FSC and nonionic surfactant octanol on Teflon, contact angle hysteresis is substantially higher than that for pure water. Hydrophobic bonding of the surfactant molecules at the solid-liquid interface appears to be responsible for this change. Although inhomogeneities on the Teflon surface cause the advancing and receding contact angles to vary at a fixed surfactant concentration, their difference displays significantly lower scatter, indicating that hysteresis is a more reproducible material property than the individual contact angles. Experimental dimensionless sessile drop volumes at the critical inclination angle are compared to an analytical prediction by E. B. Dussan V. (J. Fluid Mech. 151, 1 (1985)). For the cationic and anionic surfactant solutions these volumes are between three and four times the predietion from the analysis. This disagreement is especially surprising because the analysis represents a force balance on the drop at the critical configuration, and a reasonable match was obtained for pure liquids by H. V. Nguyen et al. (J. Colloid Interface Sci. 115, 410 (1987)). For solutions of the weak surfactant 1-octanol, the experimentally observed drop volumes at the critical inclination angle match the analytical predictions, indicating that the surfactant strength has an important bearing on the results. One possible explanation is that as the solid substrate is tilted from the horizontal, the sessile drop morphology is modified and the contact line shape changes from circular to one with parallel sides. Such a change must be accompanied by fluid motion. The presence of strong surfactants imposes some hydrodynamic rigidity to the solution-vapor interface and opposes this movement. Therefore, for a fixed drop volume, the inclination angle required for the drop to achieve its critical shape is greater than that predicted by the analysis. © 1988AcademicPress,Inc. INTRODUCTION

Many industrial and natural processes involve either the sticking or motion of sessile drops on solid surfaces--some examples include drop formation on heat exchangers, retention of pesticides on leaves, drop condensation on polished metal surfaces for dewpoint measurements, and rain drops on window panes and automobile windshields. On heat exchanger surfaces the design objective is to facilitate drop roll offinto a collection zone so that the cold solid surfaces can be exposed directly to the condensing vapor. Heat transfer is then not impeded by the presence of a liquid film on the solid surface. In contrast, the design

l Author to whom correspondence should be addressed.

requirement for pesticides is to allow the liquid to spread as much as possible on the leaves without rolling off. In order to successfully meet such opposing requirements, a fundamental understanding of the properties of the solid-liquid system that govern the ability of a drop to be held on a solid surface is required. A major contribution towards this end was made in the analyses by Dussan V. and Chow (1) and by Dussan V. (2). Their usefulness lies in their ability to make predictions based upon knowledge of only system material properties. Contact angle hysteresis is shown to be a key material property that impacts the ability of a drop to slide on an inclined solid (1, 2)--the greater its value, the larger the drop that can be sustained. In practical processes such as those outlined

494 0021-9797/88 $3.00 Copyright © 1988 by Academic Press, Inc. All fights of reproduction in any form reserved.

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CONTAMINATED DROPS ON INCLINED SOLIDS

above, the liquid drops are invariably "impure," either because of inadvertent contamination or because surface active agents are deliberately added. One motivation for this study is to determine the impact of the addition of surface active agents on contact angle hysteresis. The experimental technique used is to place a sessile drop on a horizontal solid substrate, then incline the solid until the drop reaches the point of incipient motion. Advancing and receding contact angles are then obtained from a single image of the drop cross section at the critical configuration. An important prediction in (2) is the maximum drop volume that can be sustained on an inclined solid substrate. This is given in dimensionless form in (2) as Eq. (5.3),

(COS OR -

×

X

(1

c o s 0A)3/2(1 q- COS 0A) 3/4 -

1.5 c o s 0 g + 0 . 5 COS30A)

(COS 0 A ~-

2)3/2(1 --

COS 0A) 9/4

[1]

,2

Here O, a, V, % 0A, and OR represent the liquid density, surface tension, and volume, the critical angle of inclination, and the advancing and receding contact angles, respectively, while g is the gravitational acceleration. In a previous paper Nguyen et al. (3) compared experimentally obtained dimensionless drop volumes at the point of incipient motion to the prediction from Eq. [ 1] for water and glycerol. Agreement was obtained within the measurement error, thereby providing validity to the underlying physics assumed in (2). From a practical perspective, however, it is more relevant to examine the effectiveness of the analysis in making predictions for contaminated liquids. Another objective of this study is to compare the experimentally obtained drop volumes to the predictions from Eq. [1] for solutions of both weak and strong surfactams. As in (3), the approach used is to fix the drop volume, then determine the maximum angle of inclination before the drop slides. This is equivalent to fixing the angle of inclination

and determining the maximum drop volume that can be sustained without sliding (2). MATERIALS AND METHODS

