Unstable van der Waals driven line rupture in Marangoni driven thin viscous films

摘要: An intriguing, dramatic and, at present, not fully understood instability often accompanies surfactant driven flows on thin films. This paper investigates a candidate mechanism that could create and drive this instability, van der Waals rupture, via numerical simulations coupled with analytical techniques. The spreading process itself is modelled pair of evolution equations for the fluid film thickness concentration are derived in lubrication approximation. These then linearized about base state corresponds to one-dimensional rupturing solution, transverse disturbances derived. investigated several ways: where perturbations by time evolving state, or frozen tf close rupture event. quasistatic initial value problem also as an eigenvalue problem, eigenva...