Phase transition induced hydrodynamic instability

Instabilides leading to oscillations in some particular properties of a system are intimately related to pattern formation. Nontrivial patterns form spontaneously as a result of the occurrence and propagation of the fronts of instability. These spontaneous patterns can be turned into functional structures at the corresponding length scale when the pattern forming processes are properly designed and controlled. In this work, we propose a scenario for mass transfer instability in a one-dimensional flow of a one-component fluid near its discontinuous liquid-gas phase transition. Instability leading to density oscillations occurs when the system fails to support steady-state flow due to the absence of mechanically stable uniform state as a consequence of a discontinuous transition. The system is modeled and simulated as a one-dimensional flow of a fluid for which the pressure tensor is derived from the equation of state of an inhomogeneous van der Waals fluid. Oscillations in fluid density occur at some appropriately tuned sets of parameters. The phenomenon may play a role in the formation of nanoscopic channel during an unstable Langmuir-Blodgett transfer reported in recent experiments and can be useful in patterning thin films.