Effect Of Odd Viscosity On The Stability Of A Thin Film Flowing Along An Inclined Plate

The effect of odd viscosity on the stability of a thin liquid film flowing along an inclined plane has been studied in this paper.The odd viscosity refers to the second viscosity coefficient in the fluid whose symmetry of time inversion is broken due to magnetic field and other factors.However,previous studies on the stability of thin films focused on the even viscosity,and did not consider the influence of the odd viscosity on its stability.Firstly,we studied the effect of the odd viscosity on the stability of a Newtonian liquid thin film under the action of electromagnetic field.By using the lubrication theory,a new liquid-gas interface evolution equation involving the odd viscosity effect is derived.Through linear stability analysis of the evolution equation,it is found that critical Reynolds number increases with the odd viscosity and the strength of magnetic field while decreases with the external strength of electric field.This indicates that the odd viscosity and magnetic field have a stable effect on the fluid flow,while the electric field makes the flow become unstable.In addition,through the weakly nonlinear stability of the evolution equation,we found that there are four regions in limited amplitude range,subcritical unstable zone,unconditional stable zone,supercritical stable zone and explosive zone.We show the effects of the odd viscosity,magnetic field and electric field on the critical Reynolds number and these regions in the form of figures.Since most of the researches on the odd viscosity have been focused on the Newton fluid so far,this paper extends the odd viscosity to the non-Newtonian fluid,and studies the effect of the odd viscosity on the stability of viscoelastic fluid,and obtains the consistent conclusion.These theoretical results can provide guidance for industrial applications of thin film flow.