Fig. 4: Evolution of thickness, disjoining pressure, and Marangoni stresses.

a–c For an NBD-PG stabilized film under an applied pressure of ΔP = 1000 Pa. a In-plane thickness maps at two different times (gray color scale). b In-plane disjoining pressure (gray color scale) and Marangoni stress maps at the same two times, with arrows indicating the orientation of Marangoni stresses; arrow lengths are proportional to stress magnitude, as indicated by the blue-to-purple color scale. c Profile view showing the thickness (blue), the interface surfactant concentration (purple), the disjoining pressure (green), and the absolute Marangoni stresses (red), corresponding to the blue line profiles marked in (a). All three scale bars are consistent across the time points shown in (a, b), the continuous line and dash line are respectively for data at t = 334 s and t=734 s. d Maps of the Marangoni stresses and disjoining pressure during drainage at ΔP = 1000 Pa at three different times for film stabilized by NBD-PC. Color scales and arrows are defined as in (b). Red arrows indicate the direction of surfactant recirculation flows within the film.