Single distilled double deionized water is distilled over alkaline potassium permanganate, then stored in loosely capped glass bottles until its conductance equilibrates to ~60 #mho/cm. This water is used for preparing surfactant solutions as well as rinsing. Three water-soluble surfactants are used--anionic and cationic fluorocarbon surfactants Zonyl FSA and FSC (DuPont), and nonionic surfactant 1-octanol (Sigma Chemicals). Aqueous solutions are prepared by withdrawing a given volume of the surfactant in a microliter pipet (Eppendorf 4710) and adding it to a known volume of clean water. The molarity of the solutions is obtained from a knowledge of the surfactant molecular weight and density. Two concentrations of FSA and FSC are used. The surface tensions, measured by the Wilhemy plate technique, as well as the variation of surface tension with composition for each of these solutions at 31°C, are shown in Table I. All concentrations are well below the CMC. Octanol is a weak surfactant, as shown by the variation of surface tension with composition, and experiments are conducted at only one concentration. Teflon film (DuPont) of 20 mil thickness is used as the solid. 2 × 5-cm pieces are soaked in Nochromix solution (Godax Laboratories) for 30 min, rinsed repeatedly with the clean

TABLE I Surface Tensions and Variation of Surface Tension with Concentration for Surfactant Solutions Surfactant Zonyl FSA Zonyl FSC l-Octanol

Concentration (g mole/liter) 1.32 3.96 1.14 2.85 7.69

× X X X ×

10-s 10-s 10-s 10-s 10-s

o -0~/0C (raN/m) (mN liter/mgmol)× 10-4 32.5 28.2 43.3 37.8 70.6

19.0 4.5 32.2 12.8 0.52

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PADMANABHAN AND BOSE

water to remove any acid, and dried in specially constructed racks in a closed dessicating chamber. The experimental apparatus is shown in Figs. la and lb. The Teflon piece is held by screws on a tilting stage which is operated remotely by an Apple II + computer interfaced (Adalab interface card from Interactive Microware) to a stepper motor and gear assembly. An Olympus variable intensity condenser serves as the light source, while drop pictures are captured on Kodak 2415 film by a Nikon

F3 camera equipped for macrophotography. The camera is kept horizontal using a level. The tilting assembly is enclosed in a glass chamber with a heating wire running down its top and sides. The temperature inside the chamber is maintained at 31 _+ 0.5°C by a YS163RC temperature controller. The relative humidity of the chamber is maintained at -~85% by leaving several uncovered petri dishes containing water inside. The relative humidity of the room is raised to -~85% using an ultrasonic humidifier. These precautions

FIG. 1. (a) The experimentalapparatus used for the sessiledrop measurements.(b) The stage for holding the Teflonsubstrate. The stage is tilted remotelyby an Apple II+ computer interfacedto the stepper motor and gear assembly. Journal of Colloid and Interface Science, Vol. 123, No. 2, June ! 988

497

C O N T A M I N A T E D DROPS O N IN C LIN ED SOLIDS

assure minimal drop evaporation during an experimental run. A 20-tA drop is withdrawn from the surfactant solution using an Eppendorf 4710 pipet, then deposited onto the Teflon surface through a hole in the top of the chamber. The hole is covered immediately to minimize any interaction of the drop with the external environment. This drop volume is selected so that the critical inclination angle is within 90 ° and its image fits within the frame of the photograph at the magnification used. Preliminary experiments with 10- and 30-~zl drops showed that the contact angle hysteresis was not sensitive to drop size, and a 20-~tl volume was considered optimal. For both FSA and FSC solutions the deposited drop takes nearly 30 s to spread to its final equilibrium position on the horizontal substrate. This is a reasonable lower limit on the amount of time necessary to wait each time the stage is tilted in order to detect drop m o t i o n - - i n these experiments the waiting time is 2 min. The spreading time for the octanol solutions is about 10 s, so that a waiting time of 1 min is considered adequate. The drop is allowed to equilibrate thermally for 10 min. The stage is then inclined 1° at a time. Two drop cross sections are captured at each angle of tilt, shown in Fig. 2. The section AA represents the projection of the drop shape on a vertical plane parallel to the direction of eventual motion, while the section B-B is the drop profile on a plane rotated by 10 ° about a vertical axis from the first one. The purpose of these dual measurements is to examine the contact angle at different locations of the contact line. Unless otherwise specified, the contact angles referred to subsequently are from the A-A section. At the critical inclination angle both the front and back of the drop start moving simultaneously. The image on the frame previous to this represents the critical configuration. After enlarging the pictures to a magnification of 50×, tangents are drawn at the front and rear positions from which the advancing and receding contact angles are obtained. Because these angles vary between 90 ° and 105 °, the error of _+1° in their measure-

