TY - GEN A1 - Richter, Sebastian A1 - Bestehorn, Michael T1 - Thin-film Faraday patterns in three dimensions T2 - The European Physical Journal Special Topics N2 - We investigate the long time evolution of a thin fluid layer in three spatial dimensions located on a horizontal planar substrate. The substrate is subjected to time-periodic external vibrations in normal and in tangential direction with respect to the plane surface. The governing partial differential equation system of our model is obtained from the incompressible Navier-Stokes equations considering the limit of a thin fluid geometry and using the long wave lubrication approximation. It includes inertia and viscous friction. Numerical simulations evince the existence of persistent spatially complex surface patterns (periodic and quasiperiodic) for certain superpositions of two vertical excitations and initial conditions. Additional harmonic lateral excitations cause deformations but retain the basic structure of the patterns. Horizontal ratchet-shaped forces lead to a controllable lateral movement of the fluid. A Floquet analysis is used to determine the stability of the linearized system. KW - Thin Film Instabilities Y1 - 2017 UR - https://link.springer.com/article/10.1140/epjst/e2016-60234-4 U6 - https://doi.org/10.1140/epjst/e2016-60234-4 SN - 1951-6401 SN - 1951-6355 VL - 226 IS - 6 SP - 1253 EP - 1261 ER -