乳化油液中椭球形水滴间电场力的理论计算

Theoretical calculations of electrostatic force between ellipsoidal drops in W/O emulsion

电场破乳过程中,乳化油液中椭球形水滴间的电场力目前尚未有好的理论求解方法。通过建立水滴的"二分子"椭球模型,利用坐标变换把椭球问题转换成圆球问题,并运用双球面坐标和Maxwell应力张量理论,推导出两椭球水滴间的径向和切向电场力的表达式。算例结果表明,"二分子"椭球模型计算的大间隔椭球水滴间电场力与偶极子圆球模型的计算结果基本一致,吸引-排斥临界角经修正后与Eow的实验结果基本吻合;模型可计算小间隔水滴间的电场力及作用临界角,计算数值均大于大间隔水滴情况下的计算结果,体现了水滴间隔对水滴表面极化电荷分布产生的影响。

At the present time, there is no good means for calculating electrostatic force between two ellipsoidal drops in the process of electro-demulsification. In this paper, a “two-molecule” model of ellipsoidal drop was established. And then the ellipsoid situation was transformed into sphere situation by coordinate transformation. By utilizing bipolar coordinates and Maxwell stress tensor, the expression of electrostatic radial and tangential forces between two drops was deduced. The numerical calculation results showed that when the space between drops was large, electrostatic forces calculated by the model agreed well with those by the dipole model, and critical angle of attraction- repulsion, after being modified, was in good agreement with Eow＇s test result. When the space between drops was small, the model was applicable to calculating electrostatic forces and critical angle between drops, and the calculating numerical values were larger than those obtained on condition that the space between drops was large, it could indicate clearly that the space between drops had a great influence on distribution of polarization charges on drops surface.