A drop of fluid, initially held spherical by surface tension, will deform when an electric or magnetic field is applied. The deformation will depend on the electric/magnetic properties (permittivity/permeability and conductivity) of the drop and of the surrounding fluid. The full time-dependent low-Reynolds-number problem for the drop deformation is studied by means of a numerical boundary-integral technique. Fluids with arbitrary electrical properties are considered, but the viscosities of the drop and of the surrounding fluid are assumed to be equal.Two modes of breakup have been observed experimentally: (i) tip-streaming from drops with pointed ends, and (ii) division of the drop into two blobs connected by a thin thread. Pointed ends are predicted by the numerical scheme when the permittivity of the drop is high compared with that of the surrounding fluid. Division into blobs is predicted when the conductivity of the drop is higher than that of the surrounding fluid. Some experiments have been reported in which the drop deformation exhibits hysteresis. This behaviour has not in general been reproduced in the numerical simulations, suggesting that the viscosity ratio of the two fluids can play an important role.

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The low-frequency dielectric response of a suspension of spherical particles surrounded by thin double layers has been studied and the analysis of Dukhin and Shilov has been extended to asymmetric electrolytes. In addition to the cases of constant surface charge density and of constant surface potential, the case in which changes in the surface charge density are determined by changes in the surface potential according to a first-order kinetic equation has also been examined.

Previous studies of the distortion of the electric double layer around a charged sphere have assumed that the electric stresses are small compared with the viscous stresses. The flow around the particle is therefore changed only slightly by the presence of the charge cloud. This change is measured by the Hartmann number, and in § 6 we remove the restriction that it should be small. It is found that the previous linearized theory is sufficiently accurate for typical experimental values of the Hartmann number. Previous studies have also assumed that the potential at the surface of the particle is small. This assumption is removed in § 7 of this paper. For values of the non-dimensional surface potential smaller than 2 the predictions are altered by less than 10 %. For higher values the differences between linear and nonlinear theory are not negligible, especially when the charge cloud is thin compared with the radius of the charged sphere.

The deformation of a drop as it flows along the axis of a circular capillary in low Reynolds number pressure-driven flow is investigated numerically by means of boundary integral computations. If gravity effects are negligible, the drop motion is determined by three independent parameters: the size a of the undeformed drop relative to the radius R of the capillary, the viscosity ratio λ between the drop phase and the wetting phase and the capillary number Ca, which measures the relative importance of viscous and capillary forces. We investigate the drop behaviour in the parameter space (a/R, λ, Ca), at capillary numbers higher than those considered previously. If the fluid flow rate is maintained, the presence of the drop causes a change in the pressure difference between the ends of the capillary, and this too is investigated. Estimates for the drop deformation at high capillary number are based on a simple model for annular flow and, in most cases, agree well with full numerical results if λ ≥ 1/2, in which case the drop elongation increases without limit as Ca increases. If λ < 1/2, the drop elongates towards a limiting non-zero cylindrical radius. Low-viscosity drops (λ < 1) break up owing to a re-entrant jet at the rear, whereas a travelling capillary wave instability eventually develops on more viscous drops (λ > 1). A companion paper (Lac & Sherwood, J. Fluid Mech., doi:10.1017/S002211200999156X) uses these results in order to predict the change in electrical streaming potential caused by the presence of the drop when the capillary wall is charged.