Shapes of Splattered Drops - Langmuir (ACS Publications)

Article pubs.acs.org/Langmuir

Shapes of Splattered Drops Sri Vallabha Deevi, Nachiketa Janardan, and Mahesh V. Panchagnula* Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai, India S Supporting Information *

ABSTRACT: Drops that impact and stick to a surface (splattered drops) commonly show noncircular triple lines. Physical or chemical defects on the surface are known to pin the triple line in this static metastable state. We report an experimental study to relate the defect distribution on a surface to the triple-line microstructure of such drops. Triple lines of an ensemble of splattered drops have been imaged on a range of surfaces varying in wetting properties. Local contact angles have been calculated, and the microscale pinning force distribution has been estimated. We propose a novel method of estimating defect strength distribution from the pinning forces, using extreme value analysis. From this analysis, we show that pinning force distributions have finite upper and lower bounds. We show that most common surfaces show both hydrophobic and hydrophilic defects, but their strength distributions are asymmetric in relation to the surface’s advancing and receding angles. In addition, we show that the range of microscopic pinning forces varies linearly with macroscopic contact angle hysteresis but, surprisingly, with a nonzero intercept. We explain the intercept by drawing an analogy to static and dynamic friction.

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their wetting characteristics or both.8,9 A defect could be more hydrophobic than the substrate (such as specks of Teflon embedded in glass substrate). In such a case, the defect would likely pin an advancing triple line.10 In the other case, such as when specks of glass are embedded in a Teflon substrate, the receding triple line could be affected. Irrespective of their nature, the effect of the defectswhether differing in size or chemical characteristicsis the same; they induce pinned states in sessile drops which occur via the triple line.11,12 Several applications could benefit from the knowledge of a substrate’s defect strength distribution. For example, in printed circuit boards, solder is applied as a molten liquid drop on the surface to bond two or more electrical connections. The area on the board to be wetted and the thickness of the wires to be connected determine the volume of solder to be applied, based on the assumption of a circular triple line. If the triple line is noncircular due to surface defects, solder may protrude out and come into contact with neighboring connections, shorting the circuit.13 In coatings and painting, surface defects may cause a noncircular drop that on drying will leave a different pattern from what is expected.14 Similarly, in the case of waterproofing, surface defects play a role in determining drop shape and adhesion.15 The direct approach to obtain defect strength distribution is to measure the surface chemistry as well as topography. This approach is both time-consuming and expensive. In addition, such surface characterization techniques do not yield information on application-relevant length scales. In this

INTRODUCTION In nature, circular footprint sessile drops are an exception rather than the rule. While surface tension attempts to make the footprint of small drops circular, a host of surface factors physical and chemicalprevent the drop from becoming so. This process of pinning, induced by surface defects, has been widely described and studied in the literature.1,2 At thermodynamic equilibrium, an ideal surface can be characterized by a single and unique contact angle, usually referred to as the Young’s contact angle (θY) as well as a circular triple line. The contact angle subtended by a sessile drop is widely used as a measure of surface wettability and sometimes even as a quality control tool.3 In addition, the triple line, defined as the interface between the solid surface, liquid drop, and the vapor phases, was also shown to be important.4 It is common observation that the triple line takes on noncircular, arbitrary, and often interesting shapes (see Figure 1a for an example) on real surfaces. These surfaces also exhibit contact angle hysteresis (CAH). CAH is experimentally characterized by two limiting contact angles: a receding contact angle (θr) obtained from a dewetting experiment and an advancing contact angle (θa) obtained from a wetting experiment. A good overview of various methods for contact angle measurement and its applications is given in Biolè et al.5 One imaging approach to measure contact angle is given by Meiron.6 The causes of contact angle hysteresis are manifold, but all of them implicate the role of surface defects. While an ideal surface can be thought of as a chemically and topologically homogeneous surface, a hysteretic surface can be modeled as one where microscale specks of one material (called defects) are embedded in an otherwise ideal substrate.7 These defects can be characterized by various measures, such as their size or © 2017 American Chemical Society

