Deformation and breakup of Newtonian and non-Newtonian conducting drops in an electric field

In this article, we considered experimentally the deformation and breakup of Newtonian and non-Newtonian conducting drops in surrounding fluid subjected to a uniform electric field. First, we examined three distinctive cases of Newtonian-fluid pairs with different relative conductivities, namely highly conducting drops, conducting drops and slightly conducting drops. The results on the Newtonian fluids demonstrated that when the conductivity of the drop is very large relative to that of the surrounding fluid, the deformation response of such highly conducting drops is described well by the electrohydrostatic theory, especially with regard to the prediction of the critical point. Specifically, when the ratio of drop to continuous-phase resistivity, R, was less than 10−5, the electrohydrostatic theory was quite satisfactory. Then, the non-Newtonian effect on the drop deformation and breakup was studied for highly conducting drops which satisfied the condition R < O(10−5). The highly conducting drop became stable in a weak or moderate field strength when either the drop or the continuous phase was non-Newtonian. On the other hand, when both the phases were non-Newtonian, more complicated responses were observed depending on the ratio of zero-shear-rate viscosities. Although the effects of the rheological properties are minimal on all features away from the critical conditions for breakup or prior to the instability, the non-Newtonian properties have a significant influence during drop burst, which is accompanied by large velocities and velocity gradients. In particular, when the ratio of the zero-shear-rate viscosity of the drop to that of the ambient fluid was much larger than unity, non-Newtonian properties of the drop phase enhanced the drop stability. Conversely, the elasticity of the continuous phase deteriorated the drop stability. Meanwhile if the zero-shear-rate viscosity ratio was much smaller than unity, the elasticity of the continuous phase produced a stabilizing effect. The effects of resistivity and viscosity ratios on the breakup modes were also investigated. When at least one of the two contiguous phases possessed considerable non-Newtonian properties, tip streaming appeared.

The dependence of the shape and stability of captive rotating drops on multiple parameters

The dependence of the shape and stability of rigidly rotating captive drops on multiple parameters is analysed by applying asymptotic and computer-aided techniques from bifurcation theory to the Young-Laplace equation which governs meniscus shape. In accordance with Brown and Scriven, equilibrium shapes for drops with the volume of a cylinder and without gravity are grouped into families of like symmetry that branch from the cylindrical shape at specific values of rotation rate, measured by the rotational Bond number E. Here, the evolution of these families with changes in drop volume Y , drop length B , and gravitational Bond number G is presented. Criteria are laid out for predicting drop stability from the evolution of shape families in this parameter-space and they circumvent much of the extensive solution of eigenproblems used previously. Asymptotic analysis describes drops slightly different from the cylindrical ones and shows that some shape bifurcations from cylinders to wavy, axisymmetric menisci are ruptured by small changes in drop volume or gravity. Near these points at least one of the shape families singularly develops a fold or limit point. Numerical methods couple finite-element representation of drop shape which is valid for a wide range of parameters with computer-implemented techniques for tracking shape families. An algorithm is presented that calculates, in two parameters, the loci of bifurcation or limit points; this is used to map drop stability for the four-dimensional parameter space (E, / B , G ). The numerical and asymptotic results compare well in the small region of parameters where the latter are valid. An exchange of axisymmetric mode for instability is predicted numerically for drop volumes much smaller than that of a cylinder.