Instability Analysis Of Oldroyd-B Fluid Electrohydrodynamic Convection

Convection with electric field,or even convection caused only by electric field,is widespread in nature and industrial production.In addition,most of the convection in nature is accompanied by crossflow.Therefore,it is of practical and theoretical value to conduct in-depth exploration of electrohydrodynamic convection with and without crossflow.Previous studies on electrohydrodynamic convection only concentrated on the Newtonian fluid.However,common fluids in nature and industrial applications are non-Newtonian fluids,and most of them exhibit viscoelastic effects.For example,polyacrylamide,biological mucosa,etc.are all viscoelastic fluids.Therefore,the research on the stability of viscoelastic electrohydrodynamic convection is of reference significance for industrial applications and medical research.At the same time,it can also supplement the understanding of the effect of viscoelasticity on the stability of electrohydrodynamic convection.For these purposes,this paper introduces the regular model of perturbations and studies the linear stability of the electrohydrodynamic convection of viscoelastic fluid with and without crossflow through the method of linear stability analysis.In the mathematical model,the Maxwell equations under the electrostatic assumption are used as the governing equations of electric field and charge.And the Oldroyd-B model is used to describe the stress-strain relationship of the viscoelastic ffluid.In this paper,the spectral method is used to numerically solve the eigenvalue problem,and the stability results of the numerical solution are discussed in detail.Firstly,the unstable mode of the viscoelastic fluid with lcrossflow under the action of the normal electric field is discussed and analyzed.I discover a new unstable mode caused by the combined action of viscoelasticity and electric field.The paper discuss the influence of viscoelasticity and normal electric field on unstable modes.Then,the stability of electrohydrodynamic convection without crossflow and the influence of viscoelasticity and normal electric field on stability are also discussed and analyzed.Finally,this paper conducts a numerical simulation of electrohydrodynamic convection,and compares the simulation with the linear stability analysis results.