Computer simulation is an important tool for studying the dynamical behavior of thin films. The existing models of liquid film flows are based on the evolution equation (EE) and lubrication theory, which are approximations to the Navier-Stokes continuum equations. The validity conditions for these approximations and disadvantages of numerical schemes impose serious limitations on these continuum models. Thin liquid layers in nanoscale technology may exhibit microscale features, which cannot be described by using the EE equations. We propose new numerical models for falling film and falling sheet. They are based on the particle paradigm and the dissipative particle dynamics (DPD) method. DPD represents a system of mesoscopic-sized particles, which can interact via direct conservative, two-body potentials. The particles can exert friction and Brownian forces on each other. We consider two cases of fluid film flows for which the main driving force is the gravity. In the first case the fall of a fluid film positioned on the underside of a plate (the Rayleigh-Taylor flow) is studied. We show the results of simulation, which display the short-time rupture of the thin film, its break-up into "contracted" droplets, break-up of spikes and formation of bubbles. We have employed two discrete-particle techniques, molecular dynamics (MD) and dissipative particle dynamics (DPD) for thin-film flowing down a vertical wall. Two-dimensional models are constructed by assuming that the contact line dynamics control the thin-film flow. The flow patterns obtained are realistic in appearance and are in qualitative agreement with experimental and theoretical results. We have also unveiled the formation of fingering instability, rivulets and have observed horseshoe patterns.
Bibliographical noteFunding Information:
We thank Dr. Witold Alda for stimulating discussions. The work is supported by the Minnesota Supercomputer Institute, DOE “Office of Science’s Laboratory Technology Research Program” and partially by the Polish Committee for Scientific Research (KBN) Grant No. STllCOO615.
- Coating flows
- Computer simulations
- Discrete particle schemes
- Dissipative particle dynamics
- Falling film flow