We consider the deformation and burst of small fluid droplets in steady linear, two-dimensional motions of a second immiscible fluid. Experiments using a computercontrolled, four-roll mill to investigate the effect of flow type are described, and the results compared with predictions of several available asymptotic deformation and burst theories, as well as numerical calculations. The comparison clarifies the range of validity of the theories, and demonstrates that they provide quite adequate predictions over a wide range of viscosity ratio, capillary number, and flow type.

A computer-controlled four-roll mill is used to examine two transient modes of deformation of a liquid drop: elongation in a steady flow and interfacial-tensiondriven motion which occurs after the flow is stopped abruptly. For modest extensions, drop breakup does not occur with the flow on, but may occur following cessation of the flow as a result of deterministic motions associated with internal pressure gradients established by capillary forces. These relaxation and breakup phenomena depend on the initial drop shape and the relative viscosities of the two fluids. Capillary-wave instabilities at the fluid-fluid interface are observed only for highly elongated drops. This study is a natural extension of G. I. Taylor's original studies of the deformation and burst of droplets in well-defined flow fields.

In this paper we describe the design and operating characteristics of a computercontrolled four-roll mill for investigations of particle and drop dynamics in twodimensional linear flows. The control system is based upon the use of: a video camera to visualize the instantaneous position of the drop or particle ; a PDP 11/23 computer, with a pipeline processor acting as an interface between the camera and computer, to calculate the position and implement a control strategy, and d.c. stepping motors to convert an electronic signal to angular velocities of the four rollers. The control objective is to keep the centre of mass of the drop/particle at the centre of the region between the rollers where there is a stagnation point in the undisturbed flow, while maintaining the shear-rate and the ratio of vorticity to strain rate in the flow at fixed values. The resulting system is suitable for studies of: the rotational motions of single solid particles; the deformation and burst of single droplets; or the hydrodynamic interactions of two particles or drops, one of which is held with its centre-of-mass fixed at the stagnation point of the undisturbed flow. In all cases, the flow can be varied from pure rotation to pure strain, and the shear rate can be either steady or changing as a prescribed function of time.