Abstract
In the minutes immediately preceding the rupture of a soap bubble, distinctive and repeatable patterns can be observed. These quasistable transient structures are associated with the instabilities of the complex Marangoni flows on the curved thin film in the presence of a surfactant solution. Here, we report a generalized Cahn-Hilliard-Swift-Hohenberg model derived using asymptotic theory that describes the quasielastic wrinkling pattern formation and the consequent coarsening dynamics in a curved surfactant-laden thin film. By testing the theory against experiments on soap bubbles, we find quantitative agreement with the analytical predictions of the nucleation and the early coarsening phases associated with the patterns. Our findings provide fundamental physical understanding that can be used to (de-)stabilize thin films in the presence of surfactants and have important implications for both natural and industrial contexts, such as the production of thin coating films, foams, emulsions, and sprays.
Highlights
The Marangoni effect inherently produces nonlinear structures within fluid flow; the formation of these structures will inevitably lead to symmetry breaking within the system
To examine the effectiveness of the leading-order theory derived, we use appropriate metrics, which quantify the complexity of the patterns of both the experimental images and the simulated result. This provides a baseline result for future studies of transient morphogenic phenomena in a thin liquid film in physiochemical and biophysical systems
We demonstrated that an effective field theory derived systematically using asymptotics provides a good quasiquantitative description of the surface pattern formation in nonplanar viscous thin liquid films in the presence of a surfactant solution
Summary
The Marangoni effect inherently produces nonlinear structures within fluid flow; the formation of these structures will inevitably lead to symmetry breaking within the system. The premise of symmetry breaking is present in a wide range of phenomena, not least in the interfacial fluid context, from the Higgs mechanism [1] in particle physics to solid crystallization [2] and to the functions of the cell structure [3]. The analysis of these symmetry-breaking phenomena typically involves a reduction of the complex system into field variables, which form an effective field theory. Under certain limits of hydrodynamic motion, they remain effective at predicting the formation of local structures that typify a certain configuration of field variables
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