An experimental investigation of drop deformation and breakup in steady, two-dimensional linear flows

We consider the deformation and burst of small fluid droplets in steady linear, two-dimensional motions of a second immiscible fluid. Experiments using a computer-controlled, 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 spherical particle straddling a fluid/gas interface in an axisymmetric straining flow

Numerical solutions, obtained via the boundary-integral technique, are used to consider the effect of a linear axisymmetric straining flow on the existence of steady-state configurations in which a neutrally buoyant spherical particle straddles a gas–liquid interface. The problem is directly applicable to predictions of the stability of particle capture in flotation processes, and is also of interest in the context of contact angle and surface tension measurements. A primary goal of the present study is a determination of the critical capillary number, Ca_c, beyond which an initially captured particle is pulled from the interface by the flow, and the dependence of Ca_c on the equilibrium contact angle θ_c. We also present equilibrium configurations for a wide range of contact angles and subcritical capillary numbers

A computer-controlled four-roll mill for investigations of particle and drop dynamics in two-dimensional linear shear flows

In this paper we describe the design and operating characteristics of a computer-controlled four-roll mill for investigations of particle and drop dynamics in two-dimensional 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

The rheology of a suspension of nearly spherical particles subject to Brownian rotations

A set of constitutive equations, valid for arbitrary linear bulk flows, is derived for a dilute suspension of nearly spherical, rigid particles which are subject to rotary Brownian couples. These constitutive equations are subsequently applied to find the resulting stress patterns for a variety of time-dependent bulk flow fields. The rheological responses are found to exhibit many of the same qualitative features as have been observed in recent experimental investigations of polymeric solutions and other complex materials

Strong flows of dilute suspensions of microstructure

We consider dilute suspensions that have a microstructure that may be characterized by an axial state vector. Examples include axisymmetric particles, line elements of the fluid itself, or, as an approximation, droplets of fluid or polymer molecules. Past studies, in which sufficient conditions for stretch or coherent orientation of the microstructure are obtained for steady flows with homogeneous velocity gradient tensors are shown not to apply to the general situation. Instead, a careful analysis of the microdynamical equations reveals that stretching and orientation of the microstructure by the flow must be analyzed over a time interval. Using techniques from the theory of dynamical systems, a quantitative measure is developed to determine orientations and/or stretched lengths of the microstructure, that are robust and attractive to nearby states. This leads to a strong flow criterion for unsteady flows with inhomogeneous velocity gradient tensors in which the effects of history dependence are apparent. A particular model system is treated in the case of general two-dimensional flow. The sensitivity of the results to changes in the modeling assumptions is investigated

Kinetic modelling of epitaxial film growth with up- and downward step barriers

The formation of three-dimensional structures during the epitaxial growth of films is associated to the reflection of diffusing particles in descending terraces due to the presence of the so-called Ehrlich-Schwoebel (ES) barrier. We generalize this concept in a solid-on-solid growth model, in which a barrier dependent on the particle coordination (number of lateral bonds) exists whenever the particle performs an interlayer diffusion. The rules do not distinguish explicitly if the particle is executing a descending or an ascending interlayer diffusion. We show that the usual model, with a step barrier in descending steps, produces spurious, columnar, and highly unstable morphologies if the growth temperature is varied in a usual range of mound formation experiments. Our model generates well-behaved mounded morphologies for the same ES barriers that produce anomalous morphologies in the standard model. Moreover, mounds are also obtained when the step barrier has an equal value for all particles independently if they are free or bonded. Kinetic roughening is observed at long times, when the surface roughness w and the characteristic length $\xi$ scale as $w ~ t^\beta$ and $\xi ~ t^\zeta$ where $\beta \approx 0.31$ and $\zeta \approx 0.22$, independently of the growth temperature.Comment: 15 pages, 7 figure

Natural convection in a shallow cavity with differentially heated end walls. Part 2. Numerical solutions

Numerical solutions of the full Navier-Stokes equations are obtained for the problem of natural convection in closed cavities of small aspect ratio with differentially heated end walls. These solutions cover the parameter range Pr = 6.983, 10 ≤ Gr ≤ 2x10^4 and 0.05 ≤ A ≤ 1. A comparison with the asymptotic theory of part 1 shows excellent agreement between the analytical and numerical solutions provided that A ≾ 0.1 and Gr^2A^3Pr^2 ≾ l0^5. In addition, the numerical solutions demonstrate the transition between the shallow-cavity limit of part 1 and the boundary-layer limit; A fixed, Gr → ∞

Wakes in stratified flow past a hot or cold two-dimensional body

This paper considers the general problem of laminar, steady, horizontal, Oseen flow at large distances upstream and downstream of a two-dimensional body which is represented as a line source of horizontal or vertical momentum, or as a line heat source or heat dipole. The fluid is assumed to be incompressible, diffusive, viscous and stably stratified. The analysis is focused on the general properties of the horizontal velocity component, as well as on explicit calculation of the horizontal velocity profiles and disturbance stream-function fields for varying degrees of stratification. For stable stratifications, the flow fields for all four types of singularities exhibit the common feature of multiple recirculating rotors of finite thicknesses, which leads to an alternating jet structure both upstream and downstream for the horizontal velocity component and to leewaves downstream in the overall flow. The self-similar formulae for the velocity, temperature and pressure at very large distances upstream and downstream are also derived and compared with the Oseen solutions