Received: March 19, 2017 Revised: April 17, 2017 Published: April 19, 2017 4592

DOI: 10.1021/acs.langmuir.7b00933 Langmuir 2017, 33, 4592−4600

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Article

MATERIALS AND METHODS

Two classes of experiments were performed during the course of this study. The first class of experiments includes the quasi-static measurement of macroscopic advancing and receding angles using an optical contact angle measuring instrument (OCMI), also called as goniometer. This instrument also has a motorized syringe pump to deliver metered quantities of liquid, using which liquid can be infused or withdrawn from a sessile drop. Please refer to Figure S1 in the Supporting Information for a schematic of the OCMI setup. In this experiment, a liquid drop is placed on a surface and imaged as a profile. The contact angle is estimated by a best-fit ellipse to the drop profile and a tangent at the point of contact with the surface. The accuracy of contact angle measurement of the OCMI is ±2°. Care was taken to ensure that the needle’s influence on contact angles, especially for small drops and during the receding angle measurement was minimal.26,27 Infusing liquid into the sessile drop causes the contact line to move outward. The asymptotic contact angle during this experiment is the advancing contact angle. Similarly, withdrawal of liquid causes the contact line to move inward, yielding the receding angle. Thus, a surface can be characterized by these quasi-static limiting contact angles. We have used five liquid−substrate pairs that exhibit varying contact angle hysteresis. The corresponding advancing and receding angles are presented in Table 1.

Table 1. Properties of the Liquid−Substrates Investigateda

Figure 1. (a) Shapes of splattered toluene drops on modified silica surface. The triple line is noncircular with wrinkles resulting from pinning of the triple line. The inset shows a magnified view of a section of the triple line. Fine scale features of the wrinkled triple line can be observed. (b−e) Steps in obtaining the triple line from images. Images of drop with different directions illuminated (b, c) are added, and thresholding results in a black and white image (d), from which the triple line is extracted (e).

liquid−substrate water−glass (WG) water−acrylic (WA) glycerin−acrylic (GA) toluene−organofluorosilane (TOFS) toluene-modified silica (TMS)

θa (deg)

θr (deg)

θY (deg)

γl (mN/m)

76 72 60 53

26 39 30 34

55.2 57.1 46.9 44.3

72.0 72.0 67.8 27.7

81

72

76.5

27.7

a

Advancing angle (θa), receding angle (θr), and liquid surface tension (γl) are included. Following Vedantam and Panchagnula,29 cos θY ≈ (1/2)(cos θa + cos θr).

work, we will discuss a novel and simple technique of obtaining similar information from images of the triple line shapes of splattered drops. This is based on the idea that the triple line is an elastic body that responds to surface tension forces from both the substrate as well as any inlaid defects.1 We will show that the advancing and receding contact angles are inadequate to estimate these microscopic surface characteristics. In contrast, we will discuss an analysis of the triple line shape of randomly shaped drops, which can reveal microscopic defect strength distribution related information. Many studies have reported on the effect of surface defects on triple line dynamics 16−18 as well as on wetting hysteresis.19−21 Triple lines of slow moving drops have been used to analyze surface heterogeneities on carefully prepared surfaces.22−25 However, a study of the inverse problem of extracting defect distribution information on real surfaces from triple line shape measurements is missing from the literature. We will focus on this lacuna. We will rely on experimental observations from static splattered drops to show that the shape of the pinned triple line contains useful information about the defect strength distribution of that surface. For the purpose of this article, we will refer to defect strength distribution in a way that is agnostic to its originswhether it arises from variation in defect size or from its chemical composition. Specifically, we would like to address two questions. (1) Can we describe the nature of surface’s defect strength distribution from measuring the triple lines of static, randomly placed sessile drops? (2) What is the relation between the contact angle hysteresis of a surface measured from quasi-static drops and the shapes of purely static drops?

The second class of experiments involves the measurement of the triple line shapes of purely static noncircular, randomly shaped droplets placed on a surface. This information is used to estimate the local contact angle around the periphery of the drop. In this experiment, drops of fixed volume (15 μL) are dropped from a small height ( 0 is the standard deviation. On the other hand, ξ is the shape parameter of the cdf and is important in determining the type and bounds of the extreme value distribution. The pdf corresponding to eq 5 is given by

Figure 3. (a) Polar plot of local contact angle (θl) (solid line) as a function of azimuthal angle (ϕ) for a drop of water on glass substrate. The highly wrinkled triple line is indicative of the large number of defects and pinning sites on the surface. The triple line (dotted line) is also shown for reference. A 15° sector is shown bounded by two lines. (b) A magnified view of the variation of θl versus ϕ within the 15° sector indicated in (a). The maximum (◇) and minimum (△) θl within each sectoral block are chosen and marked. There are a minimum of 24 such blocks in one drop, and at least 15 drops are studied for each liquid−substrate combination. This provides a sufficient sample size to ensure high confidence in the conclusions.

