Numerical Study of Dielectric Fluid Bubble Behavior Within Diverging External Electric Fields

A three-dimensional mathematical model is presented that models bubble deformation of a dielectric fluid due to the presence of a nonuniform electric field and calculates the net dielectrophoretic force that is exerted by the electric field on the bubble. The study includes the development of a method of predicting the shape of a bubble based on the arbitrary distribution of stresses over its surface without requiring an axisymmetric configuration. The reciprocal effect of the bubble’s presence on the electric field is also incorporated into the model, and dimensional analysis is used to obtain a single key parameter that governs the bubble deformation phenomenon. Numerical implementation of the mathematical model shows that the bubble deformation can be significant. Furthermore, bubble deformation and electric field distortion can have significant effects on the dielectrophoretic behavior of bubbles in nonuniform fields, especially within small-scale devices where the bubble size and electrode spacing are similar in magnitude.