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As a widespread technique appliedto surface characterization, thesessile drop test (Ref. 1) has sup-

ported the study and improvement of in-numerous systems, from protective coat-ing films (Ref. 2) to joining technology(Ref. 3). The sessile drop test is commonlyapplied to brazing studies to measure thecontact angle of specific systems to evalu-ate filler metal wettability (Ref. 4) and,consequently, its adequacy for producingsuccessful brazed joints (Ref. 5).

The wettability evaluation of moltenfiller metal on base materials presents sev-

eral challenges for brazing engineers dueto the difficulties associated with the con-tact angle measurement. In-situ measure-ment at brazing temperature requirescomplex instrumentation and has inher-ent high costs, while optical microscopymeasurement of cross-sectioned samplesis a time-consuming task due to the re-quired sample preparation. In addition,the characteristic low contact angles re-quired for brazing processes seriouslycompromises the acuity of these tradi-tional methods.

Aiming the development of a simpli-

fied approach for contact angle evalua-tion, this work proposes a simplified geo-metric model and compares its results

with the optical microscopy analysis ofcross-sectioned samples for the evaluationof a copper-stainless steel brazing system.

Experimental Methods

A typical brazing thermal cycle underpure hydrogen atmosphere was applied toten samples, as shown by the time-tem-

perature profile illustrated, which appliesa peak temperature of 1150C Fig. 1.Each sample consisted of 50 50 3 mm

AISI 304 stainless steel base metal de-greased and pickled in two stages withpure hydrochloric and chromic acids, anda copper filler metal (C11000) piece withapproximately 50 mg freely placed on topof the base metal.

The copper-stainless system contactangle was evaluated on the sessile dropusing two different methodologies, thestandard cross-sectioning and the pro-posed drop projected area method, which

is described in the next section. For thecross-sectioning method, the sampleswere sectioned using a precision saw(Buehler IsoMet 4000) followed by metal-lographic preparation and optical mi-croscopy (Leica DMLM 100) observa-tion. Finally, the contact angle wasobtained from the digital images using Im-ageJ software. On the other hand, forthe projected area method, plain view dig-ital images of the brazed samples were ob-tained using a digital camera (NikonCoolpix 5200 5.1M). The image was digi-tally scaled using a reference object

(caliper). The projected area of the brazeddrop sitting on top of the base metal wasevaluated by color contrast on the digitalimages using ImageJ software.

Proposed Projected AreaMeasurement Method

The proposed method is based on fun-damental geometry and assumes that anysessile drop can be considered as a spher-ical cap, which is a good approximation

when the drop is small and surface tensiondominates over the gravity (Ref. 6) Fig.2A. From this assumption, it is possible toevaluate the contact angle, when

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Results and Discussion

Figure 4A shows the drop plain viewdigital image taken after the sessile droptest, and Fig. 4B presents a detail of thedrop cross-section image obtained after

metallographic preparation, which was

used for contact angle measurement.The results obtained using the contact

angle measurements on cross-sectionedsamples and the projected area methodsfor the copper-stainless steel systembrazed under pure hydrogen atmosphere

are presented in Table 1. These results in-

dicate very good agreement between thecross-section and projected area methodresults achieving a concordance value ofapproximately 83.5%. It should be

pointed out that the cross-section methodprovides the contact angle just on theplane the drop has been sectioned. On theother hand, the projected area method al-lows calculating the contact angle basedon the whole drop behavior and not just aspecific region or sectioned plane of it.Therefore, this proposed method providesa quantitative and more representativemeasurement of the system contact angle,

which is useful for actual brazing applica-tions that are based on real and nonho-mogeneous materials.

Table 2 presents a statistical compari-

son of standard cross-section method and

Fig. 1 Temperature profile during sessile drop test. Fig. 2 A Illustration of contact angles for sessile drops as spher-ical caps; B geometrical parameters used on proposed method.(R: sphere radius; h: spherical cap (drop) height; A: projected spher-ical cap.)

A B

Table 1 Contact Angle in Degrees Measured on Cross-Sectioned Samples Using the Optical

Microscope and Calculated Using the Projected Area Method

Sample Number Cross Section Test Projected Area Method(deg) (deg)

1 2.9 2.72 4.7 4.2

3 1.9 2.44 3.1 2.85 1.9 2.56 2.8 2.47 3.4 2.48 2.3 2.29 3.5 4.1

10 2.6 2.3

Fig. 3 Illustration of curvature functionand derivative position for the proposedmodel.

Table 2 Statistical Comparison of the Standard Sessile Drop Test and the Proposed Method

Result (deg) Cross Section Test Projected Area Method

Standard Deviation 0.88 0.78Value for 95% Confidence Interval 2.9 1.8 2.8 1.6

Max Value 4.7 4.2Min Value 1.9 2.2

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the proposed projected area method re-sults for the contact angle measurement.Such comparison indicates the quantita-tive equivalence of both methods to meas-

ure the contact angle within a 95% confi-dence interval. As expected, the projectedarea method shows a lower standard devi-ation due to the averaging effect of thismethod.

The projected area method is based ongeometrical evaluation of a sessile drop,

which can be virtually extended to any casewhere the drop shape can be assumed as aspherical cap. However, there are restric-tions regarding the drop mass and contactangle range that can be evaluated. Largedrop masses will tend to form oblate ellip-soidal caps instead of spherical ones (Ref.

8). However, as previously stated, this con-sideration is beyond the application of theproposed method, which is applicable tocommonly used brazing systems where thecontact angles tend to be very low.

A correction on total volume of thedrop V must be performed in systems

where the filler material is partially con-sumed during the brazing process by con-sidering only the metal volume that con-tributes to the sessile drop formation. Theuse of flux cored filler material contextu-alizes this example.

Conclusions

The comparison of the results obtainedusing the very simple and easy-to-applyprojected area method proposed here andthe more conventional cross-sectionalmethod to evaluate the contact angle forthe copper-stainless steel (AISI 304) sys-tem brazed under a pure hydrogen atmos-phere showed that fundamental geometrycan be used to evaluate a sessile drop ex-periment, demanding only the measure-ment of filler metal mass and sessile dropplain-view projected area.

Experimental agreement higher than

83% was achieved when comparing both

methods results for each sample. In addi-tion, the mean value of contact angle pro-

vided by the two methods for the evalu-ated system was identical within a 95%

confidence interval. Therefore, the pre-sented results indicate that the proposedprojected area method can be successfullyapplied to analyze the sessile drop test oflow contact angle systems in both qualita-tive and quantitative manner.

References

1. Bashforth, F., and Adams, J. C. 1883.An Attempt to Test the Theory of CapillaryAction. Oxford.

2. Panwar, A. K., Barthwal, S. K., andRay, S. 2003.J. Adhes. Sci. Technol. 17(10):13211329.

3. Chen, J. C., Hao, C. Y., and Zhang,J. S. 2006. Sci. Technol. Weld. Join, Vol. 11,pp. 600605.

4. Funk, E. R., and Udin, H. 1952.Brazing hydromechanics. Welding Journal6(18): 310316.

5. Brazing Handbook, 5th ed. 1991.Miami, Fla.: American Welding Society.

6. Erbil, H. Y. 2006. Surface Chemistryof Solid and Liquid Interfaces, 1st ed.

7. Lennart, R., and Westergren, B.

1990. Beta Mathematics Handbook, 2nded. CRC Press.

8. Erbil, H. Y. 1997. J. Phys. Chem. B,Vol. 101, pp. 68676873.

A B

Fig. 4 A Plain view of an obtained sessile drop; B cross-section image detail withmeasured contact angle.

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