f (θ : ω , τ , ξ ) =

−1/ ξ − 1 ⎡ ⎤−1/ ξ 1⎡ θ − ω⎤ −⎣1 + ξ θ −τ ω ⎦ 1 + ξ e ⎢ ⎥ τ⎣ τ ⎦

(6)

In the limit of ξ = 0, eqs 5 and 6 become [−(θ − ω)/ τ ]

F(θ: ω , τ , 0) = e{−e f (θ: ω , τ , 0) =

}

(7)

1 [−(θ − ω)/ τ ] {−e[−(θ−ω)/τ]} e e τ

(8)

The value of ξ in eq 6 carries information about the parent distribution that is responsible for these maxima. We will use Figure 4 to illustrate the effect, which shows a plot of eq 6 for ω = 0, τ = 2 and for three values of ξ. If ξ = 0 (implying a Gumbel distribution of the maxima), the parent defect distribution is expected to exhibit an exponential tail, such as a Gaussian distribution. If ξ < 0 (implying that the maxima follow a Weibull distribution), the generating parent defect distribution has a finite tail (shown in Figure 4), such as in the case of the beta distribution. If ξ > 0 (implying that the maxima follow a Fréchet distribution), the parent defect distribution is expected to exhibit a polynomial tail, such as in Students’ t distribution. Therefore, we are interested in extracting a value of ξ for the set of maxima obtained from a liquid−substrate combination, since it could throw light on the nature of parent surface defect distribution. The stepwise process to implement this methodology is as follows: (1) Image the drop on surface using multiview imaging. (2) Extract the triple line coordinates from the composite image. (3) Use the analytical solution of Prabhala et al.30 to calculate the local contact angle distribution. (4) Divide the triple line into angular blocks and obtain the maximum and

Figure 4. Plot of three pdf’s from the generalized extreme value distributions with ω = 0 and τ = 2 and three different ξ values of 0, +1/2, and −1/2. Distribution with ξ = +1/2 is a Frechet distribution with a lower limit indicated by circle on the curve at xc = ω − τ/ξ. Distribution with ξ = −1/2 is a Weibull distribution with an upper limit indicated by circle on the curve at xc = ω − τ/ξ. These symbols indicate the limits on parent distribution. There are no limits in the case of curve with ξ = 0 since it follows a Gumbel distribution.

Figure 5. Plot of pdf of local contact angles from an ensemble of drops for a given liquid−substrate combination. θa and θr are also marked for reference. (a) water−glass and (b) toluene−organofluorosilane. For water−glass, most of the local contact angles lie within θa and θr. In case of toluene−organofluorosilane, most of the local contact angles are outside the bounds of θa and θr. 4595

DOI: 10.1021/acs.langmuir.7b00933 Langmuir 2017, 33, 4592−4600

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Figure 6. Plot of the pdf of distribution of water−glass for (a) maxima and minima of local contact angle (θl) and (b) maxima and minima of pinning force per unit length (- ). A comparison of the empirical pdf with the GEV fit is also shown. The lower limit for the contact angle minima pdf is indicated by a triangle. This is also shown as the upper limit in the maxima pdf in - .

reported in slowly moving drops.43 In addition, it can be seen that a significant fraction of the local contact angle values are greater than the advancing angle. In contrast, only a small fraction of the local contact angle values are less than the quasistatic receding angle. This asymmetry was also observed for the water−glass case but is much more pronounced with toluene− organofluosilane, similar to earlier observations.18,44 As mentioned before, the infusion−withdrawal experiment is a quasi-static measurement of the contact angle where the interface is in constant motion. In contrast, the local contact angle is calculated on a splattered drop which was static. The triple line in such a case would have settled down into a metastable state after numerous advancing/receding events. Thus, it is anticipated that the instantaneous triple line in the quasi-static case will be less rough than the triple line of a purely static drop. In other words, the purely static (splattered) drop is likely to exhibit a wider range of contact angles than the infusion/withdrawal experiment, leading to a higher probability of extreme values, originating (say) from surface chemical heterogeneities. Extreme Value Analysis Results. The local contact angle data were analyzed to yield a probability density function (pdf) for the extreme values of contact angles (both maxima and minima). Figure 3a illustrates the variation of the local contact angle around the drop, and Figure 3b shows the variation within a block. As mentioned earlier, a set of maxima is obtained from an ensemble of sessile randomly shaped drops for each liquid−substrate pair. A GEV cdf of the form given in eq 5 was fit to this data, using the maximum likelihood estimation technique41 to extract the values of GEV parameters, ω, τ, and ξ. Care was taken to ascertain that the number of drops (N) as well as the image resolution was sufficient to achieve converged values for these GEV parameters. See the Supporting Information for a detailed discussion of these aspects. We will now discuss the pdf’s obtained for water−glass from both maxima as well as minima data. Figure 6a depicts the pdf’s obtained from the local contact angle maxima and minima for water−glass. The figure also includes the experimental block extrema pdf along with the GEV model fit. First, it can be seen from this figure that the GEV model fits the data well. As can be

minimum contact angle for each block. (5) Fit eq 5 to the minima and maxima data separately using maximum likelihood estimation to obtain the shape parameter ξ for each data set.

