受径向振荡激励的黏弹性液滴稳定性分析

STABILITY ANALYSIS OF VISCOELASTIC LIQUID DROPLETS EXCITED BY RADIAL OSCILLATIONS

当液滴受到外部周期性的径向激励时,在其表面会形成驻波模式的不稳定,这就是在球面上的Faraday不稳定问题.不稳定的表面波的振荡频率根据流体物性参数和所施加激励条件的不同呈现为谐波或是亚谐波模式的振荡.本文基于线性小扰动理论,研究了受径向振荡体积力的黏弹性液滴表面波的不稳定性.振荡的体积力导致动量方程为含有时间周期系数的Mathieu方程,系统因此变成参数不稳定问题,采用Floquet理论进行求解.本模型中将黏弹性的特征处理为与流变模型参数相关的等效黏度,从而简化了问题的求解.基于对中性稳定曲线及增长率的分析,研究了黏弹性参数对液滴稳定性的影响.结果表明零剪切黏度和应变驰豫时间的增加具有抑制液滴表面波增长的作用,提高了使液滴表面发生谐波不稳定的激励幅值.随着振荡幅值的增加,增长率不稳定的区域减少,且随着振荡频率的增加,液滴表面波增长率减小.通过对增长率的分析可以得出,应力松弛时间的增加使得增长率增加,从而促进了液滴表面波的增长.

When a liquid drop is periodically excited by an external radial oscillation force,the instability of standing wave mode will be formed on its surface,which is known as the spherical Faraday instability problem.The oscillation frequency of the instability surface wave will render as a harmonic or sub-harmonic mode according to the different fluid physical parameters and the forced excitation conditions.Based on the linear small perturbation theory,this paper studies the instability behavior of the viscoelastic droplet surface wave subjected to the radial oscillating force.The oscillating radial force causes the momentum equations to be Mathieu equations which included time period coefficients.Therefore,the system becomes a parametric instability problem,which can be solved by Floquet theory.In this model,the characteristics of viscoelasticity are treated as an effective viscosity which related to the rheological model of the fluid,which simplifies the solving process of the problem.Based on the analysis of the neutral stability curve and growth rate of the surface wave,the influence of viscoelastic parameters on the stability of droplets were studied.The results showed that the increase of zero-shear viscosity(μ_(0))as well as deformation retardation time(λ2)can inhibit the growth of droplet surface wave,therefore increased the excitation amplitude which made the droplet unstable at a harmonic mode.With the increase of oscillation amplitude,the regions of unstable growth rate decrease,and as the oscillation frequency increase,the value of droplet surface wave growth rate decrease.Through the analysis of the growth rate,it can be concluded that the increase of the stress relaxation time(λ_(1))increases the growth rate,thereby promoting the growth of surface wave on the droplet.