Modeling and analysis of thin-film equations

Thin liquid films are omnipresent in nature, daily life, and industrial processes. These films range from nanometers to micrometers in thickness. When facing external forces like temperature disparity, surface active agents (short: surfactant), or rotation, stabilizing surface tension effects compete with destabilizing shear stresses. The fluids’ ultra-thin nature makes them highly sensitive to such disturbances, possibly leading to film-rupture, an undesirable outcome.

Mathematically, thin-film flows are described by quasilinear, degenerate-parabolic, fourth-order partial differential equations. Starting from the governing equations, which are the free surface Navier-Stokes equations, one can apply a classical tool called lubrication approximation to derive evolution equations for the film height in various geometrical and physical settings.

Possible degree projects include the modeling and analysis of

Thin fluid films under the effects of temperature

  • Modeling and well-posedness for a thin-film equation under thermal effects
  • Existence of homoclinic steady states in the case of uniform heating
  • Modeling, well-posedness, and existence of steady states when the viscosity is temperature dependent

Thin fluid films equipped with surfactant

  • Modeling and well-posedness of surfactant driven thin-film equations with two competing sources of surfactant

 

If you are interested in writing a degree project in modeling and analysis of thin-film flows please contact me (Gabriele Brüll: gabriele.brull@math.lth.se) and we can discuss a suitable problem.

 

Starting 2025, there will be a DFG (German Research Foundation) Network Program between the Lund, Stuttgart, Saarbrücken, and Bonn on Instability Phenomena in Asymptotic Models in Fluid Dynamics, where thin-film equations build a subproject. There might be the possibility to include the degree project into the study group of the network program, which enables cooperation with researchers from another network university including a research visit.

For more information on the network, check the webpage Links to an external site..