Effect of finite charge relaxation time on the breakup mechanism of critically charged drops

  Neha Gawande  ,  Y. S. Mayya  ,  Rochish Thaokar  
Department of Chemical Engineering, Ben Gurion University of the Negev, Beer-Sheva, 8410501, Israel
Department of Chemical Engineering, Indian Institute of Technology Bombay, Mumbai, 400076, India

Charged droplets generated by electro-atomization of liquids are utilized in a wide range of applications. When the charge density of these droplets is higher than a certain value, popularly known as the Rayleigh limit of charge, they become Coulombically unstable and undergo breakup by emitting a fraction of charge and mass in the form of a jet which further disintegrates into a cloud of micron and sub-micron sized progeny droplets. To understand the deformation pathway of such critically charged drops and the associated jet emission, we carried out numerical simulations using the axisymmetric boundary element method (BEM). The numerical analysis performed using generally employed perfect conductor drop model indicates that the droplet forms conic cusps and exhibits shape singularity in finite time. The limitation of the perfect conductor drop model to predict the jet and progeny formation in Rayleigh breakup process is identified and it is found that when the electrostatic model is modified by invoking surface charge dynamics, the charge transport to the deformed drop tip is restricted by the convection effects, which gives rise to tangential electric stresses, responsible for the emergence of a jet that subsequently breaks into progeny droplets. The numerical analysis is then extended to predict the effect of electrical conductivity on the breakup modes and the corresponding charge and mass losses during the fission process are predicted.