Effect of the Electric Field on Wave Motion in a Thin Suspension Layer Flowing Over an Inclined Plane

Stability of surface gravity waves in an inclined layer of rheological fluid in the presence of an arbitrarily oriented electric field is considered to investigate the effect of electric fields on wave stability. Rheological equations used for a dilute suspension of the rigid dielectric ellipsoids take into account the influence of electric fields on a particular orientation. The evolution equation is derived as a long-wavelength approximation which includes a set of nondimensional parameters responsible for the behaviour of the suspension. Solution of the evolution equation is obtained in the form of a nonlinear wave with the amplitude and phase slowly varying in time in such a way as to allow determination of the curves of neutral stability, bifurcations, suband supercritical instabilities. The results of calculations show that the electric field can both stabilise or destabilise waves.