ALBERT

Description: 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.

Description: We consider the motion of a sphere or a slender body in the presence of a plane fluid-fluid interface with an arbitrary viscosity ratio, when the fluids undergo a linear undisturbed flow. First, the hydrodynamic relationships for the force and torque on the particle at rest in the undisturbed flow field are determined, using the method of reflections, from the spatial distribution of Stokeslets, rotlets and higher-order singularities in Stokes flow. These fundamental relationships are then applied, in combination with the corresponding solutions obtained in earlier publications for the translation and rotation through a quiescent fluid, to determine the motion of a neutrally buoyant particle freely suspended in the flow. The theory yields general trajectory equations for an arbitrary viscosity ratio which are in good agreement with both exact-solution results and experimental data for sphere motions near a rigid plane wall. Among the most interesting results for motion of slender bodies is the generalization of the Jeffrey orbit equations for linear simple shear flow. © 1984, Cambridge University Press 1984. All rights reserved.

Description: The present study examines the motion of a slender body in the presence of a plane fluid fluid interface with an arbitrary viscosity ratio. The fluids are assumed to be at rest at infinity, and the particle is assumed to have an arbitrary orientation relative to the interface. The method of analysis is slender body theory for Stokes flow using the fundamental solutions for singularities (i.e. Stokeslets and potential doublets) near a flat interface. We consider translation and rotation, each in three mutually orthogonal directions, thus determining the components of the hydrodynamic resistance tensors which relate the total hydrodynamic force and torque on the particle to its translational and angular velocities for a completely arbitrary translational and angular motion. To illustrate the application of these basic results, we calculate trajectories for a freely rotating particle under the action of an applied force either normal or parallel to a flat interface, which are relevant to particle sedimentation near a flat interface or to the processes of particle capture via drop or bubble flotation. © 1983, Cambridge University Press. All rights reserved.