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An axisymmetric numerical method to simulate the dynamics of insoluble surfactant on a moving liquid–fluid interface is presented. The motion of the interface is captured using a volume-of-fluid method. Surface tension, which can be a linear or nonlinear function of surfactant concentration (equation of state), is included as a continuum surface force. The surfactant evolution is governed by a convection–diffusion equation with a source term that accounts for stretching of the interface. In the numerical method, the masses of the flow components and the surfactant mass are exactly conserved. A number of test cases are presented to validate the algorithm. Simulations of a drop in extensional flow, and its subsequent retraction and breakup upon cessation of the external flow, are performed. Even when the initial surfactant distribution is dilute, we observe that increases in surfactant concentration locally (i.e. at the drop …