Apparent Contact Angle and Triple-Line Tension of a Soap Bubble on a Substrate

Contact angle of a hemispherical bubble: An analytical approach

“…In 2D wet foams, the (circular) film prolongations into a wall PB also meet the wall at p=2 [3]. However, this appears not to be the case in 3D wet foams in contact with walls: deviations from p=2 have been reported for a single bubble on a wet porous substrate [4], e.g., / % 85 (measured inside the bubble and extrapolated to the substrate surface -see Fig. 1) for a bubble of radius R ¼ 2:4 mm.…”

“…Fig. 2c compares the first-order and second-order analytical solutions and experimental data [4]. Note that this comparison is carried out over a much smaller range of h=R than in Fig.…”

“…Finally, the second term, related to gravity effects, is also of Oðh=RÞ 2 . In fact, whether this term is of second order or not depends on the value of the dimensionless parameter qgR 2 =c, but in the cases that will be addressed -bubbles of radius R % 1-3 mm, as in [4] -this parameter is indeed of O(1), as required. For these values of R and using c ¼ 33:6 Â 10 À3 J m À2 (see [4]) gives qgR 2 =c % 0:3-2:6.…”

“…A contact angle of h 1 ¼ 0 was assumed in either case, which seemed the most sensible choice, since the bubble was in contact with the fluid in both cases. The error bars were computed taking into account that the measurement error of R is 0.05 mm, and the error of h 2 is 1° [4]. The measurement error of h was estimated as 0.028 mm [6].…”

“…Our results for the apparent contact angle, extrapolated contact angle and Plateau border shape are discussed in Section 3: we compare results at different orders in h=R with those from numerical solution of the Laplace equation, for different contact angles of the liquid on the substrate and varying gravity strengths. Comparison is also made with what is, to our knowledge, the only existing set of experimental results for this system [4]. Finally, Section 4 contains some concluding remarks.…”