E. John Hinch

‘Phase diagram’ of interfacial instabilities in a two-layer Couette flow and mechanism of the long-wave instability

A unified view is given of the instabilities that may develop in two-layer Couette flows, as a ‘phase diagram’ in the parameter space. This view is obtained from a preliminary study of the single-fluid Couette flow over a wavy bottom, which reveals three flow regimes for the disturbances created at the bottom, each regime being characterized by a typical penetration depth of the vorticity disturbances and an effective Reynolds number. It appears that the two-layer flow exhibits the same flow regimes for the disturbances induced by the perturbed interface, and that each type of instability can be associated with a flow regime. Typical curves giving the growth rate versus wavenumber are deduced from this analysis, and favourably compared with the existing literature. In the second part of this study, we propose a mechanism for the long wavelength instability, and provide simple estimates of the wave velocity and growth rate, for channel flows and for semi-bounded flows. In particular, an explanation is given for the ‘thin-layer effect’, which is typical of multi-layer flows such as pressure driven flows or gravity driven flows, and according to which the flow is stable if the thinner layer is the less viscous, and unstable otherwise.

Dielectric response of a dilute suspension of spheres with thin double layers in an asymmetric electrolyte

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.

Constitutive laws in liquid-fluidized beds

The objective of the present work is to test experimentally the two-phase modelling approach which is widely used in fluidization. A diculty of this way of modelling fluidized beds is the use of empirical relations in order to close the system of equations describing the fluidized bed as a two-phase continuum, especially concerning the description of the solid phase. We performed an experimental investigation of the primary wavy instability of liquid-fluidized beds. Experiments demonstrate that the wave amplitude saturates up the bed and we were able to measure the precise shape of this voidage wave. We then related this shape to the unknown solid phase viscosity and pressure functions of a simple two-phase model with a Newtonian stress-tensor for the solid phase. We found the scaling laws and the particle concentration dependence for these two quantities. It appears that this simplest model is quite satisfactory to describe the one-dimensional voidage waves in the limited range of parameters that we have studied. In our experimental conditions, the drag on the particles nearly balances their weight corrected for buoyancy, the small imbalance being mostly accounted for by solid phase viscous stress with a much smaller contribution from the solid phase pressure.

On stratification control of the velocity fluctuations in sedimentation

We have tested whether stratification can govern local velocity fluctuations in suspensions of sedimenting spheres. Comparison of the proposed scaling for local control of fluctuations by stratification to experimental data demonstrates that this mechanism cannot account for the reduction of the observed velocity fluctuations.

Spreading fronts in sedimentation of dilute suspension of spheres

The thickness of the diffuse front between a sedimenting dilute suspension and the clear fluid above grows linearly in time due to polydispersity in the size of the particles and due to a hydrodynamic effect in which randomly heavy clusters fall out of the front leaving it depleted. Experiments and simplified point-particle numerical simulations agree that these two effects are not simply linearly additive.

Fluctuations and stratification in sedimentation of dilute suspensions of spheres

We have tested in experiments and simulations whether stratification can control velocity fluctuations in suspensions of sedimenting spheres. The initial value and early decay of the velocity fluctuations are not affected by stratification. On the other hand, in the descending front where the stratification is strong and well defined, the velocity fluctuations are inhibited according to a previously proposed scaling. In between, after the initial decay and before the arrival of the front, the local value of the stratification does not always play a role.

Singularities and Similarity Solutions in Capillary Breakup

A variety of dynamical regimes for capillary breakup gives rise to a zoo of asymptotic similarity solutions for the flow immediately before the breakup singularity. These solutions, some new and some previously published, are summarized and the temporal order of transitions between them determined by scaling. Among the new results are that the perfectly inviscid solution is an equidimensional potential flow rather than near-unidirectional and that the asymptotic viscous solution includes the effects of the external viscosity. Breakup due to van-der-Waals forces is discussed briefly.