A

B

DIRECTION OF DROP MOTION

/ B

A

FIG. 2. Drop photographs are obtained from sections A-A and B-B. Theseperspectivesdifferby 10°.

ment can be considered insignificant. The critical inclination angle is also obtained from the same photographs. The experimentally measured advancing and receding contact angles are substituted into the right-hand side of Eq. [1 ] and a theoretical estimate of the dimensionless drop volume is obtained. The experimental value is obtained upon substituting the drop volume, solution surface tension and density, critical angle of inclination, and gravitational acceleration into the left-hand side of Eq. [1]. RESULTS A N D DISCUSSION

Following the approach used in (2), an appropriate measure of contact angle hysteresis is the hysteresis parameter cos OR -- cos 0A. Figures 3, 4, and 5 are plots of the hysteresis parameter versus the advancing contact angle for different concentrations of the anionic surfactant FSA, the cationic surfactant FSC, and the nonionic surfactant octanol on Teflon. The key feature of these plots is that all the solutions show a hysteresis parameter higher than that of pure water (3), implying that surfactant solutions are held more firmly on the Teflon Journal of Colloid and Interface Science, Vol. 123,No. 2, June 1988

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PADMANABHAN AND BOSE

0.7 0.4

0.6

0.5 0.3 ~ i ~

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98

,

,

,

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100

102

104

106

108

110

112

114

116

118

120

Advancing Contact Angle, 6A in degrees Advancing

FIG. 3. The hysteresis parameter cos OR-- c o s 0Aversus the advancingcontactanglefor 1.32× l0-5 M(O (average, . . . . )) and 3.96 × 10-5 M (V (average, --.--)) Zonyl FSA solutionson Teflon.The arrowindicatesthe hysteresis parameter for water (3). surface than water. Furthermore, this greater "stickiness" is independent of the ionic nature of the surfactant. It is well known that surface heterogeneities on a solid substrate can increase contact angle hysteresis (4). In these cases, hydrophobic bonding between the nonpolar solid surface and the surfactant molecules reduces the solid-liquid interfacial free energy and resists the motion of the drop to a fresh section of the solid surface. Consequently there is greater hysteresis. A c o m m o n feature in all these plots is the

o o v

~yE._ ....

t.) i ~= t~ o

o

~7

o.3

V 0

0

O0 0

o.202

04

98

1 0

I ~

104

106

108

110

Advancing Contact Angle, ~, in degrees

FIG. 4. The hysteresisparameter cos 0R- cos 0Aversus the advancingcontactanglefor 1.14× 10-5 M(© (average, . . . . )) and 2.85 × 10-5 M(X7(average, --.--)) Zonyl FSC solutionson Teflon. The arrowindicatesthe hysteresis parameter for water (3). Journal of Colloid and Interface Science,

Vol. 123, No, 2, J u n e 1988

Contact

A n g l e , 8 A in degrees

FIG. 5. The hysteresis parameter cos OR- cos 0Aversus the advancingcontactangle for 7.69 × l0 -5 M octanol (V (average, --. --)) solution on Teflon. The arrowindicates the hysteresis parameter for water (3). large spread in the advancing contact angle, reflecting nonhomogeneities on the Teflon surface. However, the coefficient of variation of the hysteresis parameter is less than 6% for the anionic surfactant solutions, less than 10% for the cationic, and within 15% for the nonionic surfactant. These results indicate that contact angle hysteresis is a truer material parameter than the individual advancing and receding contact angles. Figures 6 and 7 are plots of the dimensionless volume versus the advancing contact angle for the two concentrations of FSA solutions. The experimental values are nearly four times the theoretical prediction, considerably beyond any error bounds. (The solid vertical bar represents an average uncertainty in the theoretical volume, computed by the propagation of error formula with an error of +_1o in the receding contact angle; the dashed vertical line shows the average error in the experimental volume, again calculated using the propagation of error formula, with errors of _+1o in the critical inclination angle, _0.1 m N / m in the surface tension, and +0.1 tzl in the drop volume.) Figures 8 and 9 show the dimensionless drop volume versus the advancing contact angle for the two concentrations of cationic surfactant FSC. Again, the experimental values are consistently higher than the analytical predictions, implying that far higher

CONTAMINATED

499

DROPS ON INCLINED SOLIDS

1.60

~0 1.40

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•

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Advancing Contact Angle, 0A in degrees

.

