The nonmodal linear stability of a falling film over a porous inclined plane has been investigated by a team of researchers, led by LIU qiusheng, at the National Microgravity Laboratory, Institute of Mechanics, CAS. Flow of a falling film on an inclined plane is found in a wide range of natural processes as well as industrial applications and has been a subject of many theoretical and experimental studies for many years.
The researchers use Darcy’s law to describe the flow in the porous medium. A simplified one-sided model is used to describe the fluid flow. They have studied the linear stability of three-dimensional disturbances using the nonmodal stability theory. Particular attentions are paid to the transient behavior. Results show that the critical conditions of both the surface mode and the shear mode instabilities are dependent on β(the influence of the
porous layer on the flow in the film) for streamwise disturbances. However, the spanwise disturbances have no unstable eigenvalue.
The research entitled “Instabilities and transient behaviors of a liquid film flowing down a porous inclined plane” has been published in PHYSICS OF FLUIDS, 2010, 22(7), 074101, DOI: 10.1063/1.3455503.