Experiments have been performed, in capillary tubes, on the displacement of a viscous fluid (glycerine) by a less viscous one (a glycerine–water mixture) with which it is miscible in all proportions. A diagnostic measure of the amount of viscous fluid left behind on the tube wall has been found, for both vertical and horizontal tubes, as a function of the Péclet (Pe) and Atwood (At) numbers, as well as a parameter that is a measure of the relative importance of viscous and gravitational effects. The asymptotic value of this diagnostic quantity, for largePeand anAtof unity, has been found to agree with that found in immiscible displacements, while the agreement with the numerical results of Part 2 (Chen & Meiburg 1966), over the whole range ofAt, is very good. At values of the averagePegreater than 1000 a sharp interface existed so that it was possible to make direct comparisons between the present results and a prior experiment with immiscible fluids, in particular an effective surface tension at the diffusing interface could be evaluated. The effect of gravity on the amount of viscous fluid left on the tube wall has been investigated also, and compared with the results of Part 2. A subsidiary experiment has been performed to measure both the average value of the diffusion coefficient between pure glycerine and several glycerine–water mixtures, in order to be able to calculate a representative Péclet number for each experiment, and the local value as a function of the local concentration of glycerine, in the dilute limit.

Density-driven instabilities between miscible fluids in a vertical Hele-Shaw cell are investigated by means of experimental measurements, as well as two- and three-dimensional numerical simulations. The experiments focus on the early stages of the instability growth, and they provide detailed information regarding the growth rates and most amplified wavenumbers as a function of the governing Rayleigh number Ra. They identify two clearly distinct parameter regimes: a low-Ra, ‘Hele-Shaw’ regime in which the dominant wavelength scales as Ra−1, and a high-Ra ‘gap’ regime in which the length scale of the instability is 5±1 times the gap width. The experiments are compared to a recent linear stability analysis based on the Brinkman equation. The analytical dispersion relationship for a step-like density profile reproduces the experimentally observed trend across the entire Ra range. Nonlinear simulations based on the two- and three-dimensional Stokes equations indicate that the high-Ra regime is characterized by an instability across the gap, wheras in the low-Ra regime a spanwise Hele-Shaw mode dominates.

In this paper, we present an optical profilometric technique that allows for single-shot global measurement of free-surface deformations. This system consists of a high-resolution system composed of a videoprojector and a digital camera. A fringe pattern of known characteristics is projected onto the free surface and its image is registered by the camera. The deformed fringe pattern arising from the surface deformations is later compared to the undeformed (reference) one, leading to a phase map from which the free surface can be reconstructed. Particularly, we are able to project wavelengthcontrolled sinusoidal fringe patterns, which considerably increase the overall performance of the technique and the quality of the reconstruction compared to that obtained with a Ronchi grating. In comparison to other profilometric techniques, it allows for single-shot non-intrusive measurement of surface deformations over large areas. In particular, our measurement system and analysis technique is able to measure free surface deformations with sharp slopes up to 10 with a 0.2 mm vertical resolution over an interrogation window of size 450 9 300 mm 2 sampled on approximately 6.1 9 10 6 measurement points. Some illustrative examples of the application of this measuring system to fluid dynamics problems are presented.

We present an experimental study of drop impact on a solid surface in the spreading regime with no splashing. Using the space–time-resolved Fourier transform profilometry technique, we can follow the evolution of the drop shape during the impact. We show that a self-similar dynamical regime drives the drop spreading until the growth of a viscous boundary layer from the substrate selects a residual minimal film thickness. Finally, we discuss the interplay between capillary and viscous effects in the spreading dynamics, which suggests a pertinent impact parameter.