90

.

.

92

FIG. 6. Comparison of theoretical (O) and experimental (O) dimensionless critical sessile drop volumes for 1.32 X 10 -5 M FSA solution on Teflon. The stars indicate corresponding experimental and theoretical points. The solid vertical bar represents an average uncertainty in the theoretical prediction caused by an uncertainty of + 1 o in the measurement of the receding contact angle. The dashed vertical bar represents an average experimental error.

drop volumes can be sustained on an inclined surface than predicted by the analysis. These results are especially interesting because the experiment and theory matched for pure water and glycerol (3). They are also unexpected be-

.

.

06

7

.

98

100

2

'

i

104

106

108

Advancing Contact Angle. ~ in degrees

FIG. 8. Comparison of theoretical ( e ) and experimental (O) dimensionless critical sessile drop volumes for 1.14 X 10 -5 M FSC solution on Teflon. The stars and small black dots indicate corresponding experimental and theoretical points. The solid vertical bar represents an average uncertainty in the theoretical prediction caused by an uncertainty of --_1 o in the measurement of the receding contact angle. The dashed vertical bar represents an average experimental error.

cause the prediction in (2) is obtained from a force balance on the drop at the critical position, which must hold even for these surfactant solutions.

0

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.

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9o g,

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9~ 96 97 g, g9

Advancing Contact Angle, OAin degrees

FIG. 7. Comparison of theoretical ( e ) and experimental (O) dimensionless critical sessile drop volumes for 3.96 X 10 -5 M FSA solution on Teflon. The stars and small black dots indicate corresponding experimental and theoretical points. The solid vertical bar represents an average uncertainty in the theoretical prediction caused by an uncertainty of + 1 o in the measurement of the receding contact angle. The dashed vertical bar represents an average experimental error.

• 0.290

, 92

, 94

, 96

, 90

•

o*• = 100

.-

•

oi I 102

' 104

0r 1 6

, 108

Advancing Contact Angle,0 A in degrees

FIG. 9. Comparison of theoretical ( e ) and experimental (O) dimensionless critical sessile drop volumes for 2.85 x 10 -5 M FSC solution on Teflon. The stars and small black dots indicate corresponding experimental and theoretical points. The solid vertical bar represents an average uncertainty in the theoretical prediction caused by an uncertainty of-+ 1 o in the measurement of the receding contact angle. The dashed vertical bar represents an average experimental error. Journal of Colloid and Interface Science,

VoL

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2, June

1988

500

PADMANABHAN AND BOSE

In (2), the contact angles on the curved sections of the drop are assumed to be uniform. Although this can be justified physically for pure liquids, it is not obvious that this should be the case for the surfactant solutions since surfactant concentrations at different locations on the contact line could vary because of heterogeneities on the solid surface. In these experiments, advancing and receding contact angles from section B-B do not differ by more than 1° from the corresponding values from section A-A, showing that the contact angle does not vary significantly along the forward and rearmost locations of the contact line. A significant component of the force not accounted for in the analysis in (2) can be produced only by contact angle variations in the forward and rearmost sections; therefore, the cause of this large deviation lies elsewhere. The results for the weak nonionic surfactant octanol are quite different from those for the fluorocarbon surfactants as shown in Fig. 10. The deviation between the experiment and theory is well within the error bounds, paralleling the results for pure liquids (3). The strength of the surfactant, which has a strong impact on the difference between the 0.48 0.44 0_40 "~ E=

:>

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¢" E _= ,~

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0.16 0.12 0.08 96

;:;6

1 9

I 100

I 101

I 102

I 103

I 104

I 105

I 106

I 107

I 108

/ 109

110

Advancing Contact A n g l e , OA i n degrees

FIG. 10. Comparison of theoretical (e) and experimental (O) dimensionless critical sessile drop volumes for 7.69 X 10-5 M octanol solution on Teflon. The stars indicate corresponding experimental and theoretical points. The solid vertical bar represents an average uncertainty in the theoretical prediction caused by an uncertainty of -+1° in the measurement of the receding contact angle. The dashed vertical bar represents an average experimental error. Journal of Colloid and Interface Science, Vol. 123, No. 2, June 1988