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RESULTS AND DISCUSSION As discussed before, the advancing and receding contact angle values are based on macroscopic measurements derived from a quasi-static wetting process. While they are useful in understanding the macroscopic wetting hysteresis characteristics of a surface, they do not provide insight into the nature of the defects on the surface, except in a mean sense. On the other hand, local contact angle information such as that presented in Figure 2a was obtained on a purely static drop. We will make an attempt to relate these two measurements obtained from two different protocols and show that the latter contains more information about the defect distribution on a surface. Advancing, Receding, and Local Contact Angles. It has been suggested that the local contact angles on a static drop should approximately fall within the limits prescribed by the advancing and receding angles of that substrate.42 In order to investigate this proposition, 15 drops were characterized for each liquid−substrate pair, and the local contact angle variation was obtained for each drop. Figure 5a shows a pdf of the local contact angle distribution for water−glass from all the 15 drops. The advancing and receding angles for this liquid−substrate pair are marked in Figure 5a for reference. As can be seen from this figure, the local contact angle values are generally within the limits prescribed by the quasi-static advancing and receding angles. However, one can also observe from Figure 5a that a small fraction of the local contact angles lies outside the quasistatic limits. In addition, the tails of the distribution are also somewhat asymmetric in relation to the advancing and receding angles.18 Figure 5b shows a histogram similar to Figure 5a, but for the liquid−substrate pair of toluene−organofluorosilane. It can be seen from this figure that the histogram of local contact angles exhibits two peaks. For the case of water−glass (as well as for water−acrylic), it was observed that the pdf’s of the local contact angle values generally follow a normal distribution. In general, however, there is no reason to expect that the local contact angle distribution should be normal, or for that matter, even single peaked. This kind of multiple peaks have also been 4596

DOI: 10.1021/acs.langmuir.7b00933 Langmuir 2017, 33, 4592−4600

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Figure 7. Plot of the pdf of distribution of water−acrylic and glycerin−acrylic for (a) maxima and minima of local contact angle (θl) and (b) maxima and minima of pinning force per unit length (- ). The most probable extreme values of θl from (a) are different for the two cases. However, the most probable maximum as well as minimum pinning force values are the same for both water−acrylic and glycerin−acrylic. (b) Maxima and minima pdfs have upper and lower limits, respectively. The total range of pinning forces on acrylic is therefore bounded by these two values.

data obtained using two different liquids on the same (acrylic) substrate. Let us consider the two maxima curves in Figure 7a. The most probable maximum contact angle values from these pdf curves are different. However, from considering the two minima curves in Figure 7b, one can observe that the most probable value of - is the same. This is due to the fact that the substrate is the same and the differences in the most probable maxima contact angles in Figure 7a are only due to differences in the surface tensions of water and glycerin. A similar observation can also be made from comparing the two minima pdf curves in Figure 7a with the two maxima pdf curves in Figure 7b. This implies that one can use any liquid to probe a surface using the GEV framework and the extrema in - would remain unaffected. This is therefore a robust technique that can be used to compare the surface characteristics of two substrates based on their extreme pinning force distributions. For example, one could employ this technique in a glass slide manufacturing process as a quality control tool. The nature of the defect strength distribution on the substrate can be inferred from the shape parameter (ξ) of the GEV fit. Table 2 shows the shape parameters for the minima as well as the maxima in - for various liquid−substrate combinations. It may be recalled that the maxima pdf describes the nature of defects that are more hydrophilic than the

observed from Figure 6a, the pdf for the minima exhibits a slightly narrower width than that of the maxima. On an ideal surface, all drops would manifest a unique contact angle, θY. If a point on a drop exhibits a local contact angle θl different from θY, a localized pinning force is responsible.1 One can therefore define a local pinning force per unit length - as - = γl(cos θl − cos θY )

(9)

