Surface Tension Determination From Regression Between Hydrostatic Pressure Variation and Interfacial Curvature

Abstract RATIONALE: Gravity deforms gas-liquid interfaces such that interfacial curvature varies with height. Surface tension, T, can be determined from the variation in curvature. The most widely-used existing method for determining T from curvature variation is axisymmetric drop shape analysis (ADSA), which requires complex parametric integration and optimization. Here, we test an alternative and intuitive T-determination method. At any point along the interface, the Young-Laplace relation specifies that Δ P = T (k 1 + k 2 ), where Δ P is pressure drop across the interface and k 1 and k 2 are the principle interfacial curvatures. Thus if T were constant along the interface, then T could be determined as the slope of the linear regression between interfacial pressure drop and curvature. METHODS: We image saline droplets or captive bubbles with deposited monlayers of dipalmitoyl phosphatidylcholine. We identify edge pixels by Canny edge detection and sequence the edge pixels to generate an edge curve. At eight equally-spaced altitudes along the edge curve, we determine Δ P by hydrostatic offset from Δ P 0 at the top of the curve and use tangents constructed from interfacial points separated by arclength interval ds K to determine k 1 + k 2. Plotting Δ P – Δ P 0 vs. k 1 + k 2 yields a line with a slope equal to T (Figure). Values of T are exquisitely sensitive to interfacial curvature and the T value obtained from a single regression is not reliable. Thus, we run repeated regressions for a range of ds K values. From the multiple regression runs, we retain those with coefficients of determination, R2, exceeding a threshold value. We calculate T as the average of the slopes of the retained regression runs. For DPPC films compressed to different extents, we compare T values obtained by this regression method to those obtained by software (A.W. Neumann, Univ. of Toronto) that implements ADSA. RESULTS: Over a T range of 2-70 mN/m, the difference between T values determined by the alternative methods averages 0.48 ± 0.31 (SD) mN/m and is, at most, 1.05 mN/m. CONCLUSION: Linear regression between Δ P and interfacial curvature can yield accurate surface tension values.

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