TABLE II Drop Elongation From the Initial Configuration for Zonyl FSA, FSC, and Octanol Solutions

Surfactant

Zonyl FSA Zonyl FSC 1-Octanol

Concentration (g mole/liter)

1.32 3.96 1.14 2.85 7.69

X X X X X

10-5 10-5 10-5 10-5 10-5

% elongation

1.19 4.52 1.55 4.73 <1.0

experimental and predicted volumes, is a dynamic property and should be relevant only when there is liquid motion. Its importance in these static experiments is therefore puzzling. A possible explanation, necessarily speculative at this stage, can be extracted by comparing drop lengths at the initial and final positions as shown in Table II. The drop must rearrange its shape as it goes to its critical position (1, 2), thereby requiring some liquid movement. When strong surfactants are present, this motion is impaired because of the hydrodynamic rigidity of the liquid-vapor interface (a measure of this rigidity is given by the variation of surface tension with composition in Table I). It is possible that the drop morphology assumed in (2) at the critical position cannot be achieved at the predicted critical inclination of the substrate, especially if large shape changes from an initial configuration are required. These experiments indicate that an analysis that tracks drop surface and contact line shapes as the substrate is inclined would be very worthwhile. It is interesting to note that despite the large spread in the advancing contact angles for a given surfactant concentration, the theoretical dimensionless drop volume shows little scatter in Figs. 6-10. This is because the factor multiplying the hysteresis parameter cos OR -- COS0A on the fight-hand side of Eq. [1 ] is only a slowly varying function of 0A (it goes from 0.353 to 0.308 when 0A is changed from 90 ° to 100 °) and the hysteresis parameter does not vary significantly even if the advancing contact angle changes.

CONTAMINATED DROPS ON INCLINED SOLIDS CONCLUSIONS Contact angle hysteresis for dilute aqueous solutions of Zonyl fluorocarbon cationic and anionic surfactants as well as 1-octanol are greater than that for pure water. This implies that drops of these surfactant solutions are held more firmly to the Teflon surface than water. Hydrophobic bonding of the surfactant molecules at the solid-liquid interface reduces the interfacial free energy and appears to be responsible for this increase. Inhomogeneities on the Teflon surface cause large variations in the advancing and receding contact angles for a given surfactant concentration. However, the scatter in the hysteresis parameter is significantly lower, showing that hysteresis is a truer material property than the individual contact angles. The average deviation between experimentally observed maximum drop volumes that can be sustained on an inclined solid are between three and four times the analytical prediction by Dussan V. (2) for both anionic and cationic fluorocarbon surfactant solutions. The match between experiment and theory is good for solutions of the weak nonionic surfactant octanol. Along the curved portions of the contact line the contact angles are uniform, in accordance with a key assumption in (2).

501

A possible explanation for this large discrepancy is that the change in shape required when the drop goes from its initial to the critical position is resisted by the hydrodynamic rigidity of the liquid-vapor interface. This is also suggested by the match between experiment and theory obtained for the weak surfactant solutions of octanol. An analysis predicting sessile drop configurations as the substrate is tilted from the horizonal to the critical position for both pure liquids and surfactant solutions would be helpful toward confirming these ideas. ACKNOWLEDGMENTS This work was supported by grants from the National Science Foundation (CPE 8305114) and the Petroleum Research Fund of the AmericanChemicalSociety(16188G5 and 18430-AC7). We thank E. B. Dussan V. and J. Estrin for severalstimulating discussions, H. V. Nguyen for setting up the apparatus, and the DuPont company for their generoussupplyof surfactantsand Teflonsheets. REFERENCES 1. DussanV., E. B., and Chow, R. T. -P., J. FluidMech. 138, 1 (1983). 2. Dussan V., E. B., J. FluidMech. 151, 1 (1985). 3. Nguyen,H. V., Padmanabhan, S., Desisto,W. J., and Bose, A., J. Colloidlnterface Sci. 115, 410 (1987). 4. Dettre, R. H., and Johnson, R. E., Jr., J. Phys. Chem. 69, 1507(1965).

Journal of Colloid and Interface Science, Vol. 123, No. 2, June 1988