This definition of pinning force allows us to reconcile data obtained from liquids of varying γl as well as from substrates of varying θY. - is also a measure of the local defect strength that is responsible for pinning the triple line. An - < 0 (> 0) implies a pinning force directed toward (away from) the center of the drop. Since θY is difficult to measure directly, we will assume that it can be approximated from the advancing and receding angles as cos θY ≈ (1/2)(cos θa + cos θr).29 We have verified that the value of ξ remains the same for other forms of θY.45 Figure 6b is a plot of the data from Figure 6a presented in terms of the local pinning force. A maximum θl will imply a minimum - due to the decreasing nature of the cos function in eq 9. Therefore, the pdf for minima in - corresponds to extremely low-energy pinning sites that are preventing the triple line from advancing forward (akin to say, specks of Teflon embedded in a glass substrate). The maxima in correspond to hydrophilic defects that prefer to remain wetted (akin to say, specks of glass embedded in a Teflon substrate). As can be observed from Figure 6b, the width of the minima pinning force pdf is greater than that from the maxima pdf. This indicates that the glass substrate (which is generally hydrophilic) has a wide range of pinning forces originating from embedded hydrophobic defects. In other words, the richness of triple line shapes on a generally hydrophilic substrate is determined primarily by the width of the pdf corresponding to the minima in - . Figures 7a,b are similar to Figures 6a,b except that they include data from two liquid−substrate combinations: water− acrylic (WA) and glycerin−acrylic (GA). This figure presents

Table 2. Shape Parameter ξ for the Maxima and Minima Pinning Force per Unit Length (- )a liquid substrate WG WA GA TOFS TMS

maxima GEV ξ (95% confidence) −0.40 −0.29 −0.34 −0.44 0.10

± ± ± ± ±

0.04 0.06 0.07 0.03 0.08

minima GEV ξ (95% confidence) −0.04 −0.19 −0.17 −0.14 0.0

± ± ± ± ±

0.08 0.08 0.1 0.1 0.09

Values for five liquid−substrate combinations are shown. ξ < 0 implies that the extrema follow a Weibull distribution with a finite upper limit for maxima and lower limit for minima. ξ = 0 implies that the extrema follow a Gumbel distribution. a

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DOI: 10.1021/acs.langmuir.7b00933 Langmuir 2017, 33, 4592−4600

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Langmuir substrate and the minima pdf describes the nature of defects that are more hydrophobic than the substrate. As can be seen from Table 2, ξ < 0 for most liquid−substrate combinations, indicating that the extrema follow a Weibull distribution. This is true for both the maxima as well as the minima pdf’s. From the Fisher−Tippett theorem,40 one can conclude that since ξ < 0, the original parent distribution of surface defect strength has finite limits on the maxima as well as the minima (for example, a beta distribution). These finite limits imply that the strengths of hydrophilic surface defects have an finite upper bound. Similarly, the set of hydrophobic defects causing minima in pinning force have a finite lower bound in strength. Since both maxima and minima are bounded, the original parent defect distribution is also bounded. In the two cases of minima for water−glass as well as both maxima and minima for toluenemodified silica, ξ = 0 lies within the confidence interval. In these cases, it can be inferred that the defect strength has an exponential tail (such as in a Gaussian distribution). Interestingly, we have not encountered any situation where ξ > 0. This kind of information about the nature of the parent defect distribution is difficult to obtain from any other surface characterization technique. It is indeed remarkable that one can infer the nature of defect distribution from imaging the triple lines of a few drops splattered on the surface. As mentioned before, contact angle hysteresis has typically been characterized in terms of the advancing and receding angles. A mean pinning force per unit length (- G ) can be related to these angles as - G = γl(cos θr − cos θa).46,47 We

Figure 8. Plot of static pinning force (- S ) versus mean pinning force 5 per unit length (- G ). - S = - 95 max − - min is the difference between the bounds within which 90% of all extreme values will occur. They follow a linear relation, - S = 1.2- G + 19.59 with R2 > 0.98. The nonzero intercept indicates that splattered shapes are possible even at vanishingly small - G .

where - G is the lowest of all the five substrates considered. This can possibly be explained by a hypothesis that static drop shapes are primarily controlled by the extremities in the defect strength distribution while contact angle hysteresis is correlated to the mean defect strength. An analogy can be made of - S and - G to static and dynamic Coulomb friction. As discussed, - S is a measure of pinning forces that are responsible for the randomness in the purely static shapes of splattered drops. On the other hand, - G is derived from quasi-static measurements of the advancing and receding contact angles. During the quasi-static process, the triple line may experience a large number of pinning/depinning events which has been described as “flicker” by Decker and Garoff.16 In other words, the time scale associated with a single pinning/depinning event is much smaller than the time scale associated with quasi-static motion of the triple line during the measurement of θa and θr. This results in an averaged view of the resistance during motion. Static friction is responsible for the metastable equilibria shapes, while dynamic friction is a measure of resistance to triple line during motion. The latter vanishing does not automatically imply that the former follows suit. This proposition gives rise to a possibility that even on superhydrophobic surfaces, one could see metastable random shapes, owing to a few (in number) extreme strength defects. While drops placed on carefully prepared solid surfaces could take circular shapes, sessile drops on more realistic surfaces take on random noncircular shapes due to surface defects. On such surfaces, circular static sessile drops remain an exception rather than the rule. On a practical note, we have outlined a simple and robust procedure by which a substrate’s defect strength distribution can be sampled through the use of randomly placed drops as interrogation agents. The imaging tools employed need to resolve the fine scale triple-line structure. With that information on hand, we have shown that our analysis will yield a shape factor ξ, which is invariant to other experimental parameters and conditions. We propose that this shape factor can be used as a quantitative metric of a given substrate.

would like to examine the relationship between - G and a measure of the pinning force obtained from the extreme value analysis. Let us consider the case of glycerin−acrylic in Figure 7b to illustrate the point. From the GA-max pdf in this figure, it can be seen that the maxima pinning forces approximately range from 0.01 to −0.03 N/m. From the GA-min pdf, the minima pinning forces can be observed to range from 0.01 to −0.06 N/m. This implies that a range of pinning forces between 0.01 and −0.06 N/m are possible on a static drop. We 5 choose - 95 max (95th percentile in maxima) and - min (5th percentile in minima) to quantitatively describe a static pinning S G 5 force (- S ) as - S = - 95 max − - min . - is similar to - and is a statistical estimate of the range of pinning forces possible for a given liquid−substrate combination. The higher the value of - S , the greater could be the range of triple-line shapes of static pinned drops. Figure 8 is a plot of - S versus - G for the five liquid− substrate combinations investigated. As can be seen from this figure, - S is linearly correlated with - G. This indicates a good correlation between the macroscopic pinning force hysteresis and the range of microscopic pinning forces. However, as the contact angle hysteresis approaches zero, the range of microscopic static forces does not appear to asymptote to zero. This can be seen from the intercept on the - S axis at a value of about 20 mN/m. This indicates that as the advancing and receding angles approach a single value, the range of microscopic contact angles may not converge toward zero. In other words, nonaxisymmetric random drop shapes may be possible even when the contact angle hysteresis is vanishingly small. In fact, indirect experimental evidence of this fact can be seen from the drop shapes of toluene on modified silica substrate (TMS) that are shown in Figure 1. TMS is a case

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CONCLUSIONS We have investigated shapes of static randomly placed sessile drops on real surfaces. We have performed quasi-static 4598

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measurements of advancing and receding angles of these surfaces to measure its contact angle hysteresis. On these surfaces, randomly shaped drops in metastable pinned states are imaged from below, and the triple line shape is extracted from these images. Using this information, local microscale contact angles on the triple line are computed using an analytical solution. Statistical analysis of extreme values in these microscale contact angles and local pinning forces (estimated from the contact angle) is performed for various liquid− substrate combinations. We demonstrate that triple-line shapes of randomly placed drops respond to surface defect strength distribution. This response is robust and is not affected by image resolution and number of drops sampled. In addition, any liquid can be used to characterize a given surface. From this study, we conclude the following: (i) Most real surfaces appear to manifest a defect strength distributions with finite upper and lower bounds. A functional form of this distribution can also be extracted from the measured triple-line shapes. (ii) The range of local static pinning forces scales linearly with classical contact angle hysteresis. (iii) This method can be used to estimate defect strength distribution on real surfaces, say, in a real-time quality control application.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.7b00933. Figures S1−S5 and Tables S1−S5 (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]; Ph +91 44 2257 4056 (M.V.P.). ORCID

Mahesh V. Panchagnula: 0000-0003-2943-6900 Author Contributions

M.V.P. conceived and planned the work. N.J. performed the experiments. S.V.D. performed the extreme value analysis. S.V.D. and M.V.P. wrote and edited the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Avijit Baidya and Prof. Pradeep for contributing the modified silica surface used in this study. REFERENCES

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DOI: 10.1021/acs.langmuir.7b00933 Langmuir 2017, 33